How is Data stored on a Hard Drive?
Well Basically, I know how data is stored onto a hard drive (Physically and Electronically).
However, What is the difference between saving a Small Whole Number and a Very Large Whole Number?
I'm doing this for a college course assignment and it asks how the data is saved.
Thanks In Advance, DarkMantis
DarkMantis wrote: [quote]ynori7 wrote: An int is 32 bits whether it's equal to 2 or 20,000.
I think that is what I wanted to know. The assignment doesn't make it very clear on what they want.
Thanks a bunch ynori7 :)[/quote]
Also look into little vs. big-endian byte ordering. they might want that covered as well. And, if pertinent, file systems.
Your question is impossibly vague. :P
There's no such thing as a "magnetic charge" (otherwise you'd have magnetic monopoles), but there are magnetic fields. The surface of a HD platter is doped with iron oxide molecules (rust, in other words), which are magnetic. Bits are encoded using the orientation of the field on the surface, which is directed either into surface or out from it (perpendicular recording), which is a recent change from the old, parallel recording:
Rather than simply using the direction to encode bits, bits are encoded as a change (for a 1) or lack of change (for a 0) in direction. In this scheme, a long sequence of 0s would be encoded as a long stretch with no change in field direction. If the sequence is too long, the read hardware might lose track of where it is in the sequence, dropping or adding 0s. There's also a limit on the number of possible transitions in a given space, which creates an upper limit on the density of information that's lower than what's possible in the average case. To fix these issues, hard disks us a run length limited encoding, which encodes k bits as n bits (with k < n), preventing too many sequential 0s or 1s (see also the older MFM encoding). You find the same problem in optical media, which uses an 8 to 14 encoding. The data goes through additional encoding for error detection and correction, such as Reed-Solomon error correction.
All of this information is quite public. A few Google searches would have turned it up.
AldarHawk wrote: You forget that the old mechanical hard drive is not the only way of recording information.
True, but the OP was about hard drives.
There are good resources out there on youtube for how NAND flash works in flash drives. I know there's a series of videos made by a forensic investigator on youtube that explains everything up from how each flash cell works.
AldarHawk wrote: [quote]mattseanbachman wrote: True, but the OP was about hard drives.
What do you think a SSD is? it is not a floppy disk :P[/quote]
I'm not trying to split hairs here but:
http://en.wikipedia.org/wiki/Hard_disk_drive
Again about what I was talking about before, this dude covers solid-state and mag. media more in depth than most care to know about. It's from a forensic angle though, so most of the material is in that light, and the speaker can be a bit slow to get started:
wolfmankurd wrote: No one knows if magnetic monopoles exist. That's true.
wolfmankurd wrote: There's nothing to say they can't. Some theories say they can't, and some say they can.
wolfmankurd wrote: And mate please just post links to your source rather than chewing it up and spitting out incomprehensible gibberish. I'm fairly certain I included links. Perhaps your browser is broken.
If you think what I wrote was gibberish, you need to go back to school.
I may be paraphrasing but:
n bits is encoded as k bits where k<n
That's called compression. There are three reasons to put it like that, and all pointless.
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k and n have a specific meaning. But in a thread about how hard drive work it'd make sense to point these out. I doubt this as k and n are fairly generic, almost foo and bar of the maths world.
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You copied this directecly from a source taking it out of context.
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You want to sound smarter than you are.
I suspect it's a mixture of 2 and 3.
This is backed up by your stupid reply about monopoles (do I think they exist? idk i have no clue, and I suspect you have even less of a clue). But I actually cannot think of a theory where they cannot exist, I know of a few which do not need their existance but could accommodate them. Can you use your wonderful linking abilities to point me to one?
mattseanbachman wrote: young blood outis confronts a grizzled veteran wolfmankurd. A wild-west showdown for the 21st century…but who will win and claim the title of leet forum sheriff? :) Hear hear! Place your bets people, community points only, no cash or other valuables. Dignity accepted where needed.
