Spearker cables..fact or fiction?

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  • AudioGenics
    AudioGenics Posts: 2,567
    edited March 2009
    Question: Are they any dependencies to a superior cable ?
  • AudioGenics
    AudioGenics Posts: 2,567
    edited March 2009
    Question : What are the limitations placed on a superior cable
  • AudioGenics
    AudioGenics Posts: 2,567
    edited March 2009
    Question : Do we compare different materials in the construction of a superior cable ?
  • cnh
    cnh Posts: 13,284
    edited March 2009
    You do realize that Chen is 'joking', right! Pulling your leg?

    cnh
    Currently orbiting Bowie's Blackstar.!

    Polk Lsi-7s, Def Tech 8" sub, HK 3490, HK HD 990 (CDP/DAC), AKG Q701s
    [sig. changed on a monthly basis as I rotate in and out of my stash]
  • inspiredsports
    inspiredsports Posts: 5,501
    edited March 2009
    Question : Do we compare different materials in the construction of a superior cable ?

    I just bought 700 Oral-B rectal thermometers from K-Mart, broke them open and drained the mercury into a rubber hose, jammed some bananas into ends and replaced my old Cat 5 super cables. I can't tell if it's the brain damage or the new OralBrect's, but man do my SDA's sound hot!
    VTL ST50 w/mods / RCA6L6GC / TlfnknECC801S
    Conrad Johnson PV-5 w/mods
    TT Conrad Johnson Sonographe SG3 Oak / Sumiko LMT / Grado Woodbody Platinum / Sumiko PIB2 / The Clamp
    Musical Fidelity A1 CDPro/ Bada DD-22 Tube CDP / Conrad Johnson SD-22 CDP
    Tuners w/mods Kenwood KT5020 / Fisher KM60
    MF x-DAC V8, HAInfo NG27
    Herbies Ti-9 / Vibrapods / MIT Shotgun AC1 IEC's / MIT Shotgun 2 IC's / MIT Shotgun 2 Speaker Cables
    PS Audio Cryo / PowerPort Premium Outlets / Exact Power EP15A Conditioner
    Walnut SDA 2B TL /Oak SDA SRS II TL (Sonicaps/Mills/Cardas/Custom SDA ICs / Dynamat Extreme / Larry's Rings/ FSB-2 Spikes
    NAD SS rigs w/mods
    GIK panels
  • F1nut
    F1nut Posts: 50,566
    edited March 2009
    keiko wrote: »
    i put japan victor corp. In davey jones locker with c3p0 and calypso 5 pages ago. ;)

    lol.....
    Political Correctness'.........defined

    "A doctrine fostered by a delusional, illogical minority and rabidly promoted by an unscrupulous mainstream media, which holds forth the proposition that it is entirely possible to pick up a t-u-r-d by the clean end."


    President of Club Polk

  • comfortablycurt
    comfortablycurt Posts: 6,745
    edited March 2009
    .... a game that we play with infinite loops....

    OK let us all together create a proof of "Speaker Cable Superiority"... NO FUN doing it Alone .....
    Question : Is a Speaker Cable better than another ?
    Question : What are the criteria of a better Cable ?
    Question : How is it determined that one Cable is superior ?
    Question : Is Price a consideration of a superior Cable ?
    Question: What is the value of a superior cable?
    Question: Are they any dependencies to a superior cable ?
    Question : What are the limitations placed on a superior cable
    Question : Do we compare different materials in the construction of a superior cable ?

    Ok...there are 9 posts that probably all could have been put into one.:rolleyes:
    The nirvana inducer-
    APC H10 Power Conditioner
    Marantz UD5005 universal player
    Parasound Halo P5 preamp
    Parasound HCA-1200II power amp
    PolkAudio LSi9's/PolkAudio SDA 2A's/PolkAudio Monitor 7A's
    Audioquest Speaker Cables and IC's
  • Kex
    Kex Posts: 5,194
    edited March 2009
    mdaudioguy wrote: »
    Interspersed between the bobt posts and the seafire posts are some of the craziest posts I've ever read.... Everybody should go back and read some of these gems from joseph.v.chen! I think everyone was so wrapped up in the seafire saga that hardly anyone even commented on these chen posts. He's clearly on a higher plane!

    What I'd really like to see here is some mathematical proof of the superiority of certain cables/spearker wires. How about it joseph.v.chen?:confused:

    P.S. You rock, dude!:)

    P.S.S. seafire - You're a pretty intriguing individual yourself. I'm glad you inserted yourself into this fray.;)
    This is one credo to which I, for one, will not be subscribing. I am beginning to think that I prefer bippity-bobt and Seafart to this individual. They, at the very least, contribute some humor (in a twisted sort of way), and limit themselves, for the most part, to a single disastrous thread rather than several.
    Alea jacta est!
  • comfortablycurt
    comfortablycurt Posts: 6,745
    edited March 2009
    Keiko wrote: »

    Curt, I'm sorry I called you a post ****. JVC gives a whole new meaning to that term. ;)

    Mike, I'll never forgive you. In fact, I've already taken my own course of action to get my revenge. You'll be receiving a package from me in the mail shortly.:p It has a pair of dirty Daisy Dukes in it...I figured you'd want them...lol


    Speaking of post whores...ole' Seabiscuits post per day rating was at almost 17 last night...lol...that's higher than even mines ever been!:eek:
    The nirvana inducer-
    APC H10 Power Conditioner
    Marantz UD5005 universal player
    Parasound Halo P5 preamp
    Parasound HCA-1200II power amp
    PolkAudio LSi9's/PolkAudio SDA 2A's/PolkAudio Monitor 7A's
    Audioquest Speaker Cables and IC's
  • SuperG
    SuperG Posts: 34
    edited March 2009
    Ok...there are 9 posts that probably all could have been put into one.:rolleyes:

    Unrelated question, how do you add more than one quote in your reply? :confused:

    Since this thread is totally useless, I really don't mind highjackin it. :p:p:p
  • hearingimpared
    hearingimpared Posts: 21,137
    edited March 2009
    You just did it.
  • SuperG
    SuperG Posts: 34
    edited March 2009
    SuperG wrote: »
    Unrelated question, how do you add more than one quote in your reply? :confused:

    Since this thread is totally useless, I really don't mind highjackin it. :p:p:p
    You just did it.


    OK just figured it out...
  • ment
    ment Posts: 13
    edited March 2009
    just my own thought ...

    at first i was swimming in this idea of a good quality speaker wire .... but then it hit me ..... what would be the point of using grade A speaker wires from amp to speaker terminal when i wont upgrade the speaker wires used INSIDE the speaker ......

    go ahead and use the best speaker wire you can afford only if i upgraded the wires inside the speakers.... so i told myself....

    i love generic #16 wires from then on :D
  • tonyb
    tonyb Posts: 32,967
    edited March 2009
    This thread is a perfect example of why the death penalty should stay.
    HT SYSTEM-
    Sony 850c 4k
    Pioneer elite vhx 21
    Sony 4k BRP
    SVS SB-2000
    Polk Sig. 20's
    Polk FX500 surrounds

    Cables-
    Acoustic zen Satori speaker cables
    Acoustic zen Matrix 2 IC's
    Wireworld eclipse 7 ic's
    Audio metallurgy ga-o digital cable

    Kitchen

    Sonos zp90
    Grant Fidelity tube dac
    B&k 1420
    lsi 9's
  • AudioGenics
    AudioGenics Posts: 2,567
    edited March 2009
    # About Keiko

    Biography
    Which life?
    Location
    Andromeda
    Interests
    Midgets and Curly Fries
    Occupation
    Mental Patient

    # Signature

    Yeah, fairies wear boots and you gotta believe me.
    I saw it, I saw it with my own two eyes
  • AudioGenics
    AudioGenics Posts: 2,567
    edited March 2009
    KEIKO'S STORY: THE TIMELINE

    This is the story of how a two-year-old orca whale began an amazing journey that has spanned five countries and tens of thousands of miles.




    1977 or 1978:


    Keiko is born in the Atlantic Ocean near Iceland.


    1979:

    Keiko is captured by a fishing boat, separated from his family, and held in an Icelandic aquarium.


    1982:

    Marineland in Ontario, Canada buys Keiko, where he becomes a performing animal.


    1985:

    Marineland sells Keiko to Reino Aventura, an amusement park in Mexico City, for $350,000.


    1992:

    Warner Bros. Studios begins filming the movie "Free Willy" on location in Mexico City. The plot involves a young boy saving a whale, portrayed by Keiko.


