(sorry for the long post. if anyone reads all of this, i'll be impressed).
lately, i've given a lot of thought towards religion and trying to figure out what i believe in. i've always believed in a god, especially due to some highly fortunate things that have happened in my life--stuff that i would like to think goes way beyond sheer coincidence or probability. yet, i've never vehemently agreed or advocated any particular religion over another. i guess my outlook is that there are thousands of religions spanning the entire world, many of which started thousands of years ago. i find it hard to assert that one set of beliefs is the true one, and that all the others are just misled, misguided, ill-directed faiths. i don't feel i'm that wise, and can't currently speak with such conviction. nevertheless, i've been remaining open and have been actively trying to figure out what i precisely believe in.
apparently these thoughts have affected my dreams. i woke up in the middle of the night, took some dayquil to ease my sore throat, then immediately went back to sleep. yet, during those few seconds as i shifted from being awake to dreaming, i remember having this bizarre stream of consciousness. well, first, i've occasionally wondered about math and its existence. particularly, it seems fascinating to me that everything works out. how does our number system and all of the myriad of mathematical operations all cohesively work together. not only that, but math is defined in such a way and has an infrastructure whereby mathematicians are constantly formalizing new theorems, making new discoveries, and are furthering fields that all branched from the foundations that were laid out of thousands of years ago. how is this possible?
this yields to question the very nature of math. what does 1 + 1 really mean? does it only mean something to us due to the notation and language that we define for it; is there really no basis of the underlying meaning, and we only assign meaning to things based on the grammars that we define? is math just something we've invented? things like gravity, centripetal force, and sound are all real elements that exist, and we can very precisely define them. we can accurately study chaos, probability, patterns, etc, and it seems to work out; our numbers and equations are justified. they do the job, and we slowly discover more powerful methods that allow us to understand more about our world. so, maybe the language isn't just babel; maybe there is some underlying meaning found within nature and the physical world. maybe there is some truth, and we are merely discovering it as we evolve this language we call math. this platonic view would suggest that these elements of truth would exist even if humans didn't discover and realize them. moreover, they would exist even if humans didn't exist. now, that's just weird to think about. what about poorly constructed bridges that may collapse under the right conditions due to their structure being vulnerable to particular harmonic motion. (you know, those videos of crazy bridges that rock out of control like an ocean wave until they break?) humans may have never built bridges, but these properties of force would still exist anyways, eh?
well, as i was falling asleep and started to dream, i had this epiphany that religious beliefs often parallel this; however, instead of having one convention--one system--of math notation to represent the underlying meaning, we have thousands. we have thousands of religions and sets of beliefs, where each one is its own system. each of these systems is in attempt to model the underlying truth, and asserts that it is the oracle--that its representation is right. and yet, we have other people who do not follow a particular religion. these people may question the same particulars of math--do religions concern the actual truth of some unknown force, and that our believing in a religion is our way of discovery. or rather, these people would assert that religions are merely invented, and are humans' way of defining a truth.
well, a difference in this analogy is that most religious beliefs stem from actual historical accounts. there is recorded evidence of many religious figures that are subject of prayer and worship. so, this should encourage one to believe that at least one of these religions is based on true events and that it's the oracle. yet, say one accepts that, say for example, Jesus Christ, Prince Siddhartha, Prophet Muhammad, Guru Nanak, and Prophet Zoroaster all existed and were actual mortals. even with this acceptance, the battle still begins because one must determine which system to believe in--which one is the truth and actually has significance to our existence.
just remember that this questioning all happened in a dream. (i later went on to have a nerdy dream about a graph theory talk at a math conference, and that i told the lady presenter that calculating what she called the "chocolate value" at each vertex with respect to every other vertex would be in worst case O(n^2)). anyway, i don't feel too comfortable (or feel that it's kosher) publicly talking about my actual, specific religious beliefs yet. moreover, having these subconscious questions represents my yearning to find out my "actual, specific beliefs." i'm on a quest, and i'll get back to you guys later :)
in other news, i recently applied for my first passport, to see sheley! i was warned by the department of state that it takes approximately 4-6 weeks to receive a passport. i listed that i plan to visit india in just 4 weeks after the date when i applied. apparently this motivated them :) i got my passport in 8 days! i'm not going to india now, so the joke is on them.
