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RE: How is Data stored on a Hard Drive?

AldarHawk
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Posted on 21-06-10 12:39
spyware wrote:
Tsk tsk, all these posts and no one came even close to the correct answer.

OP, it's magic. A wizard did it.


...man...the answer was there all along!
Spy you know you are not supposed to tell people the true answers...:whoa:
You better be careful of the wizards will come down on your ass! :evil:


Just ask Yahoo!Taboo! http://www.erikwestlake.com
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RE: How is Data stored on a Hard Drive?

goluhaque
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Posted on 21-06-10 14:37
Which wizard? Harry Potty, Voldemort, Dumbledore or somebody different? Wink


That applause I receive from y'all on posting this post would have gotten me drunk on power if I hadn't already been high on life.
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RE: How is Data stored on a Hard Drive?

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Posted on 21-06-10 16:56
none of those...each one of the "wizards" you mentioned are nothing but fictional characters created in one series of books. Think broader...think real...not some fictional character people will lead you to think of. That is main stream and not how we should ever think.

The box shall be open and the truth shall be reveled. :right:


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RE: How is Data stored on a Hard Drive?

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Posted on 22-06-10 06:29
Wizards in real world? Man, that post I posted back there was a joke.


That applause I receive from y'all on posting this post would have gotten me drunk on power if I hadn't already been high on life.
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Posted on 22-06-10 06:58
spyware wrote:
Tsk tsk, all these posts and no one came even close to the correct answer.

OP, it's magic. A wizard did it.




Case closed.




Edited by korg on 10-07-10 12:54
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Posted on 23-06-10 19:49
COM wrote:
[...] for the variation to even exist means that the original has room for it.[...]

I could see that, from a certain viewpoint. If you're looking at the general idea behind theories, the two laws I quoted earlier (let's call the latter the Gauss's Law for Magnetic Charge, or GLfMC, since it allows for magnetic charge) look rather similar. However, at that point we are using different meanings for the term "theory" (I'll distinguish them by using the prefix "C-" for your terms and "O-" for mine).

Here's where mine comes from. In science, prediction is all. From that viewpoint, two equations that result in different predictions are different theories, no matter how similar they otherwise appear; it was from this viewpoint that I made the statement that some theories predict that monopoles can't exist. This view is also in line with what you find on Hyperphysics, [url=http://bit.ly/c3QciL ]Wikipedia[/url] and the writings of various physicists.

You don't have to use my definition for the term "theory" (I'm not yet certain how to define "C-theory"; rather than me butchering it, would you give it a try?), but to allow for discussion, you should create something in your vocabulary that my term can translate to with precision. For example, you could use "equation", since GLfM and GLfMC are undoubtedly different mathematical equations. You could also use the term "model," where everything in a model must be consistent with each other. Then there's the words "variation" or "variant", which you could pair with "theory": you could call an "O-theory" a "[C-]theory variation" or "[C-]theory variant". Do any of those terms seem appropriate? My statement would thus translate to something like "some EM theory variants predict monopoles can't exist."

As an example of what might be termed different models in the same C-theory, consider the large-scale geometry of the universe under general relativity. Depending on what value you use for the total mass in the universe, you get different overall shapes: a hyperplane, a hypersphere, or a hypersaddle. You also get different values for the net curvature and change in expansion rate of the universe. Each of these are different models because each is inconsistent with the others. As we make more observations, two of those models will be falsified, just as eventually observations will falsify GLfM or QLfM. (Aside: a key difference between the spacetime geometry example and the magnetic field example is that the equations for the former differ simply in the value of a parameter, while those for the latter differ in formulation).


COM wrote:
There is a difference between "doesn't predict" and "doesn't allow" and I'd say it's a pretty big difference.

Indeed. "some [O-]theories predict no monopoles" means those O-theories don't allow monopoles, if that's what you're referring to. (I suspect you mean more than this, but can't see what that is. If so, would you explain it more?) GLfM doesn't allow them, GLfMC does.


COM wrote:
The only reason I said that, which you should understand, is that I expect you to have understood exactly what I meant.

It's not what you said but how you said it. If we don't argue in good faith, assuming that the other person is arguing honestly, fairly and respectfully, then the discussion too quickly turns into a flame war. By almost calling me a prick, you strayed perilously close to one. Note also that the problem isn't swearing, it's swearing at the other person, which is what's disrespectful.


COM wrote:
[...]If you're trying to imply here that you don't even think that I can see that,[...]

