1381: "Margin"

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1381: "Margin"

Postby rhomboidal » Fri Jun 13, 2014 4:22 am UTC

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Title Text: PROTIP: You can get around the Shannon-Hartley limit by setting your font size to 0.

Fermat was ahead of his time in mathematical imagination. And internet trolling.

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Tharwen
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Re: 1381: "Margin"

Postby Tharwen » Fri Jun 13, 2014 4:49 am UTC

You don't have to actually do something to prove that you can do it, do you?
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da Doctah
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Re: 1381: "Margin"

Postby da Doctah » Fri Jun 13, 2014 5:02 am UTC

Tharwen wrote:You don't have to actually do something to prove that you can do it, do you?
Mathematics is full of cases where someone proves that something exists without actually identifying it. Invariably, this sort of thing infuriates non-mathematicians.

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Re: 1381: "Margin"

Postby Pfhorrest » Fri Jun 13, 2014 5:04 am UTC

I have discovered a truly marvelous proof that information is infinitely compressible, and when the expansion algorithm detailed in that proof is applied to this sentence it will output that proof.
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Re: 1381: "Margin"

Postby keithl » Fri Jun 13, 2014 5:28 am UTC

Title Text: PROTIP: You can get around the Shannon-Hartley limit by setting your font size to 0.

As the font size approaches 0, the quantum energy of the photons you need to read it becomes infinite.

Added note: The Planck length is 3.81779e-33 picas. Please include this as a limit check in your desktop publishing software, or your laser printer may collapse into a black hole.
Last edited by keithl on Fri Jun 13, 2014 5:42 am UTC, edited 3 times in total.

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Re: 1381: "Margin"

Postby Jorpho » Fri Jun 13, 2014 5:29 am UTC

Oh, my! I laughed louder at this than I have at an XKCD comic in quite some time.

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orthogon
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Re: 1381: "Margin"

Postby orthogon » Fri Jun 13, 2014 9:09 am UTC

Nice one. We needed something like this after the worthy but intractable subjects of Anthropogenic Global Warming, Evolution and Depleted Uranium Munitions. (To be fair that last one wasn't strictly Randall's fault).

I tried to combine this with "Too Much Information" but I got a NaN.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1381: "Margin"

Postby Xenomortis » Fri Jun 13, 2014 9:13 am UTC

Tharwen wrote:You don't have to actually do something to prove that you can do it, do you?

Not at all.
A proof of the existence of such a proof is sufficient.

And I think you can see where we're going with that.
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Re: 1381: "Margin"

Postby cellocgw » Fri Jun 13, 2014 11:30 am UTC

da Doctah wrote:
Tharwen wrote:You don't have to actually do something to prove that you can do it, do you?
Mathematics is full of cases where someone proves that something exists without actually identifying it. Invariably, this sort of thing infuriates non-mathematicians.


Heck, sometimes they prove both that it exists and that it can't be found (see Diophantine) :twisted:

someone else wrote: The Planck length is 3.81779e-33 picas.
<-- sigged.


And BTW, all information is infinitely compressible. - - - - - just not in a lossless manner. "I, for one," (TM) vote for infinite compression of all Celine Dion and Justin Bieber recordings.
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Re: 1381: "Margin"

Postby brandbarth » Fri Jun 13, 2014 11:41 am UTC

(1) Information is infinitely compressible
(2) Proof for (1) does not fit on the margin

If (2) is true, (1) must be false. If (1) is true, the information must fit on hanc marginem. Oder?

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Re: 1381: "Margin"

Postby pkcommando » Fri Jun 13, 2014 11:46 am UTC

Xenomortis wrote:
Tharwen wrote:You don't have to actually do something to prove that you can do it, do you?

Not at all.
A proof of the existence of such a proof is sufficient.

And I think you can see where we're going with that.

Jean Chrétien is a mathematical genius?
"A proof is a proof. What kind of a proof? It's a proof. A proof is a proof, and when you have a good proof, it's because it's proven.1"





1 - To all the Canadians on this board, both of you, you're welcome. :D

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Re: 1381: "Margin"

Postby orthogon » Fri Jun 13, 2014 12:14 pm UTC

cellocgw wrote:And BTW, all information is infinitely compressible. - - - - - just not in a lossless manner. "I, for one," (TM) vote for infinite compression of all Celine Dion and Justin Bieber recordings.

