Ive always thought it was interesting how much of first half of 20th was spent on understanding our limits. Relativity tells us we can't go past the speed of light. Quantum mechanics tells us that our ability to concretely talk about things goes to hell when we get on small scales. Turing showed us how weak our computers are, and Godel showed that we can't even really come up with a consistent model of logic. Lorenz showed how the nonlinear world behaved so erratically, making weather prediction hopeless. I guess thats 5 examples: 3 from math, 2 from physics. Thats all i can really think of that fits.
Thats what i think of that era in thought. Realizing we are limited. Ive read that at the turn of the century, many thought that physics as a field was dead because pretty much everything had been discovered. How cocky.
Dec 16, 2008
Dec 14, 2008
Games
I was thinking about monopoly a couple of nights ago and it occurred to me that the game is a piece of our culture. However, monopoly, is drastically different from lets say chess, go, shogi, chinese chess, cards... etc because its "owned". Over time the game has slowly made more and more complex until being mass manufactured has become the only option for the game.
And so now im considering what it would be like if the game were streamlined and made more abstract. I think it would be beautiful.
And so now im considering what it would be like if the game were streamlined and made more abstract. I think it would be beautiful.
Dec 13, 2008
Dec 6, 2008
Dec 4, 2008
Its that time of year again
Yes that time of year, the end of the semester. Right now im procrastinating studying for a complex analysis test. As always i use this time to review how this semester went.
If i really force myself to look at my school work, its pretty clear that this semester was educational, even if i don't want to admit it. Unfortunately, Ive also learned that im not nearly as interested in some of the subject areas i once thought i was. Completing my major will involve work that im not interested in after all and my boredom with classwork seems to border ever closer into danger. I couldn't have lasted 4 years of imsa, I can't imagine lasting 4 here.
What impresses me most is my more personal life. Even though I didn't meet any of my unrealisitic goals, it seems strange to say that just 4-5 months ago i didn't know anyone like me. I remember thinking a year ago about where id be in this process now. Whoever I was a year ago is so distant from me now, at least rationally.
If i really force myself to look at my school work, its pretty clear that this semester was educational, even if i don't want to admit it. Unfortunately, Ive also learned that im not nearly as interested in some of the subject areas i once thought i was. Completing my major will involve work that im not interested in after all and my boredom with classwork seems to border ever closer into danger. I couldn't have lasted 4 years of imsa, I can't imagine lasting 4 here.
What impresses me most is my more personal life. Even though I didn't meet any of my unrealisitic goals, it seems strange to say that just 4-5 months ago i didn't know anyone like me. I remember thinking a year ago about where id be in this process now. Whoever I was a year ago is so distant from me now, at least rationally.
Nov 15, 2008
Elegance
Elegance: original meaning "select with care".
The new abilities we acquire with computers will kill elegance.
Elegance is forced simplicity because we cannot handle the complex.
Maybe we see elegance because we can't see it otherwise.
The smarter you are, the less elegant you have to be. The more elegant you have to be, the clearer everything looks.
I would hate to believe everything looks so beautiful because we are stupid. Perhaps computers will make the world a very ugly place.
The new abilities we acquire with computers will kill elegance.
Elegance is forced simplicity because we cannot handle the complex.
Maybe we see elegance because we can't see it otherwise.
The smarter you are, the less elegant you have to be. The more elegant you have to be, the clearer everything looks.
I would hate to believe everything looks so beautiful because we are stupid. Perhaps computers will make the world a very ugly place.
Oct 25, 2008
Oct 16, 2008
what are complex numbers
I was asked once why mathematicians invented things like imaginary and complex numbers even though they “don't exist”. When we see the equation x^2=-1 we are inclined to believe that no solution exists. This was my reply.
The Island of Even Numbers.
Far far away on an distant island exists a civilization that has never heard of odd numbers. Everything on this island comes in even numbers – always. The locals count 2,4,6,8... and so on. They know nothing about any of the odd numbers which we take for granted. The following took place in a math class in this exotic land.
Teacher:
“Some algebra problems have solutions.”
6x – 8 = 40
6x = 48
x = 8
“However, many do not.”
4x -6 = 14
4x = 20
but 4*4 =16
and 4*6 =24
but there is no number between 4 and 6
so there is no solution.
“The most fundamental theorem of this course is an obvious one: Given any number A there is no number you can multiply it by and get A back. Multiplication must always result in a different value unlike addition where we can add by zero.”
“There is no number x such that ax=a.”
