<div dir="ltr"><br><br><div class="gmail_quote"><div dir="ltr">On Tue, Aug 21, 2018 at 11:35 AM William Flynn Wallace <<a href="mailto:foozler83@gmail.com">foozler83@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-family:"comic sans ms",sans-serif;font-size:small;color:rgb(0,0,0)">what does 'arbitrarily small' mean? bill w</div></div></blockquote><div><br></div><div><br></div><div>Take whatever the error rate of copying a single bit is. For a modern hard drive, it is in the neighborhood of 10^-15.</div><div><br></div><div>Roughly speaking, for every 2N bits of redundancy applied to some string of bits (which can be arbitrarily large), you can tolerate up to N corrupted bits in that string. So let's say you have a file that is 1,000,000 bits long, the probability that no bits will be corrupt is:</div><div><br></div><div>(1 - 10^-15)^1,000,000 = 0.999999999</div><div> </div><div>Which is already pretty high, but we can make it arbitrarily high. For example, by adding 2 redundant bits, we can ensure that even if 1 bit is corrupt we can fix it, which means we would need not 1 corruption, but 2 corruptions. Which would almost double the number of "nines" (an exponential increase) for an incremental cost of 2 additional bits. If we want to tolerate 5 corruptions, this requires 10 extra bits, but now you are into truly astronomically low unrecoverable error rates.</div><div><br></div><div>Jason</div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Aug 21, 2018 at 11:14 AM, John Clark <span dir="ltr"><<a href="mailto:johnkclark@gmail.com" target="_blank">johnkclark@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-family:arial,helvetica,sans-serif"><br></div><div class="gmail_extra"><span><br><div class="gmail_quote">On Mon, Aug 20, 2018 at 5:25 PM, William Flynn Wallace <span dir="ltr"><<a href="mailto:foozler83@gmail.com" target="_blank">foozler83@gmail.com</a>></span> wrote:</div></span><div class="gmail_quote"><span><br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-family:"comic sans ms",sans-serif;font-size:small;color:rgb(0,0,0)"><div style="font-family:arial,helvetica,sans-serif;display:inline">> </div>No computer expert here, but I have been told that my Windows software corrupts itself over a period of time, and so would up and downloads. </div></div></blockquote><div><br></div></span><font size="4">Every time a computer copies a file there is a chance a error will be made, however in 1948 Claud Shannon showed us a clever way to make the error rate arbitrarily small by injecting a modest but carefully placed amount of redundancy into the file. Without this brilliant insight there is no way the Internet that we know and love today could exist.</font></div><div class="gmail_quote"><font size="4"><br></font></div><div class="gmail_quote"><font size="4"><div style="font-family:arial,helvetica,sans-serif;display:inline"> John K Clark</div><br></font><div><br></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="gmail-m_1967617351710298777m_-5397603513541489075gmail-HOEnZb"><div class="gmail-m_1967617351710298777m_-5397603513541489075gmail-h5"><div class="gmail_extra"><div class="gmail_quote"><div class="gmail-m_1967617351710298777m_-5397603513541489075gmail-m_7115062867003712861HOEnZb"><div class="gmail-m_1967617351710298777m_-5397603513541489075gmail-m_7115062867003712861h5"><br></div></div></div></div></div></div></blockquote></div><br></div></div>
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