so, what are your views on the math stuff, and if you could visit any country, which would it be and why?
lately, i've given a lot of thought towards religion and trying to figure out what i believe in. i've always believed in a god, especially due to some highly fortunate things that have happened in my life--stuff that i would like to think goes way beyond sheer coincidence or probability. yet, i've never vehemently agreed or advocated any particular religion over another. i guess my outlook is that there are thousands of religions spanning the entire world, many of which started thousands of years ago. i find it hard to assert that one set of beliefs is the true one, and that all the others are just misled, misguided, ill-directed faiths. i don't feel i'm that wise, and can't currently speak with such conviction. nevertheless, i've been remaining open and have been actively trying to figure out what i precisely believe in.
apparently these thoughts have affected my dreams. i woke up in the middle of the night, took some dayquil to ease my sore throat, then immediately went back to sleep. yet, during those few seconds as i shifted from being awake to dreaming, i remember having this bizarre stream of consciousness. well, first, i've occasionally wondered about math and its existence. particularly, it seems fascinating to me that everything works out. how does our number system and all of the myriad of mathematical operations all cohesively work together. not only that, but math is defined in such a way and has an infrastructure whereby mathematicians are constantly formalizing new theorems, making new discoveries, and are furthering fields that all branched from the foundations that were laid out of thousands of years ago. how is this possible?
this yields to question the very nature of math. what does 1 + 1 really mean? does it only mean something to us due to the notation and language that we define for it; is there really no basis of the underlying meaning, and we only assign meaning to things based on the grammars that we define? is math just something we've invented? things like gravity, centripetal force, and sound are all real elements that exist, and we can very precisely define them. we can accurately study chaos, probability, patterns, etc, and it seems to work out; our numbers and equations are justified. they do the job, and we slowly discover more powerful methods that allow us to understand more about our world. so, maybe the language isn't just babel; maybe there is some underlying meaning found within nature and the physical world. maybe there is some truth, and we are merely discovering it as we evolve this language we call math. this platonic view would suggest that these elements of truth would exist even if humans didn't discover and realize them. moreover, they would exist even if humans didn't exist. now, that's just weird to think about. what about poorly constructed bridges that may collapse under the right conditions due to their structure being vulnerable to particular harmonic motion. (you know, those videos of crazy bridges that rock out of control like an ocean wave until they break?) humans may have never built bridges, but these properties of force would still exist anyways, eh?
well, as i was falling asleep and started to dream, i had this epiphany that religious beliefs often parallel this; however, instead of having one convention--one system--of math notation to represent the underlying meaning, we have thousands. we have thousands of religions and sets of beliefs, where each one is its own system. each of these systems is in attempt to model the underlying truth, and asserts that it is the oracle--that its representation is right. and yet, we have other people who do not follow a particular religion. these people may question the same particulars of math--do religions concern the actual truth of some unknown force, and that our believing in a religion is our way of discovery. or rather, these people would assert that religions are merely invented, and are humans' way of defining a truth.
well, a difference in this analogy is that most religious beliefs stem from actual historical accounts. there is recorded evidence of many religious figures that are subject of prayer and worship. so, this should encourage one to believe that at least one of these religions is based on true events and that it's the oracle. yet, say one accepts that, say for example, Jesus Christ, Prince Siddhartha, Prophet Muhammad, Guru Nanak, and Prophet Zoroaster all existed and were actual mortals. even with this acceptance, the battle still begins because one must determine which system to believe in--which one is the truth and actually has significance to our existence.
