Hallo all, my german exams are over, i think i made it, i will know in 8 (!) weeks for sure, but i think i will avoid capital letters for a while.
ANYWAY, i don't know where to put this, so i leave it here, hoping you can help me with it.
i've been inspired, i think, by a man talking like a tarot deck (on youtube but in greek), total random shit but somehow it got me thinking about some issues i have with well, (what science sees as) "reality", or actually better said, with quantum physics.
on the one hand, even though i'm a set theorist, i find it really hard to think of our four dimensions, as a continuous space. because continuous means infinitely dense. and that infinite can be really very huge (from a set theoretical point of view at least, and set theory is the base of our mathematics). somehow i got a strong hunch that there's a contradiction somewhere if we assume that our dimensions are a continuous space. there's even research on the quantum theory of gravity showing (haven't read the articles *yet*) that space should be "grainy".
on the other hand, our physics is based, and that's really based, in continuous mathematics. our equations assume continuity to work! so where's the contradiction?? :argh!:
and one more thing i'm wondering about, how come on the quantum level it's all about probabilities of existing in one place or in another, and we use aristotelian logic to understand it? we use aristotelian mathematics, even though there is a theory of quantum logic, which is a version of probabilistic logic (with truth values any real number between and including 0 and 1), and i do finally have time to learn about all this stuff (marburger's book had too many words, too few equations and concrete definitions, for my taste, i'm a logician and i like to start from the start :) ). but two questions about this logic:
how does it work side by side with aristotelian logic? is it embedded in it (in a mathematical sense)? does it "converge" there somehow? any ideas?
and how did that continuous "all truth values between 0 and 1" creep in there again? :argh!: where's my contradiction?!!?!
Over my head, but I just wanted to say good luck on your exams!
Thanks Nigel :) it's already all oooveeeeeeeeerrrr :banana: (and my self imposed english and greek ban is over :lulz:)
but they will send me the results in EIGHT WEEKS! :eek:
I think I've spent a lot of time pondering this (or something similar). The conclusion (where I stopped thinking) that I came to was that reality is most likely discrete (see Planck length) and that continuous mathematical descriptions are approximations.
Enjoy your quest.
thanks Rong! that could very well be, i'd love to see how they are approximations, if you have any links or anything at all. that would be a bit unusual for me, i'm used to seeing discrete things approximate continuous ones, not the other way around, so i'm itching to understand how this works :D
I'm not very well educated in the school of quantum mechanics, but what I was trying to say - I think - is illustrated by the following image:
(http://www.marin.edu/~npsomas/Lectures/Ch_1/images/DBP.gif)
the bars represent the REALtm data. The red line represents the continuous function that best represents or approximates the REALtm data.
to put it another way - the continuous function y(x) = ax2 + bx might describe the path of a cannon ball very well, but it does not necessarily mean that the cannon ball occupies a continuous string of positions for every x. In fact, I do not believe that - in the REALLY REAL world - that the domain of this function is actually continuous. In other words, the cannon ball probably actually jumps from one discrete position to the next. What happens in between nobody knows - or maybe a better answer would be there is no in between
Since everything gets so dang tiny, I don't think we'll ever know for sure what's going on at the very bottom (or is it turtles all the way down?) but I think it is discrete
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Also, If you are not already familiar, I think you will enjoy Zeno's Paradoxes (http://en.wikipedia.org/wiki/Zeno's_paradoxes)
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Where my thoughts changed direction on this subject involved an idea I had that kind of explains why the perceived dimensions of reality are discrete and how time possibly might work. My idea was that time comes from the universe (or reality - or whatever you like to call the "all encompassing everything that exists") trying to resolve the law that matter can neither be created nor destroyed.
The big bang (or something similar) happened and reality was all like "whoops, matter was created - we can't have that! GTFO Matter!" so everything vanished, but then the universe was like, "ah, fuck - some matter just got destroyed" so all the matter re-appeared in the next iteration of everything. And, repeat.
Throw in a little "information must be preserved" and you get kind of a foundation for progression of time with some kinda sorta explanation for how and why physical things change and there are discrete changes (not continuous ones) in states of things.
It's not a very well fleshed out idea, and the concepts are kind of right on the edge of what I know how to explain and talk about but I hope you get the idea.
My understanding is that quantum numbers basically represent probabilities. My only understanding of quantum numbers at this point is regarding electrons and their positions relative to atomic nuclei, though.
GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.
Yes, I know that doesn't seem to make sense. Quantum theory is non-intuitive. And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.
That simply doesn't happen prior to decoherence.
Quote from: LMNO, PhD (life continues) on December 17, 2013, 01:01:19 PM
GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.
Yes, I know that doesn't seem to make sense. Quantum theory is non-intuitive. And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.
That simply doesn't happen prior to decoherence.
Quantum Mechanics: If it doesn't piss you off, you didn't understand the work.