mattseanbachman wrote: I'm not trying to split hairs here but: http://en.wikipedia.org/wiki/Hard_disk_drive
See but you are splitting hairs when you bring that into play. With new technologies advancing as they are SSD is becoming more standard. A standard "Hard Drive Disk" being the standard magnetized platter set using mechanics is great. However, SSD are in the state of being called a "Hard Drive" now a days in many laptops. True it is not a conventional HDD (in the old term of Hard Drive), however it is still being used as such. I am not talking the Flash Drives or any other of these types of items. I am talking about the items like Samsungs SSD (http://www.computerworld.com/s/article/9178182/Samsung_to_release_its_fastest_512GB_notebook_SSD for some reading on them :P)
I hope you understand this is coming from one who does know what he is talking about. I have been computing for longer than most users on this site are old. I have been hacking for longer than most users on here are old. However, I do not claim to know everything. I am in no means a genius hacker or anything. I just know what I am talking about when it comes to these types of things ;)
Anyways, I hope no one is taking any of this the wrong way (as many here do). Also, those who do actually know me will vouch to what I say :evil: Anyways…I babble and digress…back to line…who wants to chirp up next?
P.S. Wolf will win :matey:
AldarHawk wrote: [quote]mattseanbachman wrote: I'm not trying to split hairs here but: http://en.wikipedia.org/wiki/Hard_disk_drive
See but you are splitting hairs when you bring that into play. With new technologies advancing as they are SSD is becoming more standard. A standard "Hard Drive Disk" being the standard magnetized platter set using mechanics is great. However, SSD are in the state of being called a "Hard Drive" now a days in many laptops. True it is not a conventional HDD (in the old term of Hard Drive), however it is still being used as such. I am not talking the Flash Drives or any other of these types of items. I am talking about the items like Samsungs SSD (http://www.computerworld.com/s/article/9178182/Samsung_to_release_its_fastest_512GB_notebook_SSD for some reading on them :P)
(snipped)
[/quote]
Most of what you say is true, and yet I still disagree. What you posted makes a crucial distinction of differentiating between SSDs and hard drives.
Why is that? Because the colloquial use of the word connotes spinning magnetic media. Now, if you want to say that in your definition, "hard drive" includes SSDs, then just call everything a hard drive and drop the distinction. You've already made the claim that SSDs are a type of hard drive so why differentiate the two in subsequent posts? My inclination is that you recognize that there's an important distinction between the two.
So I see your point better now, but I still think when most people say "hard drive" they are talking about magnetic media, spinning disks, i.e. hard disk drives, and not SSDs. But this is a minor quibble about the definition of the word and as such I'll leave it at that.
And you're wrong to read into what I said as downplaying your overall abilities and/or aptitude with computers in general. I merely disagreed with you on this one issue, nothing more. :)
wolfmankurd wrote: I may be paraphrasing but: [quote]n bits is encoded as k bits where k<n [/quote] You're not paraphrasing, you're misquoting. I actually wrote: outis wrote: To fix these issues, hard disks us a run length limited encoding, which encodes k bits as n bits (with k < n) [emph. added], That's adding redundancy, the opposite of compression (though it's related via coding theory).
wolfmankurd wrote: There are three reasons to put it like that, and all pointless.
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k and n have a specific meaning. But in a thread about how hard drive work it'd make sense to point these out. I doubt this as k and n are fairly generic, almost foo and bar of the maths world.
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You copied this directecly from a source taking it out of context.
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You want to sound smarter than you are.
I suspect it's a mixture of 2 and 3.
- Generality. RLL is a family of encodings; it isn't always, for example, 8 bits to 14 bits, so I abstracted. Take a math class.
The one incorrect simplification I made in that statement is that writing "k to n" suggests that all bit strings to be encoded are of a length and all encoded strings are of a length, which isn't true for every RLL encoding. For example, an encoding might take 010 to 100100 and 0010 to 00100100 (example from (2,7) RLL).
wolfmankurd wrote:
This is backed up by your stupid reply about monopoles (do I think they exist? idk i have no clue, and I suspect you have even less of a clue). I'm not sure why you bring up this parenthetical comment. I never accused you of thinking monopoles exist. I never accused you of thinking.
wolfmankurd wrote: But I actually cannot think of a theory where they cannot exist, I know of a few which do not need their existance but could accommodate them. Can you use your wonderful linking abilities to point me to one? Don't need to link elsewhere, but here: Gauss's law for magnetism (http://en.wikipedia.org/wiki/Gauss's_law_for_magnetism).
markup∯**B** ∙ d**A** = 0(, for those without math fonts.) For a monopole, the integral would not be 0. My failing here is I can be too much of a classicist; it's the more modern theories that predict monopoles.