“We can use this theorem to prove that certain problems do not have a solution”
4x-6=14
4x=20
4x-16=4
4(x-4)=4
“By our theorem we know that there is no number that can be equal to x-4 and therefore there can be no number that is equal to x.”
But one student asked the teacher:
“What if there was a number.... lets call it “1” such that A*1=A?”
The teacher dismissed the bizarre idea, but slowly the student found out the number was extremely useful and built an entire branch of math called the study of "odd" numbers.
Sep 23, 2008
I haven't gotten to work on any of my ideas. Its been a long month between the two weddings and bachelor party I've gone to. School of course turns my life into a haze that I get lost in.
Im pretty much done with the work i have to do in college and i have three more semesters to go after this one. I wouldn't be lying if i said that considering a viable future for myself is scary, even in the short term. I have absolutely no plans for myself that are in any way realistic.
I guess then this stupid blog thing i do, as other people refer to this, is a way of centering myself in a timeline of sorts. As one comment went, if i read it correctly, I do write alot of entries when returning to this blog and die out for a while. Thats because this blog is a crutch for me in bad times.
Im pretty much done with the work i have to do in college and i have three more semesters to go after this one. I wouldn't be lying if i said that considering a viable future for myself is scary, even in the short term. I have absolutely no plans for myself that are in any way realistic.
I guess then this stupid blog thing i do, as other people refer to this, is a way of centering myself in a timeline of sorts. As one comment went, if i read it correctly, I do write alot of entries when returning to this blog and die out for a while. Thats because this blog is a crutch for me in bad times.
Aug 29, 2008
Aug 26, 2008
school year start
Maybe its the fact I have almost nothing really to do at college anymore, and its the knowledge that I now know what needs to be done and am confident that I could do them as a homeless bum which drives me into this rage.
The way my current japanese class is taught goes against almost everything I fundamentally believe in. And the hidden axiom at the core of their logic is their belief in the lazy nature of the human intellect. Nothing they do is justified.
The build up time for restoring my day to day life has been almost 2 weeks. Its something Ive come to be aware of, how leading a rich life is something that needs some kind of stability. Like making my tea everyday. Even a simple necessary trip can screw up how things go and throw me off for a week before Ill have everything in order again.
The way my current japanese class is taught goes against almost everything I fundamentally believe in. And the hidden axiom at the core of their logic is their belief in the lazy nature of the human intellect. Nothing they do is justified.
The build up time for restoring my day to day life has been almost 2 weeks. Its something Ive come to be aware of, how leading a rich life is something that needs some kind of stability. Like making my tea everyday. Even a simple necessary trip can screw up how things go and throw me off for a week before Ill have everything in order again.
Aug 14, 2008
In other news
Im back in Urbana tomorrow, in a new and hopefully better apartment. enjoy the vectorized fish.
How scary the whole lining things up really gets
I should admit here and now that i haven't really taken a full course on logic, but this seems to fall under the same catagorizes as everything else does.
In the traditional logic they teach in undergraduate CS, member of sets are described using quantifiers(the universal and existential quantifier namely). The meaning of the expression changes based on what order the quantifers are put in. Existential quantifers "depend" on the universal quantifer they come after. This concept is a bit difficult for new students no thanks to the fact that human language is often very abigous about the meaning of sentences. Scope ambitguity is a big problem in language.
What always seemed weired to me was that it was never proven to me that all in my classes that all of the different possible relations between universal and existential quantifers could be expressed by lining them up in a row with different permutations. Turns out this was wrong like I thought. Some Swedish dude came up with "Independance Friendly Logic", which is a not too shabby notation for describing all the possible relations. You can use skolemization, but thats lame. I personally diagram the relations using circles and dots. Universal quantification are circles, existential quantification is dots. If a dot is in a circle then it depends on that universally quantified variable. In this system FOL is just all the diagrams which have concentric circles.
but ill nitpick on all this a little more later
In the traditional logic they teach in undergraduate CS, member of sets are described using quantifiers(the universal and existential quantifier namely). The meaning of the expression changes based on what order the quantifers are put in. Existential quantifers "depend" on the universal quantifer they come after. This concept is a bit difficult for new students no thanks to the fact that human language is often very abigous about the meaning of sentences. Scope ambitguity is a big problem in language.
