[ExI] physics question

[William Flynn Wallace]

No No No!!  Too much information!!!  Stop!!! Sorry I asked - will not do so
again!!
bill w

what does 'arbitrarily small' mean?  bill w
>


Take whatever the error rate of copying a single bit is.  For a modern hard
drive, it is in the neighborhood of 10^-15.

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:

(1 - 10^-15)^1,000,000 = 0.999999999

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.

Jason


On Tue, Aug 21, 2018 at 11:46 AM, Jason Resch <jasonresch at gmail.com> wrote:

>
>
> On Tue, Aug 21, 2018 at 11:35 AM William Flynn Wallace <
> foozler83 at gmail.com> wrote:
>
>> what does 'arbitrarily small' mean?  bill w
>>
>
>
> Take whatever the error rate of copying a single bit is.  For a modern
> hard drive, it is in the neighborhood of 10^-15.
>
> 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:
>
> (1 - 10^-15)^1,000,000 = 0.999999999
>
> 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.
>
> Jason
>
>
>> On Tue, Aug 21, 2018 at 11:14 AM, John Clark <johnkclark at gmail.com>
>> wrote:
>>
>>>
>>>
>>> On Mon, Aug 20, 2018 at 5:25 PM, William Flynn Wallace <
>>> foozler83 at gmail.com> wrote:
>>>
>>> >
>>>> 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.
>>>>
>>>
>>> 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.
>>>
>>>  John K Clark
>>>
>>>
>>>
>>>
>>>>
>>>>
>>>
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>>>
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