Edit: it now occurs to me that you're looking for a rigorous proof. For this, I'll switch to the derivative form of Gauss's Law for Magnetism (GLfM); I hope you'll forgive me. I also hope you'll forgive me for not including links, which I've omitted since I worked this out on my own (not that that's any great accomplishment).
markup∇∙**B** = 0
Since we have no observations of magnetic monopoles, we don't have a formula for the magnetic field produced by one. We could, with loss of generality, assume it's like an electric monopole. With less loss of generality, we could make the reasonable assumption that the field is spherically symmetrical. To make this even more general, we shall assume that the field is only somewhere spherically symmetrical. That is,
**B**(**x**) = c(|**x**|)**x** and c(r) ≠ 0 for some r>0 and all **x** such that |**x**| = r
where bold & orange indicates a vector (just bold didn't quite stand out). Applying GLfM, we have:
∇∙**B**(**x**) = c(|**x**|) (1+1+1) ≠ 0 for some r > 0 and all **x** s.t. |**x**|=r
This directly contradicts GLfM. Thus either GLfM doesn't always hold or magnetic monopoles with fields that are somewhere spherically symmetric don't exist. Though this doesn't disprove the existence of magnetic monopoles with magnetic fields that are nowhere spherically symmetrical, such a beast would be highly problematic. What could produce such an asymmetry? The possibility that a magnetic monopole produces a field that is everywhere 0 makes no sense (it would scarcely be a magnetic monopole), and thus isn't considered as a possibility.
Edit2: Even more generally, and less rigorously, assume that the field through any surface containing the monopole is either outbound or inbound. That is, B ∙ a > 0 for all outgoing surface normals a or B ∙ a < 0 for all outgoing surface normals a. This gives a surface integral ∯B ∙ dA that is > 0 or < 0 respectively, which also contradicts GLfM.
What I don't understand is why you're so defensive. You didn't understand something, so you figure the other guy must be stupid? What gives?
Going back to my original post, I shouldn't have said that there's no such thing as "magnetic charge", as that's an open question (as you were right to point out). What I should have said is that saying HDs rely on magnetic charge is incorrect, as that means they are based on physics which hasn't been proven.
@AldarHawk and mattseanbachman: Thanks for holding a civilized discussion. Hopefully, someone will learn from you. If not, they can always read the community rules. Also, hopefully OP will return and settle your matter of whether or not he's interested in any large capacity medium used as a primary drive, or only hard disks by clarifying his original question. Personally, I'd accept that (these days) hard drive ≠ hard disk in some cases, but DarkMantis may not have been making the distinction. It seems most likely he was asking about hard disks, unless he was supposed to write a paper about the question rather than a short answer.
I should have taken those bets.
You can post what you like it could be the cure for AIDS but like 99% of the other users it looks like crap and we didn't bother to read it.
Now that I've schooled you on internet etiquette, still sounds like you're trying to seem smarter than you are.
But whatever you know what I say let the baby have her bottle. You got it okay, we're all plenty impressed with the maths crap you posted, Gauss was truly a genius. Go on, show your mum this I'm sure she'll love you now.
Edit: some of the shit you posted vanished. so don't think this applies anymore.
EDIT MOAR: now you've changed it completely. I lose? Lol okay.
@wolfmankurd: You challenged me, and I met it, so I now challenge you: read. Not only this post but also the one that you earlier ignored. Don't be a dullard.
wolfmankurd wrote: You can post what you like it could be the cure for AIDS but like 99% of the other users it looks like crap and we didn't bother to read it. It's not my fault you're not knowledgeable enough to understand the answer to your question.
Don't assume you speak for the other board members; let them speak for themselves. Don't insult their intelligence by assuming they can't understand what you can't understand.
