[ExI] physics question

[Jason Resch]

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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