I think maybe the problem he is having is that probability distributions are continuous functions...
Quote from: Dirty Old Uncle Roger on December 17, 2013, 02:12:17 PM
Quote from: LMNO, PhD (life continues) on December 17, 2013, 01:01:19 PM
GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.
Yes, I know that doesn't seem to make sense. Quantum theory is non-intuitive. And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.
That simply doesn't happen prior to decoherence.
Quantum Mechanics: If it doesn't piss you off, you didn't understand the work.
You know, it didn't irritate me at all, and I didn't find it particularly difficult. Maybe I just don't get it? But I also wonder whether there's a cultural aspect, because I was raised with a flexible perspective about the state of "being"; I am not particularly attached to "is". Sometimes the answer to an either/or question is yes.
Quote from: Radagast's Red Velvet Pancake Puppies on December 17, 2013, 08:07:54 PM
Quote from: Dirty Old Uncle Roger on December 17, 2013, 02:12:17 PM
Quote from: LMNO, PhD (life continues) on December 17, 2013, 01:01:19 PM
GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.
Yes, I know that doesn't seem to make sense. Quantum theory is non-intuitive. And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.
That simply doesn't happen prior to decoherence.
Quantum Mechanics: If it doesn't piss you off, you didn't understand the work.
You know, it didn't irritate me at all, and I didn't find it particularly difficult. Maybe I just don't get it? But I also wonder whether there's a cultural aspect, because I was raised with a flexible perspective about the state of "being"; I am not particularly attached to "is". Sometimes the answer to an either/or question is yes.
Look, the fucking cat IS or it ISN'T. It's a particle or a wave.
UNIVERSE WILL NOW MAKE UP ITS FUCKING MIND. WE'RE ON A SCHEDULE.
You'll need to provide the Universe with the proper paperwork.
Quote from: LMNO, PhD (life continues) on December 17, 2013, 08:24:17 PM
You'll need to provide the Universe with the proper paperwork.
Problem is, I know what paperwork is required, but not where it goes. :(
:argh!:
:lulz:
Quote from: Dirty Old Uncle Roger on December 17, 2013, 08:22:51 PM
Quote from: Radagast's Red Velvet Pancake Puppies on December 17, 2013, 08:07:54 PM
Quote from: Dirty Old Uncle Roger on December 17, 2013, 02:12:17 PM
Quote from: LMNO, PhD (life continues) on December 17, 2013, 01:01:19 PM
GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.
Yes, I know that doesn't seem to make sense. Quantum theory is non-intuitive. And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.
That simply doesn't happen prior to decoherence.
Quantum Mechanics: If it doesn't piss you off, you didn't understand the work.
You know, it didn't irritate me at all, and I didn't find it particularly difficult. Maybe I just don't get it? But I also wonder whether there's a cultural aspect, because I was raised with a flexible perspective about the state of "being"; I am not particularly attached to "is". Sometimes the answer to an either/or question is yes.
Look, the fucking cat IS or it ISN'T. It's a particle or a wave.
UNIVERSE WILL NOW MAKE UP ITS FUCKING MIND. WE'RE ON A SCHEDULE.
Cat is in an indeterminate state in which it is equally both alive and dead! What is so hard about that? :crankey:
Quote from: Radagast's Red Velvet Pancake Puppies on December 17, 2013, 08:53:42 PM
Cat is in an indeterminate state in which it is equally both alive and dead! What is so hard about that? :crankey:
GOD IS CHEATING.
Quote from: Dirty Old Uncle Roger on December 17, 2013, 09:21:59 PM
Quote from: Radagast's Red Velvet Pancake Puppies on December 17, 2013, 08:53:42 PM
Cat is in an indeterminate state in which it is equally both alive and dead! What is so hard about that? :crankey:
GOD IS CHEATING.
God's a dick. We already know this.
What I really like is that there are all of these rules that make logical sense, and then hidden in the very heart of all these rules, in the basis of all matter, is a violation of everything else.
And that's what all of existence is based on, is fuck you, that's what. :lol:
Quote from: Nigel's Red Velveteen Skinmeat Snacks on December 17, 2013, 09:55:19 PM
What I really like is that there are all of these rules that make logical sense, and then hidden in the very heart of all these rules, in the basis of all matter, is a violation of everything else.
And that's what all of existence is based on, is fuck you, that's what. :lol:
God's all like "This is reeeeeally gonna piss them off", and Gabriel's all "hahahahaha"
Quote from: Dirty Old Uncle Roger on December 17, 2013, 10:25:41 PM
Quote from: Nigel's Red Velveteen Skinmeat Snacks on December 17, 2013, 09:55:19 PM
What I really like is that there are all of these rules that make logical sense, and then hidden in the very heart of all these rules, in the basis of all matter, is a violation of everything else.
And that's what all of existence is based on, is fuck you, that's what. :lol:
God's all like "This is reeeeeally gonna piss them off", and Gabriel's all "hahahahaha"
:lulz:
Quote from: rong on December 17, 2013, 01:27:34 AM
Where my thoughts changed direction on this subject involved an idea I had that kind of explains why the perceived dimensions of reality are discrete and how time possibly might work. My idea was that time comes from the universe (or reality - or whatever you like to call the "all encompassing everything that exists") trying to resolve the law that matter can neither be created nor destroyed.
The big bang (or something similar) happened and reality was all like "whoops, matter was created - we can't have that! GTFO Matter!" so everything vanished, but then the universe was like, "ah, fuck - some matter just got destroyed" so all the matter re-appeared in the next iteration of everything. And, repeat.
Throw in a little "information must be preserved" and you get kind of a foundation for progression of time with some kinda sorta explanation for how and why physical things change and there are discrete changes (not continuous ones) in states of things.
It's not a very well fleshed out idea, and the concepts are kind of right on the edge of what I know how to explain and talk about but I hope you get the idea.
It sounds like it could develop into a great idea! No clue how though, as I said I'm too concerned trying to figure out the logic of all this.
Quote from: LMNO, PhD (life continues) on December 17, 2013, 01:01:19 PM
GS, It seems to me one of the problems you're having is that you're trying to understand quantum theory using a non-quantum type of understanding.
Yes, I know that doesn't seem to make sense. Quantum theory is non-intuitive. And I can tell by the OP that as a logician and set theorist, that you like hard numbers, and step-by-step logic that one can deduce from core principles.
That simply doesn't happen prior to decoherence.
I do like hard numbers, and step by step logic is a wonderful game, but logic doesn't necessarily mean aristotelian logic. we can just create any logical system that fits what we want to describe. or maybe this is where i'm getting it wrong, is this what you mean? If that's the case then how should i approach quantum theory you think? i just feel that if i really look through the details of these definitions it will make sense. and once more, thank you for your post LMNO, always in the right direction: i didn't even know what decoherence is! :) man, i need to take holidays from work to look through all this.
Quote from: rong on December 17, 2013, 07:09:00 PM
I think maybe the problem he is having is that probability distributions are continuous functions...
this is exactly my problem there! by the way i'm a she, why do you guys keep calling me he today? :lol:
There IS a logical system that fits what we're trying to describe. It just doesn't work the same way any other logical systems work.
Quote from: Nigel's Red Velveteen Skinmeat Snacks on December 17, 2013, 11:18:45 PM
There IS a logical system that fits what we're trying to describe. It just doesn't work the same way any other logical systems work.
:D i want to try and understand how it works! any clues where to look?
Probability theory.
The probability of certain interactions. Though there is nothing to interact, the interaction is what makes the things that the -action is inter- to.
Though it is not really an action the way we normally understand action either. Nothing is acting, there is no cause and effect in the usual sense.
I'm quite confused about this subject, but that seems to be the norm.
Quote from: GrannySmith on December 17, 2013, 11:00:02 PM
Quote from: rong on December 17, 2013, 07:09:00 PM
I think maybe the problem he is having is that probability distributions are continuous functions...
this is exactly my problem there! by the way i'm a she, why do you guys keep calling me he today? :lol:
terribly sorry.
Quote from: LMNO, PhD (life continues) on December 17, 2013, 11:35:05 PM
Probability theory.
Quote from: :regret: on December 18, 2013, 09:17:08 AM
The probability of certain interactions. Though there is nothing to interact, the interaction is what makes the things that the -action is inter- to.
Though it is not really an action the way we normally understand action either. Nothing is acting, there is no cause and effect in the usual sense.
I'm quite confused about this subject, but that seems to be the norm.
Sounds like this "quantum logic" i've been reading about lately:
http://plato.stanford.edu/entries/qt-quantlog/
QuoteAt its core, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic. [...] Some have argued that the empirical success of quantum mechanics calls for a revolution in logic itself.
I could not agree more! But this with my half knowledge of this field.
Here's also the wikipedia article about quantum logic, it's slightly less technical:
http://en.wikipedia.org/wiki/Quantum_logic
Still, continuity creeps in when we talk of intervals but it's not so serious there i guess. Anyway, it's all so exciting! :D
This may simply be the result of a very incomplete understanding of quantum behavior, but as I understand it the main deviation from classical logic is that rather than having one "yes", there are multiple "yeses" that all exist with equal probability. In a sense all this means is that you are dividing up as well as dividing down.
Which is probably a horribly inarticulate way of describing it, but it's how it makes sense to me.
IOW instead of "this happens 1/3 of the time" the answer means "this 1/3 happens all of the time".
I like it. And when someone asks, "well, then which third is it?" you just say, "go check, and let me know."
Quote from: LMNO, PhD (life continues) on December 20, 2013, 01:12:26 PM
I like it. And when someone asks, "well, then which third is it?" you just say, "go check, and let me know."
:lulz: