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Quite an interesting thread, even though I should be studying I got quite a few ideas reading this thread & I think I have something useful to contribute to the conversation.
If I didn't stop using Halliday and Resnick when I did I would have quit studying physics, what a terrible book! Jeesh, Pure terrible... But, talking about how it "feels" to be on a ferris wheel doesn't make a book any less "adultey", it's just the quality of that particular book...
If you want more "axiomatic" undergrad physics I suggest you get Kleppner & Kolenkow's "An Introduction to Mechanics". It's short & is jam packed with a lot of math and very little use of numerical example. There's also the book Introduction to Classical Mechanics by David Morn that is pretty hefty, especially compared to Halliday/Resnick, [in the undergrad sense].
As for the rigour you seek, My advice, [for what it's worth], is to relax because you've still got a lot of it coming to you, (you mentiond you're in Calc III and are using Halliday so I assume that level). There are some things that really annoy me for their vaguery but you have to A) deal with it remembering to remember that you still have unanswered questions on a topic, or B) Look elsewhere for an explanation. I practise both lol.
If you're looking for serious elementary rigour, I can suggest something that I haven't studied but looks very interesting to me for when I have time in the future.
Do you know who Michael Spivak is? Well he has written an [as of yet] unfinished course on Physics for Mathematicians, "Elementary mechanics from a mathematician's viewpoint". Check here, http://en.wikipedia.org/wiki/Michael_Spivak, to get the pdf and the video's if you're interested, based on the quality of his Calculus book I'm dead set on reading this pdf in the future, no buts...
As for Kinetic & Potential energy, these topics seem very vague (but still interesting) to me too, you just have to accept them for now. What I am aware of is how important & exact they become when looking at the more mathematical Lagrangian/Hamiltonian formulation of Classical mechanics. I think you'll find a few answers when you get there, (I assume & don't know if you know this stuff already lol..). Hey, if you're not happy then ask questions on these forums
Nice it's been around 2000 years since we began, who knows in another 2000 :tongue:
My understanding of Quantum physics [quite basic] tells me that this is theoretically impossible. Maybe I'm wrong but due to the nature of electrons & the randomness they would almost certainly act in a way that would change your predictions. I'm not sure, I'll get back to you in about 4 years :tongue2:
Even things like wavelengths of light etc... can alter base pair orderings & damage parts of dna etc... If you want to find a mathematical formalism you can start by using a simple combinatorics equation to see how much complexity you'd need to account.
Holding every single other factor constant, [environment, cellular & atomic activity etc...],
Count every single base pair in a "standard" sample of dna, compute the possibility of what happens when the first base pair is changed to one of the three other possibilities. This is the number of potential experiments you do to find out what dna's full theoretical capability is. Then, Holding every single other factor constant, [environment, cellular & atomic activity], take note of the macroscopic outcome of what happens on 3 test subjects who all have a different base pair to that of your "control" subject throughout somebodies life [with every single other base pair remaining stable]. Then, redo it all with a separate test subject with this base pair missing.
Once you've collected that data, move on to the second base pair. Rinse & repeat until you go through every single base pair in this particular dna sequence.
Then, do it all again by changing the first & second base pairs & acounting for them being missing. then with three base pairs etc...
You've successfully predicted what dna does!
But that is all about DNA alone! Dna is not the only factor determining evolution... Add up all the proteins & pretty much everything that goes on throughout somebodies life... Nevermind atoms, intermolecular bonds, random Van der Walls fluctuations etc... Need I continue...?
[That was a word problem, you'll have to convert that into symbols yourself ]
got a bit carried away... Back to the books :tongue2:
farleyknight said:Why can't Halliday and Resnick talk like that? Geez.. It's like, how does it make you feel when someone tries to explain centripetal acceleration by talking about what it feels like to be on a ferris wheel, something I probably haven't done for years, instead of just giving me the god damn theorem in R^2 like I'm an adult?
If I didn't stop using Halliday and Resnick when I did I would have quit studying physics, what a terrible book! Jeesh, Pure terrible... But, talking about how it "feels" to be on a ferris wheel doesn't make a book any less "adultey", it's just the quality of that particular book...