At least you admit that you wouldn't recognise the truth if pointed out to you.
wolfmankurd wrote: Now that I've schooled you on internet etiquette, You can't teach what you don't understand. Apparently, you're also incapable of learning it. The only thing you've taught is how to troll: keep spewing schoolyard insults and ignore anything anyone else says.
wolfmankurd wrote: still sounds like you're trying to seem smarter than you are. Let me get this straight: by (successfully) answering the OP's question, and by (successfully) complying with your challenge for me to support a claim, I'm trying to show off and (moreover) somehow failing? Wrong on both counts, particularly as I'm not the one starting anything, I'm merely responding to other posters.
wolfmankurd wrote: But whatever you know what I say let the baby have her bottle. This from someone who still craps himself. See? I can do schoolyard, too. Doesn't add much to the conversation, does it?
wolfmankurd wrote: You got it okay, we're all plenty impressed with the maths crap you posted, Gauss was truly a genius. Math is the language of science. If you can't do the math, you can't do the science. It's not even advanced math. Multi-v is a lower-division course. Now I see why you insisted on links. Since you can't understand the math, you need an authoritative source to make the mental effort and tell you that "such-and-such a theory predicts that monopoles can't exist".
I was going to let this slide earlier when you claimed no theory predicts that monopoles can't exist, assuming that you had simply forgotten about Maxwell's Equations, but… That you don't recognize one of Maxwell's Equations speaks volumes of your ignorance. They're the fundamental equations for classical electromagnetism. They're as well known and as important as Newton's laws of motion and gravity. It's like someone claiming they're know about cars but not knowing what internal combustion is, or saying you understand electrical engineering and not recognizing a battery, or someone who's never heard of Shakespeare claiming to know literature. Or maybe you just refuse to recognize Maxwell's equations because they show you're wrong. I rarely attribute maliciousness what I can attribute to stupidity, so it's probably not the last option. By the way, if you feel anything I've written about you is incorrect, address it directly. Otherwise you're admitting it's true.
wolfmankurd wrote: Go on, show your mum this I'm sure she'll love you now. I've got my inheritance, so the rest doesn't matter.
wolfmankurd wrote: Edit: some of the shit you posted vanished. so don't think this applies anymore.
EDIT MOAR: now you've changed it completely. I lose? Lol okay.
I didn't want to reward your laziness, so before your response appeared I removed the bit where I summarized my post before it. Here it is, for posterity:
outis wrote: Rather than admit defeat, you admit laziness and willful ignorance? Now you're just trolling.
I'll shorten it to fit your attention span: you're wrong. Gauss's Law of Magnetism. ∯B ∙ dA = 0 (or, equivalently, ∇∙B = 0). For a monopole, ∯B ∙ dA ≠ 0 for a surface enclosing the monopole. Also, ∇∙B ≠ 0 for a spherical surface enclosing the monopole.
You lost (and continue to lose) because you don't follow through.
I had been giving you the benefit of the doubt, assuming your reactionary behavior was a response to the sort of person you typically have to deal with. About this I was wrong, and the reason for your behavior becomes more clear. Insecure as you are about your own intelligence, you feel the need to assert yourself as the smartest one in the room, the king of your own tiny, imaginary hill, insulting anyone else who you feel challenges your petty illusion. When you fail in your offensive and are shown to be in the wrong, you feel humiliated and recourse to ad hominem attacks, steadfastly refusing any point but your own. In short, you're a bully.
The biggest difference between us is that I don't expect to be the smartest person in the room. However, I now know whom to expect to have the least grace, integrity and maturity in the thread.
@ynori7: I don't suppose "he started it" is an acceptable defense, is it? Is wolfie normally like this?
outis, I feel I should point out that what wolfie said was that there isn't a theory without room for monopoles. Existing laws and theories can and do get changed and expanded to incorporate new discoveries, you ought to know that. There can always be a fundamental flaw or something we have just previously missed which means that we have to polish up/change something that we have thought to be absolute. There are plenty of examples in both physics and math, especially math. Just take imaginary numbers, a very simple example. Laws state that negative numbers don't have roots, so we had to expand our existing set of numbers. Similar case with the number 0 and all other subsequent sets in general.
On a slightly unrelated topic, did you happen to read The Number Devil when you were little?
Locking the thread is fine with me.
COM wrote: outis, I feel I should point out that what wolfie said was that there isn't a theory without room for monopoles. That is exactly the point I understood him to make. I argued against it, and showed it to be false.
COM wrote: Existing laws and theories can and do get changed and expanded to incorporate new discoveries, you ought to know that. You're completely right in that. On this, we're in complete agreement. There are even versions of Maxwell's equations that allow for monopoles. However, since true monopoles have yet to be observed, we don't have sufficient evidence to say which version is more valid. Also, this isn't the issue.