This is brilliant. Measured objectively, the resulting impairment is equal to the signal level, and yet in subjective tests the lossy compression would actually improve the score. (Bieber definitely fits the "Very Annoying" category on the MOS scale).
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1381: "Margin"

Postby pkcommando » Fri Jun 13, 2014 12:47 pm UTC

cellocgw wrote:And BTW, all information is infinitely compressible. - - - - - just not in a lossless manner. "I, for one," (TM) vote for infinite compression of all Celine Dion and Justin Bieber recordings.

Can we define compression as 'toss into a black hole'? And include the individuals as well?

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Re: 1381: "Margin"

Postby Carteeg_Struve » Fri Jun 13, 2014 12:52 pm UTC

When someone questions any theory you put into a margin, just be sure to stand Fermat.

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Re: 1381: "Margin"

Postby shon » Fri Jun 13, 2014 1:03 pm UTC

All information *is* infinitely compressible. You xor the first half of your data with the second half of your data, cutting your data size in half. Repeat until you're left with a single bit.

Don't ask me how to uncompress it; I don't know.

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Re: 1381: "Margin"

Postby orthogon » Fri Jun 13, 2014 1:25 pm UTC

shon wrote:All information *is* infinitely compressible. You xor the first half of your data with the second half of your data, cutting your data size in half. Repeat until you're left with a single bit.

Don't ask me how to uncompress it; I don't know.

Your method would still leave one bit of Bieberishness. You should go the final step and XOR it with itself to give zero.
Regarding the decompression: if your final bit is a 1, it means that there was definitely a 1 somewhere in the original data. If it's a zero, then there might not have been. This should allow you to construct the original sequence with a bit error rate less than 0.5. One problem is that you don't know the sequence length, except that it has to be a power of two for your method as described.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1381: "Margin"

Postby Xenomortis » Fri Jun 13, 2014 1:50 pm UTC

What if you have an odd number of bits?
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Re: 1381: "Margin"

Postby richP » Fri Jun 13, 2014 2:15 pm UTC

Xenomortis wrote:What if you have an odd number of bits?

Use the middle one. :roll:

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Re: 1381: "Margin"

Postby orthogon » Fri Jun 13, 2014 2:31 pm UTC

Xenomortis wrote:What if you have an odd number of bits?

I believe shon's method as originally stated is only defined when the input length N is a power of two. However, in such cases it is equivalent to d0 XOR d1 XOR d2 XOR ... XOR dN-1 since XORing (=modulo-2 addition) is commutative and associative. When expressed in this form, it is easy to generalise to any N.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1381: "Margin"

Postby Coyoty » Fri Jun 13, 2014 2:37 pm UTC

I said FORMAT your document!

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Re: 1381: "Margin"

Postby Scur » Fri Jun 13, 2014 2:46 pm UTC

You could do this with a single mark in the margin and bring the info back again, assuming you can make exact measurements. Convert all the info into ASCII, put a decimal point at the beginning, convert it into a fraction, and make a mark dividing the height of the page at the distance equal to the fraction. Bing, bang, boom, measure and convert back into decimal form to decompress.

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Re: 1381: "Margin"

Postby jpvlsmv » Fri Jun 13, 2014 3:51 pm UTC

Carteeg_Struve wrote:When someone questions any theory you put into a margin, just be sure to stand Fermat.

Ah, the internet in a nutshell[1]...

"When challenged, stand Fermat your marginal theories"

--Joe
[1] Warning: may contain nuts. Or the nuts might not be contained.

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Re: 1381: "Margin"

Postby cellocgw » Fri Jun 13, 2014 4:00 pm UTC

jpvlsmv wrote:
Carteeg_Struve wrote:When someone questions any theory you put into a margin, just be sure to stand Fermat.

Ah, the internet in a nutshell[1]...

"When challenged, stand Fermat your marginal theories"

--Joe
[1] Warning: may contain nuts. Or the nuts might not be contained.