    1993:

    Free Willy is a surprise hit at the theaters, especially with millions of school children around the world. That support, along with media coverage detailing Keiko's unacceptable living conditions in Mexico City, prompts the movie studio, the park, and animal protection advocates to find Keiko a new home. Dr. Lanny Cornell comes on board as Keiko's lead veterinarian.


    1994:

    Earth Island Institute, an environmental advocacy group for marine wildlife, begins the search for a location where Keiko can be brought back to health and trained for potential release to the wild. The Free Willy Foundation is formed in November with a $4 million donation from Warner Bros., and an anonymous donor.


    1995:

    The Mexico City amusement park donates Keiko to the Free Willy/Keiko Foundation. The foundation announces Keiko will be moved to a new, $7.3 million rehabilitation facility at the Oregon Coast Aquarium. Craig McCaw is revealed as the anonymous donors of $2 million, which helped start the Free Willy/Keiko Foundation. The Humane Society of the United States also becomes a sponsor.


    1996:

    United Parcel Service sponsors the airlifting of Keiko to the aquarium on January 7. Weighing just 7,720 pounds, Keiko is placed in his new pool and experiences natural sea water for the first time in 14 years. Keiko gains more than 1,000 pounds, and by year's end his skin lesions begin to heal. Keiko is featured on the cover of Life Magazine and in a popular documentary, The Free Willy Story, on the Discovery Channel. More than 2 million visitors come to see Keiko in Oregon.


    1997:

    Keiko's staff begins introducing him to live fish in an effort to teach him to hunt for food. His skin lesions have all disappeared and he is determined to be in excellent health. He catches and eats his first live fish in August. By June, Keiko weighs 9,620 pounds. The staff of the Free Willy/Keiko Foundation sets a goal of releasing Keiko into a pen in the North Atlantic by 1998. After an intensive search and negotiations with foreign governments the decision is made to reintroduce Keiko to the wild in Iceland.


    1998:

    A medical panel determines that Keiko is healthy and exhibiting the normal behavior patterns of a killer whale. Keiko is eating live steelhead weighing from three to 12 pounds each, comprising up to half of his daily intake of food. On September 9, Keiko is lifted from his tank and transported by a US Airforce C-17 transport jet from Newport directly to Klettsvik Bay in Vestmannaeyjar, Iceland.


    1999:

    During his first full year back in his native Icelandic waters, Keiko, now under the day-to-day care of the Ocean Futures Society, continues training to prepare him for his potential reintroduction to the wild. An essential component of his program is moving his attention from above to below the surface of the water. In doing so, Keiko depends less on his human caretakers and develops greater interest in his natural environment.


    2000:

    Keiko is fitted for a tracking device that will allow staff to take him out to the open ocean. Keiko makes amazing progress during his sea "walks," even beginning to interact with wild orcas in the vicinity of his sea pen. His health and stamina improves as he comes closer to returning to his wild ways.


    2001:

    Early in the year, Keiko exhibits behaviors consistent with wild whales-competing with other animals for food. Keiko begins initiating contact with wild orcas in the vicinity and spends several days away from his human companions. The primary challenge ahead is for Keiko to begin maintaining himself on wild fish and regularly associating with wild orcas.


    2002:

    On his first day out of the netted bay pen in the summer of 2002, Keiko leaves the tracking boat and begins spending considerable time in the company of whales. He is monitored in and around groups of wild whales for the next three weeks. He then begins an epic journey covering nearly 1000 miles across the North Atlantic, by the Faeroe Islands, and to the coast of Norway.

    The first observations of Keiko in Norway document that he is in excellent physical condition. Keiko has been on his own for close to 60 days without food from humans. His lead veterinarian, and a variety of other orca scientists, come to the conclusion that Keiko has successfully fed himself in the wild, a major milestone in his journey to the wild.

    Keiko follows a fishing boat inside a Norwegian fjord in the Halsa Community. He is an instant hit there with people coming from throughout Europe. Thousands of visitors come to see the friendly whale. The Project staff work closely with the Norwegian government to put in place regulations to keep people from swimming with, feeding, or getting too close to Keiko.

    Meanwhile, the Craig McCaw Foundation and Ocean Futures Society turn over the management of the project to the Free Willy Keiko Foundation and the Humane Society of the U.S.

