Grandfather passed away.
I wonder if my major is what i should be doing. I don't seem to enjoy it, but when my mind is free it thinks about it compulsively.
Are the tomato plants i keep alive indoors well into fall tortured by their prolonged existence?
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
Subscribe to:
Posts (Atom)