Alternatively, to avoid any shocking events , be sure to.. Ground Your Stand.
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Re: 1381: "Margin"

Postby FrobozzWizard » Fri Jun 13, 2014 4:05 pm UTC

pkcommando wrote:Jean Chrétien is a mathematical genius?
"A proof is a proof. What kind of a proof? It's a proof. A proof is a proof, and when you have a good proof, it's because it's proven.1"



Of course he's a mathematical genius. For example, his in-depth examination of pi:
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Re: 1381: "Margin"

Postby alanbbent » Fri Jun 13, 2014 4:09 pm UTC

orthogon wrote:(Bieber definitely fits the "Very Annoying" category on the MOS scale).


That's a pretty Mean Opinion.

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Re: 1381: "Margin"

Postby Pfhorrest » Fri Jun 13, 2014 5:31 pm UTC

This reminds me a bit of a quote from a friend of mine, abridged:

Someone else: Anyone got an opinion for what currently passes for a typic top and bottom page margin in a paper?
My friend: well math papers are all a single column
My friend: pages become unbearable if dont leave gracious space
My friend: plus there is a "never again" attitude after that whole fermat's last theorem thing
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Re: 1381: "Margin"

Postby Envelope Generator » Fri Jun 13, 2014 5:35 pm UTC

That was even funnier than the strip!
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Re: 1381: "Margin"

Postby da Doctah » Fri Jun 13, 2014 8:36 pm UTC

cellocgw wrote:Alternatively, to avoid any shocking events , be sure to.. Ground Your Stand.


Die Carpem - Daze the sea!

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Re: 1381: "Margin"

Postby Brian-M » Sun Jun 15, 2014 2:28 am UTC

Pretending to take the comic seriously for a moment...

In order for a compression method to be useful (regardless of whether or not it refers to infinite compression) the process of recovering the original information must be known. Since the person reading the margin comment doesn't know the method for recovering the information, the explanation must be given uncompressed... and so might not fit into the margin even if it were true.

Infinitely compressible doesn't necessarily mean compressible to an infinitely small size. It could mean being able compress an unlimited amount of information into a finite area. This area doesn't have to be small enough to fit into a margin.

Here's my "proof" of the infinitely compressible nature of information by description of a "practical" compression method which would allow unlimited information to be expressed as an 76-digit hexadecimal value...

Step one: divide the information into n blocks of no more than 65462 bytes.
Step two: Let X = n
Step three: Express the MD5, SHA-1 and a 16 bit value indicating the length of block X as an ASCII hexadecimal string
Step four: Let X = X - 1
Step five: Append current hexadecimal string to block X.
Step six: If X > 1 then goto Step three
Step seven: Output current hexadecimal string.

This outputs a 76-digit hexadecimal value representing the first block.

To recover the information, go through every possible combination of data with the length described by the 16-bit length value and throw away any combination that doesn't produce the right MD5 and SHA-1 values. Then throw away any remaining combination that's just meaningless gibberish.

This will leave you with the first block of the data, along with 76 bytes describing the next block.

Then you take the 76-digit hexadecimal code describing the next block and repeat the process until all the blocks are recovered.

This will let you encode potentially infinite information in only 76 bytes, proving that information is infinitely compressible.

Unfortunately, this process has two flaws...

Firstly, you'll end up with lots of false positives, so not only will you end up with the information you started with, you'll also end up with lots of information that never existed before, and you may not be able to tell which information is the information that was originally encoded.

Secondly, it'll take an absurdly long time to extract even a tiny amount of information this way. You don't want to have to dedicate the resources of a million supercomputers for a billion years just to decode a 30-second MP3 file.

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Re: 1381: "Margin"

Postby JustDoug » Sun Jun 15, 2014 11:51 am UTC

brandbarth wrote:(1) Information is infinitely compressible
(2) Proof for (1) does not fit on the margin

If (2) is true, (1) must be false. If (1) is true, the information must fit on hanc marginem. Oder?


Not necessarily. The infomation might compress just fine, while the proof requires several volumes to eludicate properly.

SEE: Poincaré conjecture for example.

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Re: 1381: "Margin"

Postby Envelope Generator » Sun Jun 15, 2014 2:02 pm UTC

JustDoug wrote:
brandbarth wrote:(1) Information is infinitely compressible
(2) Proof for (1) does not fit on the margin

If (2) is true, (1) must be false. If (1) is true, the information must fit on hanc marginem. Oder?