For my part, much of what I write I expect you to already know and even agree with some of it (the differences between the expansion of math & physics is a prime example). I put that stuff in because when we disagree on some statement, I'm saying the reason I disagree by including a more basal statement that you hopefully agree with. If you don't agree, then you state why and we can then trace the disagreement back to its source. Overall, the approach burns the candle from the middle, but it can work.


COM wrote:
I currently trust you to be able to understand an example and not get hung up on differences [...] tiniest detail.


Subtle distinctions and tiny details can make all the difference, especially in math & science.

Your purpose in employing the imaginary number example is important as to whether or not the example is applicable, whether the statement was explanatory, supportive or something else. I assumed one where you might have meant another. For example, if it was intended as simply an explanation of your viewpoint, that change happens to intellectually created systems, it works fine. However, if it's intended as evidence for your statement, it doesn't work so well. It's the difference between understanding something and proving something. Comparing space to a rubber sheet helps explain general relativity, but it doesn't show its validity. It took things like deflection by our sun of the light from other stars and time dilation in atomic clocks to show G.R. was valid. (Incidentally, you could have relativistic theories that incorporate curved spacetime but that aren't general relativity.) By my comment, I was trying to say that by sticking to examples from science, you can make a stronger argument.


COM wrote:
True, you could state that it implicitly said that, but I would still say that the fact that they didn't have the set of imaginary numbers is exactly what adds the weight to that the law obviously had to change, since afterwards you could no longer state it to be true for all, something which on the other hand you could state before.

It seems we agree that the law was changed, but disagree as to the nature of the change. I'd say that the law was clarified, but the old law wasn't shown to be false. This also appears to be caused by a difference in definitions for terms (specifically, the terms "absolute" and "overturn" when applied to laws & theories). I can best analyze this in terms of formal logic.

As I'm sure you'll agree, some logical statements are tautologies: true regardless of context (e.g. "Aw44;A"). Others are only true in certain contexts. The context "Numbers are real" was implicit in the old way of thinking, which can be summarized as "Numbers are real |- negative numbers don't have square roots" (aside: "A |- B" means "B is provable in context A"; for a tautology T, we write "|- T", e.g. "|- Aw44;A"). Without the context, you can't say whether the law is true or false. When we changed the context, the old statement was no longer provable, so we use a different, though related, statement. We then had "Numbers are complex |- negative real numbers don't have real square roots". From the viewpoint of formal logic, "Numbers are real |- negative numbers don't have square roots" still holds true, thus it is absolute. However, the context isn't as useful, so we usually use the "Numbers are complex" context.

I can see your way of thinking, I just express it differently: we replace systems with ones that are more generally applicable.



COM wrote:
[...] So I wouldn't tell you not to give it a try, that's for sure.

True; I shouldn't dismiss it so readily. It should at least present an interesting approach to teaching the topics.
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Posted on 23-06-10 20:04
stealth- wrote:
(although this kind of math is a little out of my league)

Some of it isn't too bad. w11; is the divergence operator. The name "divergence" is fairly descriptive: the operator is a measure of how much a field expands (positive divergence) or compresses (negative divergence). The reason we say "negative divergence" rather than "convergence" is that the latter has another meaning in math. For more, see Duane Nykamp's "The idea of divergence and curl" and the thread "Understanding Divergence Graphically" on Physics Forums.



Edited by on 23-06-10 20:08
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Posted on 23-06-10 21:45
outis wrote:
COM wrote:
[...] for the variation to even exist means that the original has room for it.[...]

I could see that, from a certain viewpoint. If you're looking at the general idea behind theories, the two laws I quoted earlier (let's call the latter the Gauss's Law for Magnetic Charge, or GLfMC, since it allows for magnetic charge) look rather similar. However, at that point we are using different meanings for the term "theory" (I'll distinguish them by using the prefix "C-" for your terms and "O-" for mine).

Here's where mine comes from. In science, prediction is all. From that viewpoint, two equations that result in different predictions are different theories, no matter how similar they otherwise appear; it was from this viewpoint that I made the statement that some theories predict that monopoles can't exist. This view is also in line with what you find on Hyperphysics, [url=http://bit.ly/c3QciL ]Wikipedia[/url] and the writings of various physicists.

You don't have to use my definition for the term "theory" (I'm not yet certain how to define "C-theory"; rather than me butchering it, would you give it a try?), but to allow for discussion, you should create something in your vocabulary that my term can translate to with precision. For example, you could use "equation", since GLfM and GLfMC are undoubtedly different mathematical equations. You could also use the term "model," where everything in a model must be consistent with each other. Then there's the words "variation" or "variant", which you could pair with "theory": you could call an "O-theory" a "[C-]theory variation" or "[C-]theory variant". Do any of those terms seem appropriate? My statement would thus translate to something like "some EM theory variants predict monopoles can't exist."