    In December Keiko is walked to the Taknes bay staff continue to work with and feed Keiko. For the first time ever, Keiko is in an area where he can come and go as he chooses. The Free Willy Keiko Foundation and the Humane Society of the US continue to care for Keiko while allowing his historic journey to the wild to move ahead.

    The Norwegian government gives its full support to the continued effort to give Keiko the chance to return to the wild.


    2003:

    December 12, 2003 -- The Free Willy Keiko Foundation and The Humane Society of the United States (HSUS) reported today that Keiko, the orca whale, died today in the Taknes fjord, Norway, in the company of staff members who have been caring for him there.

    Keiko's veterinarian believes that acute pneumonia is the most likely cause of death, though he also cited that Keiko was the second oldest male orca whale ever to have been in captivity.

    The two organizations managing Keiko's reintroduction effort expressed sadness at Keiko's death while also heralding his amazing journey.

    Yesterday, Keiko exhibited signs of lethargy and lack of appetite. Consultation was continuous between his caretakers and Dr. Cornell. His behavior was still abnormal this morning and his respiratory rate was irregular, but, as is often the case with whales and dolphins in human care, these were advanced signs of his condition. With little warning, Keiko beached himself and died in the early evening local time. A decade ago, Keiko was featured in the Hollywood movie, Free Willy, prompting a worldwide effort to rescue him from poor health, in an attempt to allow him to be the first orca whale ever returned to the wild.

    In 1996 Keiko was flown aboard a United Parcel Service plane to a new rehabilitation facility in Newport, Oregon. There he was returned to health and trained in the skills necessary to be a wild whale. In late 1998, Keiko was flown in a U.S. Air Force jet to a sea-pen in Iceland. In the summer of 2002, Keiko joined the company of wild whales and swam nearly 1000 miles to the Norwegian coast. Since then, Keiko has been cared for in a fjord where he was free to come and go by his own choice.

    Keiko inspired millions of children to get involved in following his amazing odyssey and helping other whales. Keiko's journey also inspired a massive educational effort around the world and formed the basis for several scientific studies. Thousands of people traveled to Norway in the past year to see Keiko, continuing his legacy as the most famous whale in the world.



    Get Your Keiko Adoption Kit Today!

    Become a Member Today!
  • treitz3
    treitz3 Posts: 19,033
    edited March 2009
    STFU already and then get a life. WTF is it with some of these new members?
    ~ In search of accurate reproduction of music. Real sound is my reference and while perfection may not be attainable? If I chase it, I might just catch excellence. ~
  • mdaudioguy
    mdaudioguy Posts: 5,165
    edited March 2009
    Keiko wrote: »
    I put Japan Victor Corp. in Davey Jones locker with C3P0 and Calypso 5 pages ago. ;)
    cnh wrote: »
    You do realize that Chen is 'joking', right! Pulling your leg?

    cnh
    Kex wrote: »
    This is one credo to which I, for one, will not be subscribing. I am beginning to think that I prefer bippity-bobt and Seafart to this individual. They, at the very least, contribute some humor (in a twisted sort of way), and limit themselves, for the most part, to a single disastrous thread rather than several.

    Yes... however, his posts have a certain randomness that kind of amuses me... which possibly means that I'm the crazy one.:eek::confused:(EDIT: Ok, that last, long post was perhaps a tad annoying.) Perhaps it's because I started with JVC components in 1982... good stuff.;)

    With the potential for getting slammed by asking a question too directly related to the original topic... What are some of the mid-priced IC cables that I could consider trying, AND is there any way to judge the effect of a particular cable before trying it? I really can't afford the higher $$ ICs, but am interested in upgrading my radio shack specials.
  • mdaudioguy
    mdaudioguy Posts: 5,165
    edited March 2009
    Hmm.. I just noticed that the Similar Threads list at the bottom of the page includes an older thread about spearkers...
  • tonyb
    tonyb Posts: 32,967
    edited March 2009
    treitz3 wrote: »
    STFU already and then get a life. WTF is it with some of these new members?


