Evolution, QM and Metaphysics

[funyun]

Sadly, I'm afraid I don't. I've only covered it this last few months at university. If I stumble across an explanation at a level you might be more comfortable at, I'll pass it on.

Or, if you really want me to, I'll have a crack at going over how it drops out of the maths qualitatively. It may even be good for my revision purposes.

If it's not too much of an inconvenience, that would awesome if you just gave me a general idea of how the phenomenon occurs mathematically. I'd be very appreciative.

Mathematics underpins reality. Especially in quantum physics, our predictions are amazingly accurate. I agree it's weird; I do not think it's unexplainable.

What I meant when I said "unexplainable" is that eventually, when asking the question "why", you just have to come to a point where you say "because that's just the way things are". I believe that point is logic/math, so if all of existence doesn't ultimately boil down to that, where does it come from? Just some arbitrary arrangement, I suppose.

I agree, that would be nice. You'll note that this is how God's attributes are usually explained when questioned. And I'm not sure the other explanation - randomness - does anything but push the question further back. Where did the rule of randomness come from?

But you get all this.

Yep. That's why after years of soul searching and questioning everything, I not too long ago (2, 3 weeks, maybe) finally decided that logic and math, being the same thing represented in two different languages, are the absolute. There is no power or thing beyond them. I no longer question even math-logic as the absolute. because I've come to the conclusion that you can't question the absoluteness of it without evoking the absoluteness of it. Some might call that god; I personally prefer not to do that-- to just define things how I wish to-- but I could understand how some might arrive at a conclusion like that. I personally find a certain level of inescapable profoundness, if not purpose, in that.

The Uncertainty Principle is a required the moment you start making everything out of waves, I think. There is disagreement amongst the scientific community (the Professor giving our lectures last semester disagreed with the set reading text on this point!) about what the UP means, however.

I guess that'd all depend on what you intend when you use the word "mean". I think it's a rather ambiguous term, and I cringe when people use it in that kind of context.

 

[Dragar]

If it's not too much of an inconvenience, that would awesome if you just gave me a general idea of how the phenomenon occurs mathematically. I'd be very appreciative.

Okay. It may take some time for me to put it together, since it's very new in my mind. But I'll see what I can do (if I have time between exams - eep!).

What I meant when I said "unexplainable" is that eventually, when asking the question "why", you just have to come to a point where you say "because that's just the way things are". I believe that point is logic/math, so if all of existence doesn't ultimately boil down to that, where does it come from? Just some arbitrary arrangement, I suppose.

It's completely fascinating, I agree. Considering how I'm rapidly discovering my thinking really is baseless (we don't reason our way to desires, morality, nor are the laws of logic grounded in anything, etc. (and no, God doesn't help It just pushes the question further back!)).

Yep. That's why after years of soul searching and questioning everything, I not too long ago (2, 3 weeks, maybe) finally decided that logic and math, being the same thing represented in two different languages, are the absolute.

This reminds me of something Feynman said.

Mathematics is not just another language. Mathematics is a language plus reasoning; it is like a language plus logic. Mathematics is a tool for reasoning. It is in fact a big collection of the results of some person's careful thought and reasoning. By mathematics it is possible to connect one statment to another. From "Character of Physical Law by Richard Feynman.

There is no power or thing beyond them. I no longer question even math-logic as the absolute. because I've come to the conclusion that you can't question the absoluteness of it without evoking the absoluteness of it.

Bingo. It's important to note we can't ever question these things without using these things. We can't even comprehend a situation these things did not apply. It becomes nonsense without them being true.

I can only 'hope' that reality isn't cruel enough to have played a nasty trick upon us. (One which I cannot even consider the logical possibility of! ) But we seem to be doing well enough so far.

Some might call that god; I personally prefer not to do that-- to just define things how I wish to-- but I could understand how some might arrive at a conclusion like that. I personally find a certain level of inescapable profoundness, if not purpose, in that.

It adds a certain level of completeness, I admit.

I guess that'd all depend on what you intend when you use the word "mean". I think it's a rather ambiguous term, and I cringe when people use it in that kind of context.

The problem - and this makes a great many physicists uncomfortable - is that quantum mechanics gives us a mathematical picture without a physical picture. And it may even be a physical picture is impossible to create. I have one, but I'm unsure if it gets contradicted by experiment - I'll have to wait and see over the next year and a bit.

