Son Ted, who teaches calculus and statistics, presented a puzzler over dinner one evening that goes something like this:
You know that information transmitted over the internet is in binary (digital) form, a series of Ones and Zeros.
Also that errors in transmission occur with some frequency.
What is the maximum error rate that can exist in terms of intelligibility?
That's the puzzle, and all that he tells you.
You have to figure it out from there.
***
So when a friend posted this on a hometown site that I visit, I sent it to Ted.
AN INTERESTING THING ABOUT THE HUMAN MIND...
Please do not delete this because it looks too weird to be readable.
Believe it or not, you really can read it!
I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdgnieg.
The phaonmneal pweor of the hmuan mnid. Aoccdrnig to a rscheearch at
Cmabrigde Uinervtisy, it deosn't mttaer inwaht oredr the ltteers in a
wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer
be in the rghit pclae. The rset can be a taotl mses and you can sitll
raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed
ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh? Yaeh and
I awlyas thought slpeling was ipmorantt.
Ted replied:
Now taht was isnertniteg. Smees lkie a ceevlr way to edocne a mgesase
taht a cmpoteur pagrrom clnudo't sacehr for.
-Tydde
To which I responded:
I bet that a cleverly written computer program could ferret such a coded message out over several iterations, esp. in light of letter frequency distributions in language, like more 'e's than 'z's.
I do think you should drop a rmesue fof ta na ancegy iretseenetd ni scuh tgnhis.
-Dda
Ted's response was cleverer than mine. His reply added unnecessary letters to inject confusion. He made sure to follow the rule of the item I sent him, which requires only that the first and last letters of each word remain in their proper places to remain intelligible. The friend's item that I sent him seems to allow the failure to insert a space between some words.
The correct answer to Ted's original puzzler is not a 100% error rate.
For if all of the ones and zeros were reversed in perfect order you'd have the same message in reverse with no errors. You might have to read the thing backwards or with a mirror or, more likely, turn each word and sentence around first.
The closer the error rate in transmission approaches 50% the more unreadable it becomes. We're all used to reading sentences with a minuscule spelling-error rate.
It might make a difference whether the encoded bit stream is read in a stream or presented whole after transmission is complete and re-ordered as words. I dunno about that, either, but I'd wonder about it.
I suppose that "errors in transmission" includes: accidentally, or on purpose, dropped letters, added letters, misplaced letters, transposed words, dropped word-spaces, and whatever other 'noise' may exist in a signal.
Signal-to-noise ratio, I believe this is called.
None of this is very difficult for me, I'd like to point out.
I read law student exam blue books when I have nothing better to do...
I do hope Teddy submits that resume to an agency interested in such things.
Odd how I didn't bother using the spell-checker on this post.
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