Error correcting codes

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Fault tolerance is important in distributed systems and in organizations.

Redundancy can be used to detect and correct errors (discrepancies).

Bar codes, ISBN, Credit card numbers, UPC, CRC checks, parity checks, etc.
Space shuttle: Four redundant computers with one backup (cross-checking 500 times a second).
Accounting (manual) method of casting out nines.
Masoretic Hebrew text copying rules.
Two (reliable) witnesses (at least) needed.

An understanding of FTC (Fault Tolerant Computing) techniques and that of an ECC (Error Correcting Code) are important in understanding the differences in various Bible texts.

The key to fault tolerance is redundancy. The simplest model is to use redundancy and take a majority vote of the various ways. There are many more advanced methods not discussed here.

More: Logical implications of inerrency

More: An errant look at Biblical inerrancy and infallibility

Any fault tolerant system needs to account for parts of the system (e.g., members) not operating properly or operating with motives against the organization or organizational goals (which might or might not be the same thing).

A code is a way to encode a language and is concerned not directly with meaning but with preserving the integrity of a message from source or sender to target or recipient.

An ECC is a code that contains redundancy in some form such that that redundancy can be used to detect and/or correct errors in the message from source to target.

The key idea is that controlled redundancy is added to detect and/or correct transmission errors.

[check digits, parity codes, Hamming codes, etc.]
[bar codes, credit card numbers]
[RAID (Redundant Array of Independent Disks)]

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Error detection and correction requires controlled redundancy.
Discuss: How does Hebrew use redundancy to allow error detection and correction? For example, in Psalms, Proverbs, etc. [sound bites]
Discuss: How does Jesus use redundancy to allow error detection and correction? For example, Matthew 15, Matthew 18, etc.

[TR (Textus Receptus), model breaking]

More: Matthew 15:1-21 Blind leading the blind

More: Matthew 17-18 The greatest little discourse

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If the bit in error is known, a single-bit error can be corrected.

Fault tolerance detection and correction at the bit level can be extended to a collection of drives each with a huge number bits.
Even parity will detect a one bit error and allow correction if the bit in error can be identified (e.g., a RAID).

Here are some acronyms and other terms.

ECC = Error Correcting Code.
BER = Bit Error Rate.
FEC = Forward Error Correction, or channel coding.
LDPC = Low Density Parity Check.
CRC = Cyclic Redundancy Check.
Repetition code
Block codes, convolutional codes
Reed-Solomon coding as often used in DVD (Digital Video Disk) encoding.
Hamming ECC as often used to correct NAND flash memory errors.

[copy-update problem, human-checked redundancy, computer-checked redundancy]

An ECC is customized for the physical reality in which it will be used.

The human DNA (Deoxyribonucleic Acid) code has many fault-tolerant and error correcting properties.
Human communication incorporates many fault-tolerant and error correcting properties.

Discuss: Why does the Bible text need to be viewed as a logical system that needs to be accurate or invariant in every aspect of the text in order for the underlying message to be clear?

[spell checker, backup system]
[teachers saying the same thing in different ways]

DNA has limited copy error correction at the lowest level (i.e., via other molecular copying engines). There are other error correction systems at higher levels (e.g., healing from a non-fatal injury).

A simple ECC for credit cards uses a check digit. One must scan or type again if an error is detected.
A simple ECC for DNA copying, if not correctable, requires that the copy be restarted.

One usually wants to be correct or right.

There are times when this may not be clear.

More: Matthew 18:15-17 Conflicting and faulty resolutions

Matthew 11:15 He that hath ears to hear, let him hear. [kjv]

ο εχων ωτα ακουετω [gnt]

Gather the facts and get them right. This may not be easy. If you pluck out your "eyes", would you be able to "see"? If, by extension, you pluck out your "ears", would you be able to "hear"? This is an example of a many-to-one relationship or association.

More: Song: Open my eyes that I may see

Story:

I was getting tired of getting the wife admitting that she had a hearing problem. Aside: A hearing problem, not a listening problem.
One day, I decided to gather proof with which to confront her (in love, of course).

Matthew 11:15

All

KJV: He that hath ears to hear, let him hear.

Greek: ο εχων ωτα ακουειν ακουετω

Latin: qui habet aures audiendi audiat

Wessex: se þe earan haebbe to geherene ge-hyre.

Wycliffe: He that hath eris of heryng, here he.

Tyndale: He yt hathe eares to heare let him heare.

Luther: Wer Ohren hat zu hören, der höre!

Coming home, I quietly opened the door. She was working quietly in the kitchen two rooms away. Just inside the door, I said softly, "Dear, can you hear me?".

No response. Just as I thought. A hearing issue.

I went to the next room and did the same thing again, softly. "Dear, can you hear me?".

No response. This is worse than I suspected. Now I had proof.

Finally, I got right outside the room she was in and said softly. "Dear, can you hear me?".

Finally, a response, as I heard her say, "For the third time, yes!".

Romans 8:31 What shall we then say to these things? If God be for us, who can be against us? [kjv]

τι ουν ερουμεν προς ταυτα ει ο θεος υπερ ημων τις καθ ημων [gnt]

Many use this verse as a "battle cry" or puffed-up-in-pride "badge of honor". Some pastors (and others) promote this misconception.
Sir, my concern is not whether God is on our side; my greatest concern is to be on God's side, for God is always right. Abraham Lincoln (16th U.S. President)

If God is the primary customer, then the customer is always right.

Man's "righteousness" is "what is right" as in an "opinion" that is the "glory" of man (humanism).
God's "righteousness" is "what is right" as in an "opinion" that is the "glory" of God (theism).

More: Romans 8: Battle cry separation for the love of Christ (part 1)

More: Abraham Lincoln

It is often said that 80% of security problems come from inside and not outside the organization.

A malicious insider is someone inside the company who is a non-cooperating user. This type of user is very dangerous because the entire system depends on cooperating users inside the system.

More: Inside security threats

There have been solutions found to various problems that involve ideas of fault tolerant computing or distributed decisions in the presence of incomplete information.

Suppose that two individuals want to use a coin flip to settle a dispute, but neither person trusts the other.

How would you use a (possibly biased) coin to perform the coin flip so that neither individual has an advantage?

John Von Neumann provided in interesting solution to this problem.

More: Sample space for a coin flip

The Ethernet network protocol was originally designed in the following way.

Each side can talk any time it wants.
Each side can detect if there is a collision in that someone else is trying to talk at the same time.
If a collision happens, both sides wait a random amount of time and then try again.

This helps resolve talking conflicts in a distributed and local manner without a global level of control - as long as all sides agree to the rules.

Ethernet is a CSMA/CD, for CSMA (Carrier sense multiple access) , CD (Collision detect) system.