As an example...you're familiar with the double slit experiment, I assume? If asked you 'which slit did the electron pass through?' there are a number of answers possible. 'Top', 'bottom', 'both', 'neither' or 'not a sensible question'.

QM doesn't really tell us which of these is the correct response to the question. It certainly tells us we can never know if it was the top or the bottom. I'm currently in the 'not a sensible question' camp, because I'm unsure that what we percieve as particles are actually particles, and are rather the interactions of the wave function with...well, the measuring equipment. But I have no idea if that is correct or not; it just makes it easier for me to get some basic expectations behind how things work without it making my head hurt.

UP can be viewed the same way. When we say 'where is the particle?' are we even asking a sensible question? Or what? That's what I mean be 'mean'.

Oh, and Funyun...tell me you're going to study physics as further education! To most people, this is terribly dry and boring stuff. People who enjoy thinking about it are a rarity, and (in my opinion) a valuable asset to the scientific community.

 

[theotherguy]

Surely it is not right to dismiss the possiblity of a different logic system just because it doesn't match ours?

This is a self-defeating position. It is not possible to have a "proper understanding" of something within a binary logical system if the subject in question does not obey the same system.

 

[Dragar]

Surely it is not right to dismiss the possiblity of a different logic system just because it doesn't match ours?

Logically, anything which contradicts our logic is false.

 

[Aeschylus]

Mathematics and othe formal systems of logic never claim to say anything about the real world, so I don't think it's a good idea to say they are the absolute as they are absolute within themselves and infact most matehematical systems are incomplete in the sense of Goedel's first theorum.

 

[funyun]

Okay. It may take some time for me to put it together, since it's very new in my mind. But I'll see what I can do (if I have time between exams - eep!).

No problem at all. By the way, you're just taking exams now? I guess yall do things differently in England.

It's completely fascinating, I agree. Considering how I'm rapidly discovering my thinking really is baseless (we don't reason our way to desires, morality, nor are the laws of logic grounded in anything, etc. (and no, God doesn't help It just pushes the question further back!)).

That's right. Simply defining god as "the thing that doesn't need to be created" or "the thing that is absolute" and then going from there, whether to affirm its existence or whatever, is poor logic. Looking at something like math-logic speculatively, and eventually arriving at the point where you realize it must be the thing that doesn't need to be created, and it must be absolute, is a better approach. I think there's a real difference between those two ways of thinking, and I think it's similar to the differences between the scientific method and the method of Creationists.

This reminds me of something Feynman said.

Mathematics is not just another language. Mathematics is a language plus reasoning; it is like a language plus logic. Mathematics is a tool for reasoning. It is in fact a big collection of the results of some person's careful thought and reasoning. By mathematics it is possible to connect one statment to another. From "Character of Physical Law by Richard Feynman.

I've never seen that quote before-- it's a cool one. I agree 100%. I think if you can prove something mathematically, it's proven. Dissenting opinion is ill-founded and that's all there is to it. That's why I think the Uncertainty Principle outright disproves omniscience as a possibility or characteristic. The only question left is if matter-energy behaves as waves, and it does. So, all the thesists can throw out the concept of omniscience, and I applaud those like Lucaspa who actually do it.

Bingo. It's important to note we can't ever question these things without using these things. We can't even comprehend a situation these things did not apply. It becomes nonsense without them being true.

It's more than nonsense, really. It's divine nonsense. I don't think the word nonsense does the calamity justice.

I can only 'hope' that reality isn't cruel enough to have played a nasty trick upon us. (One which I cannot even consider the logical possibility of! ) But we seem to be doing well enough so far.

Reality is a meaningless term if logic falls apart. I mean, it'd be crazy. You think QM is crazy, you ain't seen nothing.

It adds a certain level of completeness, I admit.

That revelation combines with my new understanding that the problem of infinite regression vs. first cause only applies if time is something beyond the universe, to give me a whole new outlook on philosophy and science. But time isn't beyond the universe! I subscribe to a variation of the No-Boundary proposal, so the universe just is, and has always been, and it needs no act of creation, because time is in the universe just as space is.