    Ahmen to that......and they wonder why they get picked on?
    HT SYSTEM-
    Sony 850c 4k
    Pioneer elite vhx 21
    Sony 4k BRP
    SVS SB-2000
    Polk Sig. 20's
    Polk FX500 surrounds

    Cables-
    Acoustic zen Satori speaker cables
    Acoustic zen Matrix 2 IC's
    Wireworld eclipse 7 ic's
    Audio metallurgy ga-o digital cable

    Kitchen

    Sonos zp90
    Grant Fidelity tube dac
    B&k 1420
    lsi 9's
  • Fongolio
    Fongolio Posts: 3,516
    edited March 2009
    This thread's got more chen's than a Chinese phonebook!
    SDA-1C (full mods)
    Carver TFM-55
    NAD 1130 Pre-amp
    Rega Planar 3 TT/Shelter 501 MkII
    The Clamp
    Revox A77 Mk IV Dolby reel to reel
    Thorens TD160/Mission 774 arm/Stanton 881S Shibata
    Nakamichi CR7 Cassette Deck
    Rotel RCD-855 with modified tube output stage
    Cambridge Audio DACmagic Plus
    ADC Soundshaper 3 EQ
    Ben's IC's
    Nitty Gritty 1.5FI RCM
  • AudioGenics
    AudioGenics Posts: 2,567
    edited March 2009
    The Fongolio chimps of Senegal will break off a branch, sharpen it with their teeth, and use it to hunt bush babies. That's just one of the recent discoveries that underscore the ape-human connection.

    DAYBREAK IS SUDDEN and swift, as though an unseen hand had simply reached out and raised a dimmer switch. Cued by the dawn, thirty-four chimpanzees awaken. They are still in the nests they built the previous night, in trees at the edge of an open plateau.

    A wild chimpanzee does not get out of bed quietly. Chimps wake up hollering. There are technical names for what I'm hearing—pant-hoots, pant-barks, screams, hoos—but to a newcomer's ear, it's just a crazy, exuberant, escalating racket. You can't listen without grinning.

    These are not chimps you've seen in these pages before. They're savanna-woodland chimps, found in eastern Senegal and across the border in western Mali. Unlike their better-known rain forest kin, savanna-woodland chimps spend most of their day on the ground. There is no canopy here. The trees are low and grow sparsely. It's an environment very much like the open, scratchy terrain where early humans evolved. For this reason, chimpanzee communities like the Fongoli group—named for a stream that runs through its range—are uniquely valuable to scientists who study the origins of our species.

    By 8 a.m. my chintzy key-chain thermometer says it's 90 degrees. Our shirts are marked by the same white salt lines that appear on people's boots in winter. Here it's salt from sweat. The plateau we're crossing is a terrain of nothing, of red rocks and skin cancer, with no trees to break the fall of equatorial sun. In our backpacks we each carry three liters of water. It was cool when we set out. By noon it will be hot enough to steep tea.

    I'm not complaining. I'm making a point. Life on the savanna—even so-called mosaic savanna, tempered by patches of lusher gallery forest along the streambeds—is exceptionally harsh. If you are a primate used to greener terrain, you must adjust your behavior to survive. Our earliest hominin (meaning bipedal ape) ancestors evolved more than five million years ago during the Miocene, an epoch of extreme drying that saw the creation of vast tracts of grassland. Tropical primates on the perimeter of their range no longer had plentiful fruits and year-round streams and lakes. They were forced to adapt, to range farther in their search for food and water, to take advantage of other resources. In short, to get creative.

    In 2007 Jill Pruetz, an anthropologist at Iowa State University, reported that a Fongoli female chimp named Tumbo was seen two years earlier, less than a mile from where we are right now, sharpening a branch with her teeth and wielding it like a spear. She used it to stab at a bush baby—a pocket-size, tree-dwelling nocturnal primate that springs from branch to branch like a grasshopper. Until that report, the regular making of tools for hunting and killing mammals had been considered uniquely human behavior. Over a span of 17 days at the start of the 2006 rainy season, Pruetz saw the chimps hunt bush babies 13 times. There were 18 sightings in 2007. It would appear the chimps are getting creative.