COM wrote: There can always be a fundamental flaw or something we have just previously missed which means that we have to polish up/change something that we have thought to be absolute. There are plenty of examples in both physics and math, especially math. Physics examples are much better than math. For one thing, mathematical laws are never overturned, only extended. For another, distinct and irreconcilable mathematical systems are entirely valid, whereas valid scientific models must agree over the domain in which they apply. In other words, math isn't empirical.
COM wrote: On a slightly unrelated topic, did you happen to read The Number Devil when you were little? Sadly, no. I hadn't heard of it until now.
wolfmankurd wrote: TL;DR That is why you fail.
wolfmankurd wrote: You just don't learn. Neither do you.
wolfmankurd wrote: TL;DR
You just don't learn. Also lockage no wonder we have database issues with the kind of posts outis comes out with.
@wolfmankurd, you didn't come across very well in this thread. Flip back to the first page, it was you who started this argument responding to outis' post on the read/write heads of a hard drive. Right after outis posts a serious response you flame it. WTF?
outis wrote: That is exactly the point I understood him to make. I argued against it, and showed it to be false. … There are even versions of Maxwell's equations that allow for monopoles. The way I see it, as I said, is that seeing as the law can be modified and you've now even said that there are versions of it that do allow for it, showing that the law does have room for it, means exactly that there isn't anything that really can state that it isn't possible. If what you're saying is simply that something currently says that it doesn't exist, that doesn't really have much weight, especially not since you just said yourself that there are versions allowing for monopoles. Because if that really is all you're saying, then it doesn't matter what the law says, if it turns out monopoles exist, then at the end of the day it was wrong anyhow.
Physics examples are much better than math. For one thing, mathematical laws are never overturned, only extended. For another, distinct and irreconcilable mathematical systems are entirely valid, whereas valid scientific models must agree over the domain in which they apply. In other words, math isn't empirical. Come on now, don't be a prick with this. I did say that there are plenty of physics examples as well, I just happened to choose math off the top of my head and I trust you to know examples within physics yourself. Furthermore I trust you to know damn well what I meant with it. Though I would disagree a tad as I think the example I gave shows exactly a mathematical law overturned. A law stated that you could not have roots for negative numbers, we then extended math and with that followed that the aforementioned law was overturned.
Sadly, no. I hadn't heard of it until now. Too bad, it's a lovely book. As you probably have guessed, it's mainly for younger people to get into math, but it's just presented in such a nice and charming way. I loved it and still love it, it's quite basic stuff, but it shows exactly the right mindset to math: to just play and have fun with it. Your comment in another thread just reminded me of that, so I had to ask.
mattseanbachman wrote:
@wolfmankurd, you didn't come across very well in this thread.
Oh noes what will my public image be like if this gets out… :/
wolfmankurd wrote: [quote]mattseanbachman wrote:
@wolfmankurd, you didn't come across very well in this thread.
Oh noes what will my public image be like if this gets out… :/[/quote]
Outis and Matt both have a point. You didn't understand, so now your making yourself look much, much worse. Senior member or not, you should probably stop….
COM wrote: The way I see it, as I said, is that seeing as the law can be modified and you've now even said that there are versions of it that do allow for it, showing that the law does have room for it,… The thing is, the variations aren't the same theory. ∇∙B=0 is not the same theory as ∇∙B=k ρ_m, since each results in different predictions in certain situations (such as the existence of monopoles). In the same way, "all swans are white" and "all swans are white or black" are different. The derivative and integral forms of GLfM are the same theory because, though they have different forms, they result in the same predictions in all cases.
COM wrote: If what you're saying is simply that something currently says that it doesn't exist, I'm saying that some theories predict no monopoles, some theories predict monopoles, and some theories merely allow for monopoles. If a monopole is observed, it will falsify the theories that don't allow monopoles. They may still apply in limited cases, but not generally. Classical gravity, for example, was only falsified at relativistic speeds. At non-relativistic ones, it still holds. Since you can't observe that a monopole doesn't exist, something else would need to falsify the monopole-predicting theories.
COM wrote: Come on now, don't be a prick with this. I did say that there are plenty of physics examples as well, I just happened to choose math off the top of my head and I trust you to know examples within physics yourself. Furthermore I trust you to know damn well what I meant with it. I don't mean to be prickish, just precise. Subtle distinctions make all the difference in science and math.