The problem is now, though, to piece that understanding with the possible existence of the multiverse. This obviously would require another dimension of time, or for time to not be contained within the unvierse.

The problem - and this makes a great many physicists uncomfortable - is that quantum mechanics gives us a mathematical picture without a physical picture. And it may even be a physical picture is impossible to create. I have one, but I'm unsure if it gets contradicted by experiment - I'll have to wait and see over the next year and a bit.

As an example...you're familiar with the double slit experiment, I assume? If asked you 'which slit did the electron pass through?' there are a number of answers possible. 'Top', 'bottom', 'both', 'neither' or 'not a sensible question'.

QM doesn't really tell us which of these is the correct response to the question. It certainly tells us we can never know if it was the top or the bottom. I'm currently in the 'not a sensible question' camp, because I'm unsure that what we percieve as particles are actually particles, and are rather the interactions of the wave function with...well, the measuring equipment. But I have no idea if that is correct or not; it just makes it easier for me to get some basic expectations behind how things work without it making my head hurt.

UP can be viewed the same way. When we say 'where is the particle?' are we even asking a sensible question? Or what? That's what I mean be 'mean'.

I'm in an "all of the above" camp. It may be top, bottom, both and/or an unsensible question. QM is crazy, man! I'm not sure that that physical picture does exist. When you really think about that long enough, that's kind of a Copenhagen Interpretation, semi-solipsist way of lookig at the problem, but it really may not. Anyway, if ever you have time, I'd love to hear about your interpretation; I'm sure it's interesting.

Oh, and Funyun...tell me you're going to study physics as further education! To most people, this is terribly dry and boring stuff. People who enjoy thinking about it are a rarity, and (in my opinion) a valuable asset to the scientific community.

Well, I've thought long and hard on that. I'm extremely interested in particle physics, and I think quantum chromodynamics is fascinating. The last 5 or 6 books I've read have been about physics (in fact, the one I'm reading now, Understanding the Universe by Don Lincoln is brand new, very good, and I recommend it highly), and the more I learn, the more I want to know.

The problem is, I'm just I'm just not the math type. In terms of academics, I've always been the english/history type. I do well enough to get by in trig, but I don't exactly find it interesting (except early on in the year, when we learned about how everything just fits together neatly in a triangle..I'm sure you know what I mean). But nothing to me interesting about digits. On the flip-side, I think chemistry is just fascinating, even as all my friends fall asleep in it, and I don't mind at all doing a little simple algebra in that class in order to learn something which, I think, is cool.

So I suppose I approach physics from a more philosophical viewpoint, and I'm not sure that that's the best way to go into it. To be honest though, I think some major things are going to happen in my lifetime, and I don't want to miss out (Higgs boson, supersymmetry, graviton-- so many new things that may be out there still).

 

[funyun]

Mathematics and othe formal systems of logic never claim to say anything about the real world, so I don't think it's a good idea to say they are the absolute as they are absolute within themselves and infact most matehematical systems are incomplete in the sense of Goedel's first theorum.

I think that if we can find them at all, they must apply, or else we wouldn't have found them in the first place. But I'm not exactly sure what you mean by "apply", in terms of logic and math.

 

[Dragar]

No problem at all. By the way, you're just taking exams now? I guess yall do things differently in England.

Yes. Our Autumn semester has a number modules. We finish those modules, and have exams straight after the Christmas break. Then we have a new set of modules, and are examined before we break of for the Summer break.

That's right. Simply defining god as "the thing that doesn't need to be created" or "the thing that is absolute" and then going from there, whether to affirm its existence or whatever, is poor logic.

As Zoot would say, it's pointing at a problem in our 'rules', saying that we don't know anything that could break the rules, and then defining God as 'that which breaks the rules'.

Looking at something like math-logic speculatively, and eventually arriving at the point where you realize it must be the thing that doesn't need to be created, and it must be absolute, is a better approach. I think there's a real difference between those two ways of thinking, and I think it's similar to the differences between the scientific method and the method of Creationists.

I'm not sure. Aeschylus has pointed out, there are dangers with getting carried away like this. I agree mathematics appears to be fundemental linked to reality; I do not know why or even that it must be (or why it must be).