As an example of what might be termed different models in the same C-theory, consider the large-scale geometry of the universe under general relativity. Depending on what value you use for the total mass in the universe, you get different overall shapes: a hyperplane, a hypersphere, or a hypersaddle. You also get different values for the net curvature and change in expansion rate of the universe. Each of these are different models because each is inconsistent with the others. As we make more observations, two of those models will be falsified, just as eventually observations will falsify GLfM or QLfM. (Aside: a key difference between the spacetime geometry example and the magnetic field example is that the equations for the former differ simply in the value of a parameter, while those for the latter differ in formulation).


COM wrote:
There is a difference between "doesn't predict" and "doesn't allow" and I'd say it's a pretty big difference.

Indeed. "some [O-]theories predict no monopoles" means those O-theories don't allow monopoles, if that's what you're referring to. (I suspect you mean more than this, but can't see what that is. If so, would you explain it more?) GLfM doesn't allow them, GLfMC does.


COM wrote:
The only reason I said that, which you should understand, is that I expect you to have understood exactly what I meant.

It's not what you said but how you said it. If we don't argue in good faith, assuming that the other person is arguing honestly, fairly and respectfully, then the discussion too quickly turns into a flame war. By almost calling me a prick, you strayed perilously close to one. Note also that the problem isn't swearing, it's swearing at the other person, which is what's disrespectful.


COM wrote:
[...]If you're trying to imply here that you don't even think that I can see that,[...]

For my part, much of what I write I expect you to already know and even agree with some of it (the differences between the expansion of math & physics is a prime example). I put that stuff in because when we disagree on some statement, I'm saying the reason I disagree by including a more basal statement that you hopefully agree with. If you don't agree, then you state why and we can then trace the disagreement back to its source. Overall, the approach burns the candle from the middle, but it can work.


COM wrote:
I currently trust you to be able to understand an example and not get hung up on differences [...] tiniest detail.


Subtle distinctions and tiny details can make all the difference, especially in math & science.

Your purpose in employing the imaginary number example is important as to whether or not the example is applicable, whether the statement was explanatory, supportive or something else. I assumed one where you might have meant another. For example, if it was intended as simply an explanation of your viewpoint, that change happens to intellectually created systems, it works fine. However, if it's intended as evidence for your statement, it doesn't work so well. It's the difference between understanding something and proving something. Comparing space to a rubber sheet helps explain general relativity, but it doesn't show its validity. It took things like deflection by our sun of the light from other stars and time dilation in atomic clocks to show G.R. was valid. (Incidentally, you could have relativistic theories that incorporate curved spacetime but that aren't general relativity.) By my comment, I was trying to say that by sticking to examples from science, you can make a stronger argument.


COM wrote:
True, you could state that it implicitly said that, but I would still say that the fact that they didn't have the set of imaginary numbers is exactly what adds the weight to that the law obviously had to change, since afterwards you could no longer state it to be true for all, something which on the other hand you could state before.

It seems we agree that the law was changed, but disagree as to the nature of the change. I'd say that the law was clarified, but the old law wasn't shown to be false. This also appears to be caused by a difference in definitions for terms (specifically, the terms "absolute" and "overturn" when applied to laws & theories). I can best analyze this in terms of formal logic.

As I'm sure you'll agree, some logical statements are tautologies: true regardless of context (e.g. "Aw44;A"Wink. Others are only true in certain contexts. The context "Numbers are real" was implicit in the old way of thinking, which can be summarized as "Numbers are real |- negative numbers don't have square roots" (aside: "A |- B" means "B is provable in context A"; for a tautology T, we write "|- T", e.g. "|- Aw44;A"Wink. Without the context, you can't say whether the law is true or false. When we changed the context, the old statement was no longer provable, so we use a different, though related, statement. We then had "Numbers are complex |- negative real numbers don't have real square roots". From the viewpoint of formal logic, "Numbers are real |- negative numbers don't have square roots" still holds true, thus it is absolute. However, the context isn't as useful, so we usually use the "Numbers are complex" context.

I can see your way of thinking, I just express it differently: we replace systems with ones that are more generally applicable.


I'll just try to sum up instead of separating everything here.
First some minor things.
I have to agree that minor details and subtle differences do matter within science, however, in cases like these I don't see that as relevant, but let's just leave that.
I will have to disagree with you about predictions and science. In science, prediction is far from all. Plenty of things have been discovered, not by properly predicting and formulating a theory, but by accidentally stumbling across it and proceeding to give it an explanation. Or by having a very, very weak theory and then just try shit randomly until you got it right and only then formulating the rules for it. This is disheartening, but I guess it can't be helped sometimes. Predictions mostly come into play when we are dealing with things that we can't really observe normally, which for many fundamental parts of physics even up to and including things like induction haven't been the case.

