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A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover Books on Mathematics) https:
This book would help.
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thanks for the info. I bought this kindle version of book.
diligent hands rule....
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at my time 12 midnight. i won't watch: not a Mac anything in my hardware. as a former paid up apple fanbois, twenty years ago, i do appreciate the quality/design and innovation$
what do you expect to see if you watch ?
«The mind is not a vessel to be filled but a fire to be kindled» Plutarch
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I expect Apple to claim USB-C as something they invented.
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i expect it to be renamed "teleport max." 
«The mind is not a vessel to be filled but a fire to be kindled» Plutarch
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People to start complaining that their previous generation phone has slowed down ... and Apple to shrug and say "Buy a new one"
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
AntiTwitter: @DalekDave is now a follower!
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OriginalGriff wrote: and Apple to shrug and say "Buy a new one"
"And here's a gizmo ($24.95) you can place on your new USB cable ($19.95 separate purchase) to improve its performance. The Apple USB cables are superior to others, so you really should only buy them to get the best out of your device. The gizmo will not work as well on non-Apple cables." - or something to that effect.
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Like the people who buy oxygen-free copper cables for their car stereos because it conducts better!
The difficult we do right away...
...the impossible takes slightly longer.
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Richard Andrew x64 wrote: oxygen-free copper cables for their car stereos
Or for any purpose, really...
But for a car, in particular? Cars aren't exactly the ideal listening environment to start with.
I haved a neighbor - describing himself as an audiophile - who bought gold-plated USB cables going from his PC's dedicated audio card (you don't really see these anymore) to his high-end receiver. I asked him whether the 1s were sharper and the 0s were rounder. He didn't know what to reply.
This is a guy who also had a $3,000 MP3 player and was looking at the $4,500 upgraded version. I didn't even know these devices existed, let alone a market for them...
[Edit]
I hope his hearing was better than his sight. He was colorblind, and his TV was "calibrated" (ahem) with a distinctively pink-ish tone.
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dandy72 wrote: But for a car, in particular?
Are you not aware of the practice of putting 3000 watt stereos into automobiles with giant, thumping subwoofers?
The difficult we do right away...
...the impossible takes slightly longer.
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Loudness != quality
My point was that a rolling car is just about the last place you want to be to listen to something if you are serious about sound quality.
And yes, I've seen cars with speakers so huge, if you place them facing the back of the car, they can help push it forward and achieve better mileage...
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I didn't realize you were making an assertion. I thought you were saying there is no such thing.
The difficult we do right away...
...the impossible takes slightly longer.
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Believe me, I've seen them. And I hear them drive by every day night.
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dandy72 wrote: Loudness != quality
Actually, that is wrong, from a subjective point of view 
It is well known that if you set up two 100% identical systems, but adjust one to play 1 to 2 dB louder than the other, in a blind test a listening panel will not hear the loudness difference, but will describe the louder system as having a firmer bass and a more distinctive upper middle range.
The salesmen know that very well. Notice that when you are out shopping for a new stereo system, speakers or whatever, the salesman presents the more expensive alternative (i.e. the one he want to sell), he cranks up the level a little tiny bit when he tells you to listen closely for the bass clarity, or the middle and upper range quality.
Many years ago, there was a craze in the HiFi world about green felt tip pens: You could buy these super expensive pens to color the edges of your CDs to improve the sound quality. You had to use these special expensive pens: They were the exact complimentary color to the infrared laser. (Green being a complimentary color of IR????)
One of my friends, an electronics engineer, laughed wildly about this. But as a scientist, he wanted to verify that it was plain BS. So he made a setup with two CD players to the same amplifier, same speakers, and two identical copies of the same CD, except that one had its edge painted with this super-expensive green felt tip pen. When he switched between the two inputs, changing nothing else, he was slightly shocked: The green-painted copy certainly did sound firmer in the bass, and more distinct in the upper middle tones.
He knew that it was crazy, it couldn't be the case, and set out to find the explanation. As an EE guy, he had available all sorts of meters, and it didn't take him long to discover that the output from the CD player with the "green" CD was slightly more than 1 dB higher than the other one. 1 dB is not discernible as a loudness difference. He added a small resistor to the cable, to bring the signal level down to that of the other CD player. Now it impossible to distinguish about the two CDs. The subjective difference was solely caused by the very slight loudness difference, not perceived as such.
This little experience suggested an obvious verification test: He removed the level correcting resistor, but switched the CDs in the players: Now the un-green CD was in the player with the higher signal output, the green in the one with the lower signal. Now the un-green CD was the one with the firmer bass and the more distinct middle range.
So, if your car stereo really isn't that good: Crank up the volume, and it might sound a lot better.
Bonus story: When I was considering buying a Ford Transit box car (I did end up with one!), the salesman let me test drive a used Transit, for which they already had a buyer so it wasn't available: The buyer wanted it to give room for his bass speakers, that wouldn't fit into any sedan. He needed a Transit size car to fit his speakers in!