I've never seen that quote before-- it's a cool one. I agree 100%. I think if you can prove something mathematically, it's proven. Dissenting opinion is ill-founded and that's all there is to it. That's why I think the Uncertainty Principle outright disproves omniscience as a possibility or characteristic. The only question left is if matter-energy behaves as waves, and it does. So, all the thesists can throw out the concept of omniscience, and I applaud those like Lucaspa who actually do it.

Actually, I'd say that UP doesn't factor into omniscience. I'm starting to wonder if there's something we're missing - especially looking at the mathematics side of things - that means that when you say 'there particle is precisely here', asking 'What is its momentum?' becomes a nonsensical question. But I need to read more about this. I get another module this coming semester.

Reality is a meaningless term if logic falls apart. I mean, it'd be crazy. You think QM is crazy, you ain't seen nothing.

I know. I hope we are not crazy.

I'm in an "all of the above" camp. It may be top, bottom, both and/or an unsensible question. QM is crazy, man!

But not to the point of contradictory answers.

Seriously, QM is weird, and odd - but only when you look at the results of the simple rules. The wavefunction, for instance, follows perfectly deterministic and well defined rules.

I'm not sure that that physical picture does exist.

Me neither. But I really don't like that thought!

When you really think about that long enough, that's kind of a Copenhagen Interpretation, semi-solipsist way of lookig at the problem, but it really may not. Anyway, if ever you have time, I'd love to hear about your interpretation; I'm sure it's interesting.

I basically explained it in my last post. The wave function is the 'thing'. When we say 'the probability of finding an electron at this point', we mean 'the probability of the wavefunction interacting as if there were an electron at this point'. For averages, this evens out to our approximations of standard Newtonian physics (in fact, one of my lecturers teaching us quantum explained that you could get back to Newtonian physics by using the expectation values of quantum effects - the expected results over many measurements).

Well, I've thought long and hard about this kind of thing. I'm extremely interested in particle physics, and I think quantum chromodynamics is fascinating. The last 5 or 6 books I've read have been about physics (in fact, the one I'm reading now, Understanding the Universe by Don Lincoln is brand new, very good, and I recommend it highly), and the more I learn, the more I want to know.

Yup.

The problem is, I'm just I'm just not the math type. In terms of academics, I've always been the english/history type. I do well enough to get by in trig, but I don't exactly find it interesting (except early on in the year, when we learned about how everything just fits together neatly in a triangle..I'm sure you know what I mean). But nothing to me interesting about digits.

How about algebra? Have you touched calculus yet?

On the flip-side, I think chemistry is just fascinating, even as all my friends fall asleep in it, and I don't mind at all doing a little simple algebra in that class in order to learn something which, I think, is cool.

Chemistry becomes almost as mathematical as physics at the higher levels. It's all quantum mechanics (only, mostly they just use the results we derived for them, and that the mathematicians solved for them ).

So I suppose I approach physics from a more philosophical viewpoint, and I'm not sure that that's the best way to go into it.

I agree.

To be honest though, I think some major things are going to happen in my lifetime, and I don't want to miss out (Higgs boson, supersymmetry, graviton-- so many new things that may be out there still).

I know! Life is so exciting, and I'm looking forward to the latest discoveries. I'm sure there are things beyond our wildest dreams still waiting to be discovered.

 

[funyun]

Yes. Our Autumn semester has a number modules. We finish those modules, and have exams straight after the Christmas break. Then we have a new set of modules, and are examined before we break of for the Summer break.

Man, they may be few, but there are some reasons I'm glad I don't live in England.

As Zoot would say, it's pointing at a problem in our 'rules', saying that we don't know anything that could break the rules, and then defining God as 'that which breaks the rules'.

That's a good way to put it, and I think really brings to light the stupidity inherent.

I'm not sure. Aeschylus has pointed out, there are dangers with getting carried away like this. I agree mathematics appears to be fundemental linked to reality; I do not know why or even that it must be (or why it must be).

I don't udnerstand where the rationale behind treating the properties of reality is and math as two seperate entities comes from.

Actually, I'd say that UP doesn't factor into omniscience. I'm starting to wonder if there's something we're missing - especially looking at the mathematics side of things - that means that when you say 'there particle is precisely here', asking 'What is its momentum?' becomes a nonsensical question. But I need to read more about this. I get another module this coming semester.