just remember that this questioning all happened in a dream. (i later went on to have a nerdy dream about a graph theory talk at a math conference, and that i told the lady presenter that calculating what she called the "chocolate value" at each vertex with respect to every other vertex would be in worst case O(n^2)). anyway, i don't feel too comfortable (or feel that it's kosher) publicly talking about my actual, specific religious beliefs yet. moreover, having these subconscious questions represents my yearning to find out my "actual, specific beliefs." i'm on a quest, and i'll get back to you guys later :)
in other news, i recently applied for my first passport, to see sheley! i was warned by the department of state that it takes approximately 4-6 weeks to receive a passport. i listed that i plan to visit india in just 4 weeks after the date when i applied. apparently this motivated them :) i got my passport in 8 days! i'm not going to india now, so the joke is on them.
so, what are your views on the math stuff, and if you could visit any country, which would it be and why?
great thoughts, man. that's some deep stuff. it's like you are stroking your beard while typing.
ReplyDeleteseems like all the things you are writing reflects your respect for the supernatural in the universe, and the different languages of the supernatural. math is certainly one of those languages. you start at an important place in your religious quest--the premise that there is more than meets the eye in this world.
best wishes, my friend.
Some have argued that the only meanings we find, we have put there ourselves. But as you point out, often mathematics/logic seems to contradict this! Its results often surprise us. All you do is set the rules, and you get all sorts of things out of it, many that you may not have expected.
ReplyDeleteMany that correspond very nicely to actual mechanical processes that happen in the world.
I like the bridge example you brought up. I think that works great for even showing the equations in action; so the natural vibration of the structure (in a very simplified form) you could say
is like a spring:
y'' + y = 0
But then you can drive it with an external force...
I got a kick out of comparing the solution of the resonant frequency version,
y'' + y = sin(t)
to the 'almost resonance' version
y'' + y = sin(a t), a != 1
Exercise to the readers. (Which you may have already done at some point in your lives.) Also what's neat is you can shift the phase of the driving force, and it doesn't change much... Because you can use trig identities to show you've just turned sin(t + p) into a linear combination of sin(t) and cos(t)!
Anyway, the biggest contradiction to the "the only meaning we have, we have put there" is the fact that we exist. --><--
Keep on searching, man. I'll do the same.
For I know the plans I have for you, declares the LORD, plans for welfare and not for evil, to give you a future and a hope. 12 Then you will call upon me and come and pray to me, and I will hear you. 13 You will seek me and find me, when you seek me with all your heart. I will be found by you, declares the LORD
ReplyDeleteJeremiah 29:11-13
Although I could never understand you at times, this train of thought has some merit. But, as most engineers often do, you forgot about Biology and Chemistry's roll in all of this. If not for them, there would be no gravity, and you wouldn't exist!
ReplyDeleteoh, Hi Kazi!
"Beneath the surface lies the future." - SeaQuest DSV
Interesting thoughts. I appreciate your candor and openness to the journey of faith in God.
ReplyDeleteLet me suggest two books that may be of benefit to you.
#1 Mathematics: Is God Silent? by By James Nickel
#2 More than a Carpenter by Josh McDowell order a copy here
You can read Chapter 2 for free here
Found out more about the author here
More Than a Carpenter Chapter 2 (the link didn't work in the earlier post for some reason.
ReplyDeleteThe foundations of mathematics was in a state of disarray at the beginning of the 20th century, it was through the work of Cantor, Godel, Church, etc... (at an age comparable to yours) that people really understood the constructions/limitations of formal proof systems. It is interesting to note that many of these logicians were in some ways obsessed with the pursuit of 'truth'.
ReplyDeleteMath is built on top of axioms (e.g. there exists an infinite set)--things that are held to be "true", and theorems are proved on top of a particular system of axioms (e.g. ZFC set theory). The point of axioms is that they are supposed to represent reality in some way.
There is a famous result called Godel's incompleteness theorem which essentially says the following:
For any 'computer checkable' system of axioms, there are formal statements for which one cannot prove to be true or to be false (in particular the consistency of the system itself).
Mathematical models of the physical world do not have to be entirely "correct", some of them are very nice models with cute results (e.g. there always exist a mixed Nash equilibria) but many times they don't capture everything that happen in reality.