    There are individuals who are uncomfortable with Pruetz's tales of spear-wielding chimps, and not all of them are bush babies. Harvard professor of biological anthropology Richard Wrangham, who has studied chimpanzee aggression in Uganda's Kibale National Park, has been skeptical. Wrangham is widely known for his "demonic male" theory, which holds that the savage murders carried out by male chimps while policing their turf are suggestive of a violent nature at the core of man. Primatologist Craig Stanford, author of The Hunting Apes, also downplays the importance of Pruetz's findings. "This behavior is fascinating, but the observations are so preliminary that it merits only a short note in a journal."
  • hearingimpared
    hearingimpared Posts: 21,137
    edited March 2009
    If you would write something audio related it would be appreciated.
  • comfortablycurt
    comfortablycurt Posts: 6,745
    edited March 2009
    I think I'm done even paying attention to JVC's posts...they're exceedingly stupid.
    The nirvana inducer-
    APC H10 Power Conditioner
    Marantz UD5005 universal player
    Parasound Halo P5 preamp
    Parasound HCA-1200II power amp
    PolkAudio LSi9's/PolkAudio SDA 2A's/PolkAudio Monitor 7A's
    Audioquest Speaker Cables and IC's
  • AudioGenics
    AudioGenics Posts: 2,567
    edited March 2009
    If you would write something audio related it would be appreciated.
    OK...my little something about Audio....

    I was fortunate to meet and have dinner with a person named Doug Sax.

    He was an engineer for a very small record company called Sheffield Labs.

    He told me that he wanted to capture the essence of the artists' performance and preserve it a way that others may share.

    The Music was the central focus.

    You are either the performer or You are the audience.
    In the Master - which is directly cut - was the closest to the performer.

    Each subsequent copy or generation was degraded.

    We produced one recording that featured the Chicago Symphony players.... a small group of musicians that were members of the Chicago Symphony Orchestra.

    Mr Sax understood exactly what an audiophile preferred.
    He went on to explain the playback system that he built and designed.

    And yes I did see the speaker cables that was in use at the time......
  • hearingimpared
    hearingimpared Posts: 21,137
    edited March 2009
    . . . and they were . . . ?
  • AudioGenics
    AudioGenics Posts: 2,567
    edited March 2009
    Keiko wrote: »
    The ignore feature works great. You don't even see the post. Try it, you'll like it. ;)
    * About Keiko

    Biography
    Which life?
    Location
    Andromeda
    Interests
    Midgets and Curly Fries
    Occupation
    Mental Patient

    * Signature

    Yeah, fairies wear boots and you gotta believe me.
    I saw it, I saw it with my own two eyes.
  • comfortablycurt
    comfortablycurt Posts: 6,745
    edited March 2009
    Keiko wrote: »
    The ignore feature works great. You don't even see the post. Try it, you'll like it. ;)

    I'd been considering that...I was getting some amusement out of some of his posts for a while...but that seems to have went away. It's just nonsensical rambling that means absolutely nothing now.

    Welcome to the Ignore List JVC.:D
    The nirvana inducer-
    APC H10 Power Conditioner
    Marantz UD5005 universal player
    Parasound Halo P5 preamp
    Parasound HCA-1200II power amp
    PolkAudio LSi9's/PolkAudio SDA 2A's/PolkAudio Monitor 7A's
    Audioquest Speaker Cables and IC's
  • mrbigbluelight
    mrbigbluelight Posts: 9,730
    edited March 2009
    ......I can prove it..... FINALLY something that I Understand !!!

    8.1 Proof of Normal Equations

    We will assume that ATA is invertible. This is a reasonable assumption because there are more equations than unknowns. The length of the vector x is defined to be the lenght of the vector so the length of the vector squared is the length of the vector squared The square of the length of the vector Ax-b is the sum of the squares of the errors since each element of Ax - b is the error at a point. We want to minimize this quantity. We claim that the solution to the normal equations, which we will denote as x* = (ATA)-1ATb, minimizes the sum of the squares of the errors.

    We claim, and will prove, that

    ||Ax - b||2 = ||Ax* - b||2 + ||A (x - x*)||2.

    Since we are minimizing over x, ||Ax - b||2 will be minimized when x = x* so that ||A (x - x*)||2 is zero. This is true because ||A (x - x*)||2 can never be negative.