Well, if we take a photgraph of a guy running, and have infintiely fast shutter speed, there would be no bluriness or anything. We wouldn't be able to tell how fast he was going. If we took a picture with slow, slow shutter speed, though, the picture would be so blurry that we may be able to deduce how fast he's going, but probbaly wouldn't be able to telle xactly where he is within the big blurry mass. This isn't a perfect analogy, but it works well enough I think.

But I don't understand how UR doesn't encroach upon omniscience. If defiance of UR ultimately boils down to just being illogical, the definition of omniscience is at fault, not the definitions of logic.

Seriously, QM is weird, and odd - but only when you look at the results of the simple rules. The wavefunction, for instance, follows perfectly deterministic and well defined rules.

Sure. QM defies our pre-conceived notions, not the math.

I basically explained it in my last post. The wave function is the 'thing'. When we say 'the probability of finding an electron at this point', we mean 'the probability of the wavefunction interacting as if there were an electron at this point'. For averages, this evens out to our approximations of standard Newtonian physics (in fact, one of my lecturers teaching us quantum explained that you could get back to Newtonian physics by using the expectation values of quantum effects - the expected results over many measurements).

Well, sure, I knew that. But why would the wave function interact only at that one point? That's the question.

How about algebra? Have you touched calculus yet?

No, I take calculus next year, and I did 2 years of algebra (algebra I, then geometry, then algebra II), before trig.

Chemistry becomes almost as mathematical as physics at the higher levels. It's all quantum mechanics (only, mostly they just use the results we derived for them, and that the mathematicians solved for them ).

Well, sometimes the more interesting parts for me is when the line becomes blurred on whether we're doing chemistry or atomic physics. I mean, there's definitely some overlapping there, and that's the part of the subject I like the best.

I agree.

Just to clarify: I don't mean I come into physics with a philosophical agenda.
What I mean is that I go into it for my own intellectual and philosophical curiosity for the physical aspects of the subject, as opposed to the mathematical aspects. I mean, I'll finish reading a book, and go "Gee, I want to know more." But sometimes, there's only so much we know, and the only way to know more is to get into and get down in the dirt with the actual math. I find the pure knowledge interesting. Like that color is like the "charge" of the strong force, even though it started out as an ad hoc explenation. I mean that's just cool.

I know! Life is so exciting, and I'm looking forward to the latest discoveries. I'm sure there are things beyond our wildest dreams still waiting to be discovered.

And I haven't decided yet if I'll just be content to read lay books on it the rest of my life, or if I actually want to go into it. Especially with the new one at CERN going up soon, I really can't make up my mind.

 

[Aeschylus]

I think that if we can find them at all, they must apply, or else we wouldn't have found them in the first place. But I'm not exactly sure what you mean by "apply", in terms of logic and math.

Actually apply is an unfortunate word, 'describe' would be better. Maths and logic are not empirical and they are not meant to describe reality.

Whetehr something is true or false in formal logical systems depends entirely on the axioms of the systems.

To illustarte this point youn might like to read a little about topoi:

http://en.wikipedia.org/wiki/Topos

 

[Aeschylus]

Here's Wigner's essay on the role of Maths in physics, worth a read:

http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

 

[funyun]

Actually apply is an unfortunate word, 'describe' would be better. Maths and logic are not empirical and they are not meant to describe reality.

I agree. I don't think logic describes reality, I think reality describes logic, or perhaps that logic dexfibes the limits of reality. But I don't see how you can get away with asking the question of whether or not logic is applicable to reality, and keep a straight face.

 

[Dragar]

Whetehr something is true or false in formal logical systems depends entirely on the axioms of the systems.

Aeschylus, much as I agree with this point, can you possibly concieve of a world where the Law of Non-Contradiction does not hold? Can you even accept this as a (logical) possibility?

I sometimes feel very trapped in these rules nature has given my thinking to play by. I am so trapped that I cannot even concieve these rules to be false.

 

[Dragar]

I don't understand where the rationale behind treating the properties of reality is and math as two seperate entities comes from.

Wait till you see calculus. That's all I can say. It seems so far removed from reality - it is far removed from reality. And yet...reality seems to play by those rules.