Not necessarily. The infomation might compress just fine, while the proof requires several volumes to eludicate properly.


(1) and (2) can be true at the same time as long as the proof is not information.
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Re: 1381: "Margin"

Postby gmalivuk » Sun Jun 15, 2014 4:07 pm UTC

Yeah but the proof is information. It's just that it's information you'll want to present in its uncompressed form for anyone to be able to read it.
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Re: 1381: "Margin"

Postby rmsgrey » Sun Jun 15, 2014 6:01 pm UTC

The requirement to be able to decompress the information is why you need to consider the size of the decompression routine when talking about compressing information.

It's easy to write a custom decompression routine that turns the empty input into the complete works of Shakespeare:

If (input=="") output = File.Read("Shakespeare.txt");

It's the same as the incredible wonder of the scientific age - dehydrated water - just add water to bring it to any quantity desired!

The trouble is that, while the compressed data is, literally, 0 size, the decompression routine (including the external text file) is the size of the original text (plus a little) - and it doesn't work for anything else...

You could use the same trick to "compress" any data you want, and all you need to do is choose the correct decompression routine - at which point you might as well just keep the original data and choose the file you want directly, saving the overhead.

Of course, as other people have pointed out, you can also do lossy compression, in which case you can compress something down to near zero size, but what you get back will have little correlation with what you compressed...

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Re: 1381: "Margin"

Postby Klear » Sun Jun 15, 2014 6:57 pm UTC

rmsgrey wrote:It's the same as the incredible wonder of the scientific age - dehydrated water - just add water to bring it to any quantity desired!


Personally I prefer vacuum-packaged air.

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Re: 1381: "Margin"

Postby Mikeski » Sun Jun 15, 2014 7:03 pm UTC

Klear wrote:
rmsgrey wrote:It's the same as the incredible wonder of the scientific age - dehydrated water - just add water to bring it to any quantity desired!

Personally I prefer vacuum-packaged air.

Save a SKU number; an empty Thermos is both!

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Re: 1381: "Margin"

Postby rick.s » Sun Jun 15, 2014 10:37 pm UTC

Brian-M wrote:Pretending to take the comic seriously for a moment...


Secondly, it'll take an absurdly long time to extract even a tiny amount of information this way. You don't want to have to dedicate the resources of a million supercomputers for a billion years just to decode a 30-second MP3 file.


Would this not be the ultimate rickroll?

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Re: 1381: "Margin"

Postby rmsgrey » Sun Jun 15, 2014 11:00 pm UTC

rick.s wrote:
Brian-M wrote:Pretending to take the comic seriously for a moment...


Secondly, it'll take an absurdly long time to extract even a tiny amount of information this way. You don't want to have to dedicate the resources of a million supercomputers for a billion years just to decode a 30-second MP3 file.


Would this not be the ultimate rickroll?


But he said he'd filter out nonsense...

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Re: 1381: "Margin"

Postby Jorpho » Mon Jun 16, 2014 2:13 am UTC

Brian-M wrote:Firstly, you'll end up with lots of false positives, so not only will you end up with the information you started with, you'll also end up with lots of information that never existed before, and you may not be able to tell which information is the information that was originally encoded.
Clearly this must be correct, as it correlates with the Principle of Explosion.

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Re: 1381: "Margin"

Postby Paragon99 » Mon Jun 16, 2014 3:04 am UTC

Instead of "... oh never mind :("
It should have read "... oh never mind :)"
after realizing he could fit any number of proofs for any number of problems within a single marking, in this case, a single parenthesis.

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Re: 1381: "Margin"

Postby eviloatmeal » Mon Jun 16, 2014 12:05 pm UTC

gmalivuk wrote:it's information you'll want to present in its uncompressed form for anyone to be able to read it.

Says who?

Society has built up such an unhealthy obsession with information having to be useful.

Scur wrote:Convert all the info into ASCII, put a decimal point at the beginning, convert it into a fraction, and make a mark dividing the height of the page at the distance equal to the fraction.

You could do the same thing with the horizontal position of the mark, and store twice as infinite information!
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