Anyhow, I don't quite see why I would have to try to explain this if you say that you can see what I mean from a different viewpoint. But, let's try to quickly and easily explain my point of view then. Basically, the way you seem to see physics is how I see math and how you seem to see math is how I see physics.
Math is an abstract concept, something that we invented to symbolize things and thus if we have yet to expand or clarify upon its universe, it does not exist. Within physics it's the opposite of that, there things will exist regardless of what we say. Thus there we can state that a law implicitly only applied to a certain situation. A law that has worked in a certain circumstance will not be false, but will be expanded upon as it can still be used and is usually perfectly valid. In math, there wasn't anything there, so I do not consider it to implicitly have said something. It got proven false and changed, not expanded (though I realise that expanding upon a law is a change, let's just go with that word for a lack of a better one at the moment).
So while I agree that an altered law is a different law in a way, the way I see it can be likened to hierarchies, for instance within programming. There is a base class and there is an expanding class, a subclass. The subclass is still a form of the base class even though they are of course different. I honestly don't know how to explain this more clearly.


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RE: How is Data stored on a Hard Drive?

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Posted on 24-06-10 15:58
All I could get out of all this fun talk you two are having is Math, Physics and something about sheep...

I am not going to ask...


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Posted on 10-07-10 02:02
Baaaaa.

I hear ovinodynamics is the sexy new field.
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Posted on 10-07-10 03:17
COM, I don't know if you're still interested, but now that my HW issues are (mostly) sorted out...

COM wrote:
In science, prediction is far from all. Plenty of things have been discovered, not by properly predicting and formulating a theory, [...]

The statement "in science, prediction is all" needs some clarification. Firstly, it is a normative, rather than descriptive, statement. It isn't saying that in practice science is all about prediction (from the scientific revolution through the 19th century, it definitely wasn't).

The viewpoint itself arises from the problem that, historically, many scientific theories that were quite successful in their day were eventually falsified; even current theories may someday be falsified (otherwise, they wouldn't be scientific). What, then, is the significance of accepted theories? The old theories are not considered to be true in that they are longer taken to be descriptive of reality, though they still may be used to make calculations in the domains to which they still apply. Also, some theories may differ in form but predict the same outcomes; even a single theory may have many interpretations. When observation can't determine which theory (or interpretation) is the correct one, how do we determine which is "best", or which should be accepted and which rejected? At the very least, in these instances we can still talk about which theories provide the best predictions, considering the different forms or interpretations to be less significant. How good a theory is at prediction, rather than how "true" it is, provides the measure to evaluate theories. The different forms reflect different approaches to modeling some class of objects and behaviors. The different interpretations arise from our attempting to understand the theories, to internalize a scientific model. They are translations of math into human language (see Lawrence M. Krauss' response to "What is your formula?" for an example of different interpretations of a single law). Though an interpretion may be an accurate description of reality, they have more to do with human knowledge than the workings of our universe.

This view is evident amoung physicists in David Merman's edict to "shut up and calculate" rather than trying to explain why quantum mechanics works as a predictor (that is, rather than trying to figure out which interpretatin of QM is correct). It's also evident in Feynman's anecdote about his venture into philosophy from the chapter "A Map of the Cat" in Surely You're Joking, Mr. Feynman:
The electron is a theory that we use; it is so useful in understanding the way nature works that we can almost call it real. [...] Every time you break the brick, you only see the surface. That the brick has an inside is a simple theory which helps us understand things better. The theory of electrons is analogous.

Of course, both of these examples come from camps that don't consider the issue of how to view science to be a significant one. Feynman didn't consider philosophy to be important to scientists. His quote comes from a story illustrating his opinion that philosophy was bullshit.

Note that discoveries still have a very important place in this view. They provide observations that bring into question standing theories, new phenomena to be modeled and inspire new lines of inquiry.

COM wrote:
Anyhow, I don't quite see why I would have to try to explain this if you say that you can see what I mean from a different viewpoint.

I could be wrong; perhaps I only think I understand, or my understanding is incomplete. Also, examining one's viewpoint in the light of others' can be most revealing, uncovering assumptions and gaps.


COM wrote:
Math is an abstract concept, something that we invented to symbolize things and thus if we have yet to expand or clarify upon its universe, it does not exist. [...] In math, there wasn't anything there, so I do not consider it to implicitly have said something. It got proven false and changed, not expanded (though I realise that expanding upon a law is a change, let's just go with that word for a lack of a better one at the moment).