Well, if we take a photgraph of a guy running, and have infintiely fast shutter speed, there would be no bluriness or anything. We wouldn't be able to tell how fast he was going. If we took a picture with slow, slow shutter speed, though, the picture would be so blurry that we may be able to deduce how fast he's going, but probbaly wouldn't be able to telle xactly where he is within the big blurry mass. This isn't a perfect analogy, but it works well enough I think.

That's very close to one interpretation. A point of contention (between even the Proffessor who lectured us on QM last term, and the selected reading for the module!) is whether UP is about our observations or our predictions or the way reality is (or combinations of those).

But I don't understand how UR doesn't encroach upon omniscience. If defiance of UR ultimately boils down to just being illogical, the definition of omniscience is at fault, not the definitions of logic.

Then change the definition. You're allowed to do that, with words. I think of omniscience as 'knowing everything it is possible to know'.

Of course, I also think omniscience is asking for trouble - knowledge without context. Bleh.

Well, sure, I knew that. But why would the wave function interact only at that one point? That's the question.

Indeed it is! And...I have no idea. Why does mass distort spacetime?

No, I take calculus next year, and I did 2 years of algebra (algebra I, then geometry, then algebra II), before trig.

You'll like calculus, I think. If you want something truly bizarre to play with, while you wait, which doesn't require anything more than algebra, see if you can find a nice simple introduction to complex numbers. Just for kicks. The starting point is defining i. i is the square root of -1...

You've covered trigometric functions like cosine and sine...have you looked at the expoenential function, e?

Well, sometimes the more interesting parts for me is when the line becomes blurred on whether we're doing chemistry or atomic physics. I mean, there's definitely some overlapping there, and that's the part of the subject I like the best.

The most interesting parts for me are always the extremes - I love quantum, and I love astrophysics. I'm looking forward to studying more relativity (GR at some point!) though I expect them to be hard.

Chemistry is all based on quantum physics. I believe Feynman was the head of a chemistry department at one point.

Just to clarify: I don't mean I come into physics with a philosophical agenda. What I mean is that I go into it for my own intellectual and philosophical curiosity for the physical aspects of the subject, as opposed to the mathematical aspects. I mean, I'll finish reading a book, and go "Gee, I want to know more." But sometimes, there's only so much we know, and the only way to know more is to get into and get down in the dirt with the actual math. I find the pure knowledge interesting. Like that color is like the "charge" of the strong force, even though it started out as an ad hoc explenation. I mean that's just cool.

That's half the reason I'm in this. I mean, the maths is pretty and elegant, but I really really love getting under the mathematics. Seeing what's lurking behind it.

For instance, one of my modules - Stellar Structure - involves little but maths. A lot of my peers do not enjoy this in the slightest. But I really like it - because if you look hard enough, you can see what the maths is saying. It's just like reading another langauge, in many ways, not just manipulating symbols.

And I haven't decided yet if I'll just be content to read lay books on it the rest of my life, or if I actually want to go into it. Especially with the new one at CERN going up soon, I really can't make up my mind.

My best advice is to try to wait till you've done calculus, and perhaps some mechanics. I don't know what physics is like in America, pre University, but here it's truly dire. We didn't do anything more than algebra, while the jump to university involved everything from calculus to complex numbers straight away. I rather imagine a lot of people were surprised at how much more it resembled a mathematics course as opposed to physics.

That said, I know the mathematicians go through the first year without ever actually using a number...

 

[Aeschylus]

I agree. I don't think logic describes reality, I think reality describes logic, or perhaps that logic dexfibes the limits of reality. But I don't see how you can get away with asking the question of whether or not logic is applicable to reality, and keep a straight face.

We use it as a tool to describe reality, but it does not in itself describe reality.

Plus you talk about logic being absolute, but which logic? there is more than one system of logic.

 

[Aeschylus]

Aeschylus, much as I agree with this point, can you possibly concieve of a world where the Law of Non-Contradiction does not hold? Can you even accept this as a (logical) possibility?

I sometimes feel very trapped in these rules nature has given my thinking to play by. I am so trapped that I cannot even concieve these rules to be false.

But on the other hand take something like the axiom of choice, the axiom of choice seems intutively correct and it's inclusion is necessary for important theorums like 'all vector spaces have bases', however it's inclusion also results in things like the well-ordering principle which seems to a mathematician to be intutively incorrect. The axiom choice it turns out can be excluded or included pretty much by taste.