If you want more "axiomatic" undergrad physics I suggest you get Kleppner & Kolenkow's "An Introduction to Mechanics". It's short & is jam packed with a lot of math and very little use of numerical example. There's also the book Introduction to Classical Mechanics by David Morn that is pretty hefty, especially compared to Halliday/Resnick, [in the undergrad sense].
As for the rigour you seek, My advice, [for what it's worth], is to relax because you've still got a lot of it coming to you, (you mentiond you're in Calc III and are using Halliday so I assume that level). There are some things that really annoy me for their vaguery but you have to A) deal with it remembering to remember that you still have unanswered questions on a topic, or B) Look elsewhere for an explanation. I practise both lol.
If you're looking for serious elementary rigour, I can suggest something that I haven't studied but looks very interesting to me for when I have time in the future.
Do you know who Michael Spivak is? Well he has written an [as of yet] unfinished course on Physics for Mathematicians, "Elementary mechanics from a mathematician's viewpoint". Check here, http://en.wikipedia.org/wiki/Michael_Spivak, to get the pdf and the video's if you're interested, based on the quality of his Calculus book I'm dead set on reading this pdf in the future, no buts...
As for Kinetic & Potential energy, these topics seem very vague (but still interesting) to me too, you just have to accept them for now. What I am aware of is how important & exact they become when looking at the more mathematical Lagrangian/Hamiltonian formulation of Classical mechanics. I think you'll find a few answers when you get there, (I assume & don't know if you know this stuff already lol..). Hey, if you're not happy then ask questions on these forums
pgardn said:There are mathematical philosophers that tear up quite a few assumptions made by mathematics. We are only human... You think a hominid evolved over 100,000 years that somehow came up with a symbolic language is going to reach some sort of math nervana?
stay humble...
Nice it's been around 2000 years since we began, who knows in another 2000 :tongue:
pgardn said:When you go up a level to chemistry you increase the complexity enormously. And then take a step up to Biology... its nuts. The math becomes less rigorous because the complexity in modeling is crazy hard.
What breakthroughs do you see in biology and physics that will EVER allow us to predict when a person will die to the very second right when he is born?
My understanding of Quantum physics [quite basic] tells me that this is theoretically impossible. Maybe I'm wrong but due to the nature of electrons & the randomness they would almost certainly act in a way that would change your predictions. I'm not sure, I'll get back to you in about 4 years :tongue2:
farleyknight said:The point would simply be to have a paper-and-pencil simulation of evolution that would show that given certain properties of an organism (or whatever mathematical formalism we use instead) it would "mutate" and "evolve" towards a set of fitness constraints.
Even things like wavelengths of light etc... can alter base pair orderings & damage parts of dna etc... If you want to find a mathematical formalism you can start by using a simple combinatorics equation to see how much complexity you'd need to account.
Holding every single other factor constant, [environment, cellular & atomic activity etc...],
Count every single base pair in a "standard" sample of dna, compute the possibility of what happens when the first base pair is changed to one of the three other possibilities. This is the number of potential experiments you do to find out what dna's full theoretical capability is. Then, Holding every single other factor constant, [environment, cellular & atomic activity], take note of the macroscopic outcome of what happens on 3 test subjects who all have a different base pair to that of your "control" subject throughout somebodies life [with every single other base pair remaining stable]. Then, redo it all with a separate test subject with this base pair missing.
Once you've collected that data, move on to the second base pair. Rinse & repeat until you go through every single base pair in this particular dna sequence.
Then, do it all again by changing the first & second base pairs & acounting for them being missing. then with three base pairs etc...
You've successfully predicted what dna does!
But that is all about DNA alone! Dna is not the only factor determining evolution... Add up all the proteins & pretty much everything that goes on throughout somebodies life... Nevermind atoms, intermolecular bonds, random Van der Walls fluctuations etc... Need I continue...?
[That was a word problem, you'll have to convert that into symbols yourself ]
got a bit carried away... Back to the books :tongue2: