User talk:Fnagaton/Binary prefixes4

Continued discussion

Hi, I’m continuing here not to disturb the public so much.

You cannot tell me that the formulas may not be written down. So if someone asks you what the formula for a data rate is, you say ${\frac {\partial D}{\partial t}}$, or for constant data rates ${\frac {D}{t}}$. If he then asks how big a sent file is, you say 100 KB, if he asks how long it took, you say 10 s. So he puts the pieces correctly together, writing down ${\frac {100KB}{10s}}$, which of course equals to $10{\frac {KB}{s}}$. But attention, this equals to $10.24\ KB/s$. Now by the previous calculation, $KB/s$ cannot mean $(KB)/s$, but it means $K(B/s)$, which is by no means obviously implied by the notation. The slash-notation is only acceptable where multiplication (here in parts in the form of division) is associative, because in that case it is unambiguous. The operation that K performs here is not a multiplication, but a nonlinear operation, which is obviously non-associative when mixed with multiplication, so I conclude that we cannot write “KB/s” but must always write K(B/s). You must admit that this is dissatisfying. Or otherwise you must point out in which step of the argumentation you see an error. --Quilbert (talk) 16:54, 20 June 2008 (UTC)

Basically, it is obvious where the error is because the calculation as you have written it does not follow the very well known rules of how the prefixes are used in the real world. The calculation as you have written it uses a binary based quantity and then shuffles some letters around to make a decimal based quantity. Basically, it is incorrect to apply algebraic rules to the calculation as you have written it because the letters you are shuffling around are not the same value, it is very well understood that 100K actually equals 102400 (in your example) so the calculation then obviously becomes 102400/10 = 10240 which is 10K in binary but when it is data rate then the decimal is used by convention which then correctly becomes 10.24K in decimal. So actually it is more correct why the calculation as you've written it is wrong by writing it like this:

${\frac {XKaB}{Zs}}=YKbB/s$
Where Ka = 1024 and Kb = 1000.
Therefore when Z > 1 then Y <> X/Z
It is convention that algebraic rules don't apply to these prefixes in the way you've written them, so you cannot break that convention in the calculation as you've written it. So it isn't "dissatisfying" because this is how the system works in the real world. It needs explaining properly and this is done not by adding extra prefixes that the real world hardly uses, indeed not, instead it is properly explained by educating people how the rules work which is just like anything else mathematics related. For example in mathematics it is convention that the square root of minus 1 is 'i'. But, this is important, there are rules (conventions if you like) that we must follow when manipulating equations that contain i. There are similar rules when manipulating ln or log as well. This KB and KB/s is just another example of yet another commonly used convention we use in the real world. Fnagaton 18:34, 20 June 2008 (UTC)

Looking at your equation, I can only say: Exactly! That is why we need two different prefixes Ka = Ki and Kb = K. The problem: Of course you can set up certain rules contrary to all scientific sensibility, but then again: When you have a quantity reading $1\ (KB)/s$ (which is just a different way of writing ${\frac {1\ KB}{1\ s}}$), then you start interpreting: The numerator must be a file size, so it is meant as 1024 B/s. When you have a quantity reading $1\ K(B/s)$, then you interpret: I have no special rule for this, so I just apply the usual rule K = 1000, so this is 1000 B/s. Now, KB/s can mean both, as K is nonlinear. You have to omit that problem by defining $KB/s:=K(B/s)$, which really hurts, mathematically. It is convention that algebraic rules don't apply to these prefixes – Oh man, if it were convention to jump off the bridge the day your first son is born, I hope you wouldn’t do it. There is an alternative, well-established scientific norm that we can and should use, because the old convention is nonsense. Even if it is widely used nonsens. We do not build in grammatical faults made by a majority of the population either.

What rules are there when handling i that would be against a well-established mathematical notion? --Quilbert (talk) 00:01, 21 June 2008 (UTC)

No, we don't need two different prefixes at all, what we need are for people to be educated about the exceptions to the rules so that they can manipulate the equations correctly. This is exactly like the exceptions to the rules for handling i which do not follow the normal "base rules" of algebraic manipulation. For example the "base rules" for algebraic manipulation say this: a⁰ = 1 , a¹ = a , a.a = a² , a.a.a = a³ , a.a.a.a = a⁴ , etc. However the "base rules" don't apply to i, for example: i⁰ = 1 , i¹ = i , i² = -1 (first exception) , i³ = -i (second exception) , i⁴ = 1 (third exception) etc. You see? If someone doesn't know the exception to the "base rules" that i is actually the square root of minus one then they will be confused why i behaves differently to a in the example just given. Of course once someone knows the exception to the "base rules" about i then applying these exceptions, or working them out from first first principles, is easier to understand. So, the equation and working as you've written it doesn't follow the conventions (exceptions to the base rules of algebraic manipulation) for handling prefixes, so as I said before way back at the beginning "since the calculations as written are incorrect the conclusions drawn are also fallacious." Disregarding the statement about jumping off a bridge because it is fallacious, the IEC prefixes are not a "well established scientific form" so that means Wikipedia shouldn't be using them. By the way, changing from equations to writing "well established scientific form" does not logically follow. If you want to drop the equations and just go for personal opinion about "well established scientific form" then I think we are done here because it is obvious IEC prefixes are not. To sum up, we need people to be educated about the exceptions to the rules so that they can manipulate the equations correctly because these exceptions to the rules are widely used by professionals in the relevant field. Fnagaton 07:51, 21 June 2008 (UTC)

I was not writing form but norm. By well-established, I mean that the norm has been adopted by all major norming institutes. Those and the fact that the norm makes sense weigh more than the more popular deprecated convention.

Concerning your argument about i: There is no exception to algebraic base rules here. i·i=i² is of course still true, why should the equation i²=−1 make it untrue? --Quilbert (talk) 13:29, 21 June 2008 (UTC)

IEC Is not a "well established scientific norm" either. I see from your comments that you're dropping the equation argument now and instead reverting to the already refuted "makes sense weigh more than the more popular deprecated convention". The fact is of course that for Wikipedia IEC is not better, as the consensus has shown and also as WP:UNDUE states. The way i is handled is an exception of the "base rules" because as the example I gave showed a.a <> -1 whereas i.i = -1. That's a good example of the kind of exception I'm talking about. Just like the way prefixes have to be handled which shows why the way you wrote the equations is incorrect because what you wrote does not follow the convention. That's why the conclusion you reached are fallacious. Fnagaton 14:41, 21 June 2008 (UTC)

I’m not dropping anything. I just compressed the equation argument into “makes sense”. The norm is well-established in the way I mean well-established, as explained above. a·a<>-1 is not an algebraic base rule. It is a theorem that holds for real numbers. i is complex, not real. So, i·i=−1 is not an exception by any means. --Quilbert (talk) 15:13, 21 June 2008 (UTC)

(Maybe deprecated was the wrong word, I meant obsolete: “more popular, but obsolete convention”) --Quilbert (talk) 15:19, 21 June 2008 (UTC)

Also, I object to your statement that the “sensibility weighs more than popularity” argument is already refuted. WP:UNDUE refers to displaying points of view (where using IEC prefixes would qualify as a significant minority); but this discussion is not about articles about IEC prefixes, it is about whether or not to apply them in IT-related articles. --Quilbert (talk) 15:49, 21 June 2008 (UTC)

As already shown the same way as i is handled as an exception you cannot also ignore the exceptions for handling prefixes. Stating "a·a<>-1 is not an algebraic base rule" is irrelevant because it does not tackle the actual argument I wrote, it is a straw man logical fallacy. That is why when you wrote the equations the conclusions you reached are incorrect. IEC Prefixes are not well established, just looking at how rarely they are used in the real world refutes that claim this is important because the threshold for inclusion in Wikipedia is not what some standards body claims is the truth, it is what can be verified from the reliable sources used for articles. WP:UNDUE Applies very well to this situation for the reasons already given, you cannot object to policy just because you say so and expect me to believe you because that isn't a strong argument. The policy is there for good reasons and applying proper weight from the policy to IEC prefixes means that IEC prefixes shouldn't be used in articles except when those articles directly discussing IEC prefixes. Anyway, I'm not going to debate your personal opinion about what you think is better because this isn't the place, the whole point of this topic is to show you exactly why your conclusions from the equations you wrote are incorrect due to not following convention and that has been accomplished. We are done here unless you can bring up something new related to the topic. Fnagaton 17:01, 21 June 2008 (UTC)

Come on, your last post contains no argument whatsoever. You haven’t even responded to anything I said in the post before. Maybe it helps you to numerate the points:

1. i is NOT an exception. If you still insist, you have to give reasons.
2. You haven’t conclusively shown that my equations do not show that the current consensus does not make sense, as your only argument was the i argument, which is invalid, see above.
3. I haven’t read any argument from you why WP:UNDUE should apply to this situation relating to my statement that it is about displaying, not applying.

Don’t argue like a child, don’t tell me what I have agreed to when you know exactly that I haven’t. And don’t call your arguments “strong”, because I could just do the same. It says nothing. And don’t say that we’re done when we’re not. You haven’t invalidated any of my arguments yet. --Quilbert (talk) 17:19, 21 June 2008 (UTC)

Sorry, I was arguing in a wave of fury (I was reacting to an earlier version of your above post). Nevertheless, I would like to know what you have to say to the three points above. I might explain myself a little further. When you say that i is an exception because for all real numbers a·a <> -1, you are effectively saying: “A weasel is an exception to all birds not being weasels.” Point 2 follows from point 1. And I’m serious with point 3. In an article about grammar, we might say: “A majority of the population thinks that correct grammar isn’t necessary” as of WP:UNDUE, but we would still use correct grammar in our articles. --Quilbert (talk) 18:20, 21 June 2008 (UTC)

1. I already given examples and you've not refuted those examples.
2. I have conclusively shown why the equations as you wrote them mean the conclusions you reached are incorrect, as a counter you used a straw man logical fallacy which is of course not a strong argument.
3. As for WP:UNDUE search for my "21:02, 6 June 2008 (UTC)" post on this page after expanding the sections, or look for the text in the raw page source. I also note another straw man logical fallacy when you mention weasels and birds.

Basically your handling of the prefixes in the equations you wrote are contrary to the normal conventions which means your conclusions are incorrect. I've made my point and refuted your argument so now we really are done. I'm not going continue with you insulting me. I'm going to archive this section. Fnagaton 19:50, 21 June 2008 (UTC)

• I enjoy watching you two discuss this. I respect you both and hope you two don’t alienate each other while you engage in this mental thrust & parry. I agree with you both by the way. It seems to me that Fnagaton is correct that you divide binary quantities by binary quantities, and shift the value and meaning of the prefix when the measure is data rate. It also seems to me that Quilbert is correct that dual meanings for the same prefix is asinine and the convention totally blows. But then, the entire U.S. Customary system of measurement is asinine too and we Americans are still using it (I don’t though; I have a 1-meter tape measure in my pocket at all times).

  You want an example of über asinine? The U.S. system of wire gauges is beyond asinine; it is totally brain-damaged insane. How many wires of what gauge can you get into a wire nut? With the wire-gauge system, you have to have a lookup chart on the box, like so:

• 3 #16
• 5 #18
• 1 #14 + 1–2 #16
• 1 #14 + 2–3 #18
• etc.

This is profoundly simple with the Euro way of doing things: the wire nut is good for up to 5 mm² of conductors. That means the above translates as follows:

• 3 of 1.5 mm² (4.5 mm² total)
• 5 of 1.0 mm² (5.0 mm² total)
• 1 of 2.0 mm² + 1–2 of 1.5 mm² (3.5–5.0 mm² total)
• 1 of 2.0 mm² + 2–3 of 1.0 mm² (4.0–5.0 mm² total)
• etc. where you simply add your conductors and don’t exceed 5 mm² total. You need no lookup tables on the box.

You have to really know your conductors when you design fuel cells (where everything is a conductor). Every bit of resistance (there are all types, including proton resistances in the membrane separators) must be known and minimized.

So how insane is American Wire Gauge? Totally. And what can I do about it when I write an owners manual for one of our designs. Nothing. So we live with certain things, including “megabyte”, which is ambiguous. But who gives a damn, the errors of 2.4 to 9 percent don’t mean much except to us crazy Wikipedia editors. Greg L (talk) 04:15, 21 June 2008 (UTC)

Funny stuff. I see your point. But what keeps you from explaining it the “Euro way”, as you entitle it, in the owners’ manual? It makes perfect sense and is much easier to understand. I for one would do it that way and include a table that maps the AWG number to the metric cross section. By the way, I find the formula quite amusing … --Quilbert (talk) 13:29, 21 June 2008 (UTC)

Notice

I’m sorry if you feel I have insulted you. I didn’t mean to. In that little outrage I was out of my mind, I have already apologized for that. I just don’t understand why you refuse to give arguments for your claims and why you cancel the discussion this abruptly. I don’t require it from you, I just feel it’s unforunate. I have nothing to hide and I think you were losing. You thought I had already lost. Whatever, let’s not lose mutual respect. See you soon --Quilbert (talk) 20:05, 21 June 2008 (UTC)

An additional remark: Be careful with talking about “straw man logical fallacies” without substantiating that statement, because that as well is an insult in itself. --Quilbert (talk) 20:21, 21 June 2008 (UTC)

I've already given arguments so you claiming I "have refused to" is misrepresentation. As already shown you lost the argument by failing to substantiate your incorrect use of conventions when handling prefixes and by then refusing to properly debate with your use of straw man logical fallacies. I substantiated all occurrences of when you used straw man logical fallacies so your second edit is irrelevant. I accept your apology but I can see that you are not going to bring anything new to to support your refuted argument so the matter is closed. Fnagaton 20:50, 21 June 2008 (UTC)