Would you say that since math is a human creation, it can be re-formed and rewritten?

I'm curious, what do you make of Borges' Library? What of independent discovery of equivalent mathematical theorems and systems, and the cross-cultural nature of mathematical truths?

That math doesn't truly say anything is an interesting and highly relevant point, considering that proof theory is constructed in terms of syntax rather than semantics (though there are semantically-based logical systems; science can be considered to be the application of a particular formal interpretation to mathematical systems).

COM wrote:
So while I agree that an altered law is a different law in a way, the way I see it can be likened to hierarchies, for instance within programming. There is a base class and there is an expanding class, a subclass. The subclass is still a form of the base class even though they are of course different.


Are the following examples of this? General Relativity includes Newtonian gravity as a special case; the standard model combines the strong and electroweak forces (which were previously handled separately). The latter in turn combines the weak force and electromagnetism. Classical EM theory itself extended previous theories about electricity and magnetism.

The thing about GLfM and GLfMC is they apply to the same domain. It is partly for this reason that the latter isn't an extension of the former.

By "expanding class", do you mean the subclass has additional behavior?

COM wrote:
I honestly don't know how to explain this more clearly.


You could also use a Venn diagram, where the domain of the original law is entirely contained within the domain of the altered law.





On the no-roots-for-negative-numbers law, consider the following problem. You're in a tower that's 6m from the ground to the tower floor. Your friend is on the ground and has a package for you. The lift basket you'd normally use is broken so he wants to try tossing it. As a beefy fellow, he can throw the package at about 6.5 m/s. You can reach out of a window down to the 6m mark. Will he be able to toss up the package so you can grab it? The answer is no, as a consequence of a negative number not having a real square root. This scenario is very similar to the situation during the period before the discovery of complex numbers: in both cases, all numbers are implicitly real so that the no-roots-for-negative-numbers law holds.

This also illustrates that the real number system is still viable, and thus so is the law, in certain contexts. As another example of this, octonions haven't supplanted complex numbers, despite being a more general extension of complex numbers. Octionion multiplication isn't associative, but this hasn't overturned associativity of complex multiplication.

Another thing is that "negative numbers have no square roots" isn't a formal mathematical statement; it's an interpretation in English of the formal statement, and an important part is lost in the translation. The formal statement would be something like "w04; xw12;t76; w43; x<0 w07; yw12;t76; : y*y=x", which still holds. Note that this point wouldn't have been made when complex numbers were discovered, since they predate formal systems. Indeed, the situation with this law is the sort of thing that led to formal systems. The non-historical nature of this point doesn't impact its application here.

An important property of many logical systems (including proof systems used in math) is monotonicity: adding axioms doesn't invalidate previously proven theorems. With the formal statement of the no-roots-for-negative-numbers law, we see monotonicity evident in that the law still holds despite the addition of axioms related to complex numbers.

All this goes to show that the discovery of complex numbers didn't show the no-roots-for-negative-numbers law to be false, it revealed and overturned the assumption that all numbers were real and resulted in a clarification of the law.
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Posted on 10-07-10 03:53
outis, regarding your argument with wolf. He's got a point you know. Now I don't mean to say that you're wrong or shouldn't post, but I simply don't know enough physics to understand what you wrote. In fact, when I read 10 lines of the post, I looked back to see if I had clicked on the right thread. A discussion like this if far removed from computers and is largely advanced physics (for me). I'm sure most people on the site do not understand what you posted. Even if you did reply, it's simply a waste of your time because almost no one else understands what you said. It's like you're trying to defend your points in a language I do not understand.

By all means, continue your discussion with COM - now you have someone who understands what you post - but don't misunderstand wolf. You can't blame him when you post something that advanced on a computer forum.
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Posted on 10-07-10 04:15
@gregorian: I don't blame Wolf for not understanding my point (if that is indeed what's happening), nor do I misunderstand his points. I take issue with his disrespectful, inflammatory and anti-intellectual attitude he's exhibited.

As for some not getting my points, I accept that. At least I tried, and that (along with the mental stimulation) is what matters most to me.

spyware wrote:
OP, it's magic. A wizard did it.

Sure, that's what the wizard wants you to think. An imp did all the real work.
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Posted on 10-07-10 06:45
outis wrote:
COM, I don't know if you're still interested

I'm not, it's been quite some time and this will just annoy me from this point as there is a reason I said I'd sum up in my previous post. I consider this discussion complete, let's let this thread rest.


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Posted on 10-07-10 09:40
RIP.


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