What always seemed weired to me was that it was never proven to me that all in my classes that all of the different possible relations between universal and existential quantifers could be expressed by lining them up in a row with different permutations. Turns out this was wrong like I thought. Some Swedish dude came up with "Independance Friendly Logic", which is a not too shabby notation for describing all the possible relations. You can use skolemization, but thats lame. I personally diagram the relations using circles and dots. Universal quantification are circles, existential quantification is dots. If a dot is in a circle then it depends on that universally quantified variable. In this system FOL is just all the diagrams which have concentric circles.
but ill nitpick on all this a little more later
Aug 13, 2008
More rants about marked roles
One of the interesting things about marked roles is how it really goes against the standard definition of a function. Functions are really a low level concepts. A function which receives marked inputs can be thought to act more intelligently than a function which takes a fixed number of arguments and handles them without having to think about what they are. Marked-input functions do not need to have a fixed number of arguments, nor do all roles have to be filled in before the function can be evaluated.
Lets take a function which computes the area of a rectangle called "AreaofRec". There are many different ways we could feed a function the information needed to compute the area. The prototypical being:
Lets take a function which computes the area of a rectangle called "AreaofRec". There are many different ways we could feed a function the information needed to compute the area. The prototypical being:
AreaofRec(length.5, width.4);
Or these other less common ways of input:
AreaofRec(length.5, diagonal.3);
AreaofRec(width.4, perimeter.20);
I guess its a good thing Im interested in ontologies.
AreaofRec(width.4, perimeter.20);
We can compute area of anyone of these rectangles from the information given. What we have effectively described is a function which evaluates in a certain way when it has received enough information.
Its an interesting idea, so why is it not done? Well its pretty clear that the terms we use to mark the roles of the input with will be difficult to work with. Take these for example:
We would have to some sort of agreement ontology and knowledge representation. These are still fields in their infancy, and therefore we shouldn't expect anything like this until we've come farther in knowledge representation. If we don't have any intuitive way of figuring out what we are supposed to call each of the roles, then memorized the role names becomes a task worse than memorizing the place each role is supposed to take.
Its an interesting idea, so why is it not done? Well its pretty clear that the terms we use to mark the roles of the input with will be difficult to work with. Take these for example:
Sort(sorted.[1,3,6,2,4] , method. <);
Sort(list.[1,3,6,2,4], orderingfunction.<);
Sort(list.[1,3,6,2,4], orderingfunction.<);
Theres nothing to tell us which to write unless we look at the documentation. Sure you have to look at the documentation to see wether the function or the list comes first but thats not nearly as irritating as not knowing what to call your arguments.
We would have to some sort of agreement ontology and knowledge representation. These are still fields in their infancy, and therefore we shouldn't expect anything like this until we've come farther in knowledge representation. If we don't have any intuitive way of figuring out what we are supposed to call each of the roles, then memorized the role names becomes a task worse than memorizing the place each role is supposed to take.
I guess its a good thing Im interested in ontologies.
Aug 12, 2008
久ぶり
Its been a long time since i last touched this probably because I had been writing elsewhere. That and stress. But the technical stuff I should really be writing in my notes a second draft, and i should probably write about less technical stuff and more intuitive things as well.
Anyway I should use this post to sum up some general feelings I have had from my general studies this summer that I haven't yet noted.
It has come to my attention that the single system of notation for logic and math may be damaging. Even from a psycholinguistic viewpoint, if one accepts the mild version of the whorf-sapir hypothesis then it is easy to conclude that multiple syntaxes for representing things would be important. One such example is the difference between explicit and ordered based role assignment. Current mathematical notation is based on the idea that arguments to functions are passed into it in a certain order and we determine the role of the arguments play in the function by matching them to variables which are also ordered. Example:
F(x,y) = x-y.
F(4,3)
We can reason here saying "4 is the first thing so I will replace it with the first variable in the definition (x). 3 is the second so I will replace it with second variable in the definition (y)."
Now this system is intutive and easy. It has served us well. But if we look at language as a structure we find a much different mechanism. Broadly speaking language marks the arguments role in the function/predicate. This doesn't seem to be recognized as much as it should by semanticisits using logic and is pretty rare. As far as I know the only instance of it i can find in math and compsci is in ocaml where labeled roles are allowed for functions. An example is below.
F(x,y) = x/y
F(y:3 , x:6)
We evaluate here by saying oh were supposed to replace y with 3 and x with 6 and we get 2. Here we have labeled 3 and 6 with their respective "roles" in the function.
Now both of these systems are equivalent right? Both are just as good.. but if you think about it more closely, having the roles marked allows us much more flexibility. Take partial applications in lambda calculus.
Let subtract = fun xy.x-y;
If we wish to write a function that tells you what you get when you stubtract three from something we only need to write
Let 3minus = subtract 3;
However if we want to see what happens when we take something and stubtract three from it, writing that function out becomes a bit more of a hassel
let subtractfrom3 = fun a. subtract a 3;
This is plan stupid. If we used marked roles the function becomes simpler to write.
let subtractfrom3 = subtract b:3 ;
let 3minus = subtract a:3;
(instead of using a and b we could simply mark it with 1,2,3..)
more fun uses of role-marking later
Anyway I should use this post to sum up some general feelings I have had from my general studies this summer that I haven't yet noted.
It has come to my attention that the single system of notation for logic and math may be damaging. Even from a psycholinguistic viewpoint, if one accepts the mild version of the whorf-sapir hypothesis then it is easy to conclude that multiple syntaxes for representing things would be important. One such example is the difference between explicit and ordered based role assignment. Current mathematical notation is based on the idea that arguments to functions are passed into it in a certain order and we determine the role of the arguments play in the function by matching them to variables which are also ordered. Example:
F(x,y) = x-y.
F(4,3)
We can reason here saying "4 is the first thing so I will replace it with the first variable in the definition (x). 3 is the second so I will replace it with second variable in the definition (y)."
Now this system is intutive and easy. It has served us well. But if we look at language as a structure we find a much different mechanism. Broadly speaking language marks the arguments role in the function/predicate. This doesn't seem to be recognized as much as it should by semanticisits using logic and is pretty rare. As far as I know the only instance of it i can find in math and compsci is in ocaml where labeled roles are allowed for functions. An example is below.
F(x,y) = x/y
F(y:3 , x:6)
We evaluate here by saying oh were supposed to replace y with 3 and x with 6 and we get 2. Here we have labeled 3 and 6 with their respective "roles" in the function.
Now both of these systems are equivalent right? Both are just as good.. but if you think about it more closely, having the roles marked allows us much more flexibility. Take partial applications in lambda calculus.
Let subtract = fun xy.x-y;
If we wish to write a function that tells you what you get when you stubtract three from something we only need to write
Let 3minus = subtract 3;
However if we want to see what happens when we take something and stubtract three from it, writing that function out becomes a bit more of a hassel
let subtractfrom3 = fun a. subtract a 3;
This is plan stupid. If we used marked roles the function becomes simpler to write.
let subtractfrom3 = subtract b:3 ;
let 3minus = subtract a:3;
(instead of using a and b we could simply mark it with 1,2,3..)
more fun uses of role-marking later
Jun 2, 2008
May 21, 2008
May 19, 2008
I went to the new champaign public library. It sure does alot to impress. The opening requires one to weave confusingly to enter in the main library. Inside one is greated with a corbusier scale interior that looked like it was refined by groupius. Unfortunately its evident that shelves were an after thought. Its a two story warehouse with no really effective system of partitioning space.
Thats not to say it doesn't look nice. It looks very classy. The rest of it is in good taste and theres several fun surprizes. But nothing makes up for bad room by room planning.
Interestingly enough the second floor is populated by wifi users on their laptops. Lots of them holding some sort of meeting at the table. The building is rather quiet even for a library, though i can't tell if its reverence or good acousitics. I see similar behaviour in cafe kopi downtown champaign everytime i visit. More and more people seem to be using public spaces as rented working areas. This as far as i can tell doesn't happen on campus where it only appears that people study and not actually work. I can only wonder how this relates to the new "culture of renting" that I keep on hearing about. Maybe coffe shops are good investments when the economy favors small scale organizations.
I keep on searching for outdoor spaces designed for study or work. There are few and in fact all of them have to be shaded to be laptop friendly. One such spot is a neglected garden area on the northwest side of the engineering hall. The seats are very comfortable. You have many more options if you just choose to read a book, but even then i find that hard to do laying down on grass or anything. Also, these days books are printed on paper that is almost shiny its so white. Older books used to age a bit but these don't turn yellow at all. I dont want to sound like some old japanese lament of the modern but really the aging of a book is a beautiful thing, and in bright sunlight these new books reflect so much light back from their disturbingly white covers that its unreadable.
Apr 9, 2008
did i rush this?
Oh god, what have i done. I was supposed to feel better, but now i don't know. I don't even really feel like me right now.
It's often been said that I should probably remove some of the less mature content on this blog like this. Although I am sure many would disagree, preserving to myself entries such as this one is crucial and I do so intentionally. The overall tone of this blog was never intended to be professional. The choice of orthography is enough to show that. How this kind of honesty is damaging is debatable.
This entry was made right after coming out to my friends for the first time and is the best reminder of that day in my life I have. That is why it is here.
It's often been said that I should probably remove some of the less mature content on this blog like this. Although I am sure many would disagree, preserving to myself entries such as this one is crucial and I do so intentionally. The overall tone of this blog was never intended to be professional. The choice of orthography is enough to show that. How this kind of honesty is damaging is debatable.