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trønderen wrote: from a subjective point of view
And that's exactly that, subjective. Of course a system that plays louder will sound "better" than one that doesn't play as loud. But is it representative of fidelity? To make fair comparisons, you'd test two different systems at the same volume. Otherwise it's apples and oranges. I don't remember ever reading any review in a stereo magazine that didn't ensure that was the case.
And before you say I'm now contradicting myself, when I initially wrote "louder != better", I meant it's not a valid comparison if you're trying to make one.
Otherwise I have crappy speakers I could sell... 
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When you listen to music, the subjective experience is what counts.
When you listen to the stereo system, the subjective experience must yield to measurements and specs.
People crank up the sound level in their cars to make the music sound better. Subjectively. Of course it is also to impress the girls, "Mine is bigger than his". But even at listening levels that doesn't blow your eardrums out, if raising the level a little bit improves your listening experience I see no essential reason not to. (Except possibly for the neighbors.)
There is a large overlap between HiFi buffs and fidelity buffs. The former tend to judge the sound by the manufacturer label on each component, the latter look at their meters and analyzers. For several decades I have kept a collection of about 30 sound clip, almost all music of various acoustical character. These I have compressed (in some cases distorted in other ways), and converted back to .wav format. The original and the compressed-expanded files have been given a random numeric suffix to the name; I have to look up in my written notes which suffix is the HE-AAC 48 kbps, which is MP3 128 kbps and so on. I have handed out the collection to a large number of people along with an ABX program that logs the listener's guesses to whether the X alternative is identical to A or to B. Not a single person has dared to return those log to me as a proof that they can distinguish the two alternatives.
But at least two listeners have come back to me with a file they have generated by subtracting the two alternatives (original and MP3), cranking up the level by 60 dB (my amp doesn't go from 0 to 10 but from -80 dB to 0 dB), proudly declaring: There! You can hear for yourself that MP3 takes away some of the music! ... As if that was a big secret. It takes away what is masked by other sounds, those we hear. The removed part is what we won't hear, as proven by the fact that the listener was unable to hear the difference in the ABX setup. But his technical equipment proved to him that he is right it rejecting MP3 as a format suitable for music. (Several others have argued along the same lines, but I remember only two coming to me with 'diff' files to prove their point.)
The sound quality was 'good enough' for everybody since some time in the 1980s. SACD, 96 kHz and 24 bits didn't make it in the marketplace; people didn't hear any difference. You can blame the music, but people do not change their musical taste just to make SACD justified  (I know of only one single case of that: Thirty years ago, every MP3 hater had one single record, encoded in MP3 format, with a lot of castanets, for the single purpose of showing others how much the castanet sound was ruined by MP3 encoding. Other that that, they never listen to Spanish flamenco, but it serves as their final proof that MP3 is useless.)
For the fidelity part: 4+ channel sound can add enormously to the fidelity. Movie makers know. Yet, people are satisfied with without it, for their plain music listening. For the small fraction of sound records made with multi-channel sound, a major part has ruined it by making you feel like you are sitting in the middle of the orchestra, not in the middle of a top rate orchestra hall. So for all practical purposes, 4+ ch sound died out, together with 96/24.
Stated briefly: "Fidelity" hasn't been a sales point for 25 years. It is purely a measurement & analysis concept.
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trønderen wrote: When you listen to music, the subjective experience is what counts.
Fair enough.
trønderen wrote: People crank up the sound level in their cars to make the music sound better.
...and to drown out the engine and wind noises, etc.
trønderen wrote: Stated briefly: "Fidelity" hasn't been a sales point for 25 years. It is purely a measurement & analysis concept.
I'm not gonna disagree with anything you wrote. 
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Have you ever priced audiophile USB cables? It's one of the best giggles out there  .
Software Zen: delete this;
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I have talked with HiFi buffs who stay awake through the night to listen to music on their systems, because "The electric power has higher quality after midnight, more stable voltage and less electric noise".
Also, I have an old HiFi catalog where a power cable (i.e. to the wall outlet) is offered at NOK 23,999 - almost USD 2500. (The catalog is about 15 years old. At that time, NOK was much stronger, so the amount would be USD 4500. You may add 50% inflation to that.)
The people selling stuff like that, at those prices, either truly believe in it themselves, or they are extremely good actors (/salesmen). To me it seems like they actually do believe.
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With those prices, maybe it's time for a career change!
"the debugger doesn't tell me anything because this code compiles just fine" - random QA comment
"Facebook is where you tell lies to your friends. Twitter is where you tell the truth to strangers." - chriselst
"I don't drink any more... then again, I don't drink any less." - Mike Mullikins uncle
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BillWoodruff wrote: what do you expect to see if you watch ?
People who do not trust M$.
Bastard Programmer from Hell 
"If you just follow the bacon Eddy, wherever it leads you, then you won't have to think about politics." -- Some Bell.
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BillWoodruff wrote: as a former paid up apple fanbois, twenty years ago,
What happened? I thought they went after those who tried to leave the religion, much like scientologists...(oops, did I say that out loud?)
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skipped it nothing much these days...
Caveat Emptor.
"Progress doesn't come from early risers – progress is made by lazy men looking for easier ways to do things." Lazarus Long
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