 

[funyun]

Wait till you see calculus. That's all I can say. It seems so far removed from reality - it is far removed from reality. And yet...reality seems to play by those rules.

When I say reality, I don’t mean our pre-conceived notions. I mean the way it actually behaves, no matter how unintuitive. I think there's a difference between contradiction of common sense and contradiction of logic.

That's very close to one interpretation. A point of contention (between even the Proffessor who lectured us on QM last term, and the selected reading for the module!) is whether UP is about our observations or our predictions or the way reality is (or combinations of those).

Well that's the million dollar question for all of QM, isn't it?

Then change the definition. You're allowed to do that, with words. I think of omniscience as 'knowing everything it is possible to know'.

Not mine to change. People hold to the original definition. So that's the one I think in terms of.

Of course, I also think omniscience is asking for trouble - knowledge without context. Bleh.

Exactly.

Indeed it is! And...I have no idea. Why does mass distort spacetime?

Why does 2+2=4? I think eventually the answer has to be "it just does, end of story". Maybe that applies for mass, maybe it doesn't, but I think it applies for math.

You'll like calculus, I think. If you want something truly bizarre to play with, while you wait, which doesn't require anything more than algebra, see if you can find a nice simple introduction to complex numbers. Just for kicks. The starting point is defining i. i is the square root of -1...

Sure, I know what i is. We covered that in Algebra II and a little more in Trig. And I know that the mathematical definition of a Complex Number is z=a+bi. In fact, we needed that for the very last thing we covered before exams, DeMoivre's Theorem.

You've covered trigometric functions like cosine and sine...have you looked at the expoenential function, e?

Yes, we did logarithms and natural logarithms in Algebra II and of course covered Euler's Number with those.

The most interesting parts for me are always the extremes - I love quantum, and I love astrophysics. I'm looking forward to studying more relativity (GR at some point!) though I expect them to be hard.

I never found GR to be that interesting, but I think SR is fascinating.

That's half the reason I'm in this. I mean, the maths is pretty and elegant, but I really really love getting under the mathematics. Seeing what's lurking behind it.

For instance, one of my modules - Stellar Structure - involves little but maths. A lot of my peers do not enjoy this in the slightest. But I really like it - because if you look hard enough, you can see what the maths is saying. It's just like reading another langauge, in many ways, not just manipulating symbols.

I think I would enjoy math a lot more if I were able to do that-- see what's happenign udnerneath the math. I can't do that intuitively, but I think it's probably something you can pick up over time.

My best advice is to try to wait till you've done calculus, and perhaps some mechanics. I don't know what physics is like in America, pre University, but here it's truly dire. We didn't do anything more than algebra, while the jump to university involved everything from calculus to complex numbers straight away. I rather imagine a lot of people were surprised at how much more it resembled a mathematics course as opposed to physics.

That said, I know the mathematicians go through the first year without ever actually using a number...

The irony. Well, I took a physics course as a freshman, but it was little more than just simple Newtonian physics. I didn't like it much. As a junior, chemistry, like I said, is practically a physics course too, and I enjoy it a heck of a lot more. I don't know what physics or chemistry is like at the college level.

 

[Aeschylus]

Why does 2+2=4? I think eventually the answer has to be "it just does, end of story". Maybe that applies for mass, maybe it doesn't, but I think it applies for math.

Well there is an answer, for that particular question, i.e. you can prove that 2 + 2 = 4 (i.e. 1* + 1* = ((1*)*)*) in the natural numbers using Peano's axioms and the definition of addition in the naturals, though the proof is tedious.

 

[funyun]

We use it as a tool to describe reality, but it does not in itself describe reality.

Plus you talk about logic being absolute, but which logic? there is more than one system of logic.

Can you define "system"? Certainly thee are different types of logic, but systems? As in schools? Many of those are built on common sense. That isn't logic.

 

[funyun]

Well there is an answer, for that particular question, i.e. you can prove that 2 + 2 = 4 (i.e. 1* + 1* = ((1*)*)*) in the natural numbers using Peano's axioms and the definition of addition in the naturals, though the proof is tedious.

And what makes the proof what it is? It just is. Eventually, that's what it boils down to.