This entry was made right after coming out to my friends for the first time and is the best reminder of that day in my life I have. That is why it is here.
Mar 29, 2008
Champaign-Urbana Culture
Champaign urbana does have alot to offer, both on and off campus. Im feeling really disconnected from my academic life right now, and I need something else. Ive been looking on yelp and lists of things to do in the area and im happy with whats availble for me in this area: farmers market, good used bookstores, surprizingly amusing art museums, IMPE gym, good restaurants ( i need a good place i can frequent), ethnic food stores.
What i really want though is closer "regular" shopping, and maybe some forest preserve.
what i really want is a club i can really care about.
What i really want though is closer "regular" shopping, and maybe some forest preserve.
what i really want is a club i can really care about.
Mar 20, 2008
Things I Do
Im into linguistics again, mainly because i keep on thinking about resource description frameworks and why no one seems to have made one thats an actual language.
Everything out there is based on the concept of a triple (Subject Verb Object) rather than actually looking at linguistic typology and producing an actual language (one that is recursive). I really need to figure out why languages need context sensitive grammars; not so sure thats a good idea at all.
Everything out there is based on the concept of a triple (Subject Verb Object) rather than actually looking at linguistic typology and producing an actual language (one that is recursive). I really need to figure out why languages need context sensitive grammars; not so sure thats a good idea at all.
Mar 9, 2008
Hacking myself
i normally don't believe in doing things that force your will one way or another. If you don't care to do something then forcing your will (ex. having class attendance) is artificial and wrong. But, ... iono need to reevaluate, is hacking yourself in some way wrong if the will is just not willing to cut it.
Feb 26, 2008
Feb 10, 2008
Jan 17, 2008
Books
So id say 150$ is becoming common for an average textbook in my classes now. Idealy, textbook content would be free, possibly by some program set up by a university. Standard textbooks are way too pretty, and have way too many problems in them. An ideal textbook would be thin, possibly even paperback made from newspaper quality paper, and have content mostly online in a wiki format. It once again fits into the idea that proffesors shouldn't be teaching but facilitating learning by removing obstacles.
Jan 15, 2008
Intercession
I didn't want anyone to be there who didn't want to be there, but that's highschool I suppose. Theory of computer science might have been a bad choice for a couple of reasons.
- They didn't sign up for a week of it knowing what they were really getting into
- I don't think many of them were high enough on the Maslow heirachy of needs to really care. I would rather have had students eat well, sleep, and develop meaningful social ties. Theres no point in teaching to a class without these. ( I can only claim to do the first two )
- Many saw the jump into higher mathematics as merely overly specialized knowledge rather than a profound overveiw of basic philosophical thingys. The only thing i wanted them to see the entire class was the chomsky heirarchy and vaugely understand my proof about the existance of unsolvable problems.
- Many students complained about not learning anything, when in fact it was amazing how much they had learned in such a short amount of time. If there had been hands on things, it would have been easier to demonstrate that they had learned something. I think maybe they expect pain as a sign of learning, a certain sense that math/cs is a field of no pain no gain.
Frankly I did it because i believe theoretical computer science is probably the most important /beautiful thing Ive learned in college and im sad I didn't know about it earlier. It might be the fact that breaks are stressfull for me, being cut off from everyone, but i remember saying to everyone "cs273 taught me not to fear death" as a joke. It certainly affects how i see the world more than i think it was meant to.
- They didn't sign up for a week of it knowing what they were really getting into
- I don't think many of them were high enough on the Maslow heirachy of needs to really care. I would rather have had students eat well, sleep, and develop meaningful social ties. Theres no point in teaching to a class without these. ( I can only claim to do the first two )
- Many saw the jump into higher mathematics as merely overly specialized knowledge rather than a profound overveiw of basic philosophical thingys. The only thing i wanted them to see the entire class was the chomsky heirarchy and vaugely understand my proof about the existance of unsolvable problems.
- Many students complained about not learning anything, when in fact it was amazing how much they had learned in such a short amount of time. If there had been hands on things, it would have been easier to demonstrate that they had learned something. I think maybe they expect pain as a sign of learning, a certain sense that math/cs is a field of no pain no gain.
Frankly I did it because i believe theoretical computer science is probably the most important /beautiful thing Ive learned in college and im sad I didn't know about it earlier. It might be the fact that breaks are stressfull for me, being cut off from everyone, but i remember saying to everyone "cs273 taught me not to fear death" as a joke. It certainly affects how i see the world more than i think it was meant to.
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