My point with that statement is that scientific and mathematical revolutions are the same family but different species. Falsifying of electromagnetic theories won't happen the same way that imaginary roots were discovered. Something like the creation of imaginary numbers is fundamentally different than the creation of general relativity, since it doesn't compete with real number arithmetic, whereas general relativity replaces classical gravity (except at non-relativistic speeds, where they are equivalent). Mathematical truths, however, are indeed eternal. As another example, hyperbolic and elliptical geometries don't replace Euclidean geometry; rather, they are non-equivalent alternative geometries.
COM wrote: Though I would disagree a tad as I think the example I gave shows exactly a mathematical law overturned. A law stated that you could not have roots for negative numbers[…] Before imaginary numbers, roots were implicitly real numbers. The statement "negative numbers don't have a square root" was thus implicitly "negative numbers don't have a real square root," which is still true. What happened is the assumption that all number were real was overturned. This particular point may not be settled, because, to some degree, it's a matter of perspective. In other words, we're both a little right.
Incidentally, overturning assumptions (rather than laws) is the usual route of mathematical revolutions. Non-euclidean geometries were discovered in this way. Scientific revolutions happen when new observations falsify (or aren't covered by) existing theories. Of course, if you accept Kuhn, scientific revolutions happen more as a result of the intellectual climate and are thus more similar to mathematical revolutions.
The prick comment aside, this is closer to what I look for in a discussion: we can take contrary viewpoints and debate them. Misunderstandings happen, so we clarify. I don't expect everyone to agree with my position, but I do expect them to back up theirs, unless something is entirely a matter of opinion.
RE: The Number Devil. Thanks for pointing it out. It may be to late for me, but not for my friends' kids. Someone is going to wind up with a copy.
outis wrote: The thing is, the variations aren't the same theory. ∇∙B=0 is not the same theory as ∇∙B=k ρ_m, since each results in different predictions in certain situations (such as the existence of monopoles). In the same way, "all swans are white" and "all swans are white or black" are different. The derivative and integral forms of GLfM are the same theory because, though they have different forms, they result in the same predictions in all cases.
Yes I realize that variations aren't the same, that's pretty obvious since otherwise they wouldn't be variations. However, my point is merely that the way I see it, for the variation to even exist means that the original has room for it. Even if the original in its current state doesn't incorporate something, a variant of it that does, means that there was room. Which ties in to my point about the next quote.
I'm saying that some theories predict no monopoles, some theories predict monopoles, and some theories merely allow for monopoles. If a monopole is observed, it will falsify the theories that don't allow monopoles. There is a difference between "doesn't predict" and "doesn't allow" and I'd say it's a pretty big difference.
I don't mean to be prickish, just precise. Subtle distinctions make all the difference in science and math. … The prick comment aside, The only reason I said that, which you should understand, is that I expect you to have understood exactly what I meant. I currently trust you to be able to understand an example and not get hung up on differences when I have stated that there are examples from both fields. I am well aware that the expansion of the world of math and the world of physics differ. If you're trying to imply here that you don't even think that I can see that, then I honestly feel insulted. So all I'm saying is that some things are expected to be inferred in a conversation like this, you don't have to constantly elaborate on everything into the tiniest detail.
Before imaginary numbers, roots were implicitly real numbers. The statement "negative numbers don't have a square root" was thus implicitly "negative numbers don't have a real square root," which is still true. What happened is the assumption that all number were real was overturned. This particular point may not be settled, because, to some degree, it's a matter of perspective. In other words, we're both a little right. 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. Anyhow, as you also mentioned there briefly, I feel that we've reached a point in all these matters where we just have a different way to look upon the same thing. So it seems futile to continue.
RE: The Number Devil. Thanks for pointing it out. It may be to late for me, but not for my friends' kids. Someone is going to wind up with a copy. Depends on your personality. Personally I think it's charming enough for a read even as an adult, you will just happen to know what they talk about more easily. So I wouldn't tell you not to give it a try, that's for sure.
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:
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:
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. "A∨¬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. "|- A∨¬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.
stealth- wrote: (although this kind of math is a little out of my league) Some of it isn't too bad. ∇· 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.
outis wrote: [quote]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. "A∨¬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. "|- A∨¬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. [/quote]
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.
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 "∀ x∈ℜ ∧ x<0 ¬∃ y∈ℜ : 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.
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.
@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.