    To prove the claim, we will work with the right side of the equation and prove that it is equal to the left side. These equations are numbered. There are short explanations of these steps following the proof.
    = ||Ax* - b||2 + ||A (x - x*)||2 (1)
    = (Ax* - b)T (Ax* - b) + (A(x - x*))T A(x - x*) (2)
    = (A (ATA)-1ATb - b)T (A (ATA)-1ATb - b)T +
    (A(x - (ATA)-1ATb))T A(x - (ATA)-1ATb) (3)
    = (A (ATA)-1 ATb - b)T (A (ATA)-1 ATb - b) +
    (Ax - A (ATA)-1 ATb)T (Ax - A (ATA)-1 ATb) (4)
    = (bTA (ATA)-1 AT - bT) (A (ATA)-1 ATb - b) +
    (xTAT - bTA (ATA)-1 AT)(Ax - A (ATA)-1 ATb) (5)
    = (bTA (ATA)-1 ATA (ATA)-1ATb - 2bTA (ATA)-1ATb + bTb +
    (xTATAx - 2bTA (ATA)-1 ATAx + bTA (ATA)-1 ATA (ATA)-1ATb) (6)
    = (bTA (ATA)-1 ATb - 2bTA (ATA)-1 ATb + bTb) +
    (xTATAx - 2bTAx + bTA (ATA)-1 ATb) (7)
    = bTb + xTATAx - 2bTAx (8)

    Now, if we look at the left side of the equation, we can see that it equals the right side because
    ||Ax - b||2 = (Ax - b)T (Ax - b) = (xTAT - bT) (Ax - b) = xTATAx - 2bTAx + bTb.

    This proves that x = x* = (ATA)-1ATb uniquely minimizes the sum of the squares of the error for the equation Ax - b.

    The following are comments on the steps of the proof:

    1. This is the right hand side of the equation from the claim.

    2. ||y||2 = yTy

    3. Replace x* with (ATA)-1ATb.

    4. Distribute A in the second term.

    5. (M + N)T = MT + NT, (RS)T = STR T, and (A-1)T = (AT)-1

    6. Because each term is a vector and xTy = yTx, which can also be written as equations, we can multiply in a manner similar to polynomial multiplication. However, we must remember that matrix multiplication is not commutative, so the order of multiplication of the matrices matters.

    7. (ATA)-1(ATA) = I

    8. Combine like terms.



    Get to work on Fermat's Enigma, then you'll have really done something.
    Sal Palooza
  • AudioGenics
    AudioGenics Posts: 2,567
    edited March 2009
    Here is some more information that I just found on Sheffield Labs...

    Some more history. Sheffield Labs was the pioneer in the brief revival of direct to disc recordings. The story goes that Doug Sax and Lincoln Majorga, who founded Sheffield, found some old 78 records (which were all direct to disc, since they mostly were cut before tape recorders existed, but that's another story) and were astonished by how good they sounded. They then tried recording some direct to disc records, which audiophiles of the time snapped up, and this pushed some other small recording outfits such as Crystal Clear to do their own D to Ds.

    However, it didn't last for a number of reasons. First, if there were any mistakes the whole cut was blown, so musicians tended to play cautiously so as not to waste the take - hence the "great sound, so-so performance" reputation that D to D developed. Second, the groove spacing had to be varied "live" by the recording engineer to prevent grooves from cutting into each other if the musicians were playing loudly, or being spaced too wide apart during soft passages, thus wasting valuable space and limiting the duration of music that could be recorded. If the engineer made a mistake the whole side was blown. Third, since the recording went straight to the master lacquers, there were only a limited amount of records that could be generated from any take, dependent on how many record mastering machines were hooked up to the microphones. You couldn't go back and make more records for a popular title. However, the Sheffield Labs records that were released gained a reputation as some of the best sounding records ever made.

    The Mastering Lab (which was the recording cutting side of the business) for which Doug Sax was the recording engineer, also did record mastering for other record labels and earned an excellent reputation on that score.

    Another side to the Sheffield story that is not well publicized is an informal experiment that they did during some of the LA Philharmonic recording sessions, IIRC, where they compared digital recorders vs. analog recorders vs. direct to disc (using a blown lacquer as the direct to disc source) vw. live mike feed. This is something that very few audiophiles actually have a chance to experience. The results were written up in an issue of TAS, and the bottom line was that the digital recorder was felt to be the worst, and the direct to disc was felt by all the listeners to be closest to the live mike feed. Of note, the cartridge used in those informal experiments was the cartridge used by the Mastering Lab at that time as their standard cartridge - NOT some expensive audiophile approved moving coil, but a comparatively lowly Stanton 881S equalized (!) for flat response.
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