encoding Encyclopedia Britannica in one dot

[zak]

in the free magazine "the commutator (http://macsoc.weebly.com/the-commutator.html)" , issue march 2011 (http://www.scribd.com/doc/61790132/the-Commutator-Vol-2-Issue-1-Edition-1)
page 25 there is some of the martin gardner articles, in "The amazing code" he described a story in which a UFO commander described an amazing way to encode all the Encyclopedia Brittanica in just one single dot on his magical ultra precision rod.
how:
he assign a number from 1 through 999 to each letter or symbol, adding zeros on the left if needed so that each number used will have three digits. Cat might be coded 003001020.

Using his powerful pocket computer, Dr. Zeta (the UFO commander) scanned
the encyclopedia quickly, translating its entire content into one gigantic number.
By putting a decimal point in front of the number, he made it a decimal fraction.

Dr. Zeta then placed a mark on his rod, dividing it accurately into lengths a and b so that the fraction a/b was equivalent to the decimal fraction of his code.
Dr. Zeta said: When 1 get back to my planet, one of our computers will measure a and b exactly, then compute the fraction a/b. This
decimal fraction will be decoded, and the computer will print your encyclopedia for us!

[matthew]

I'd actually heard about this technique before when I was searching on Wikipedia for information on Jan Sloot (http://en.wikipedia.org/wiki/Jan_Sloot). Apparently it's also known as the Encyclopaedia on a Toothpick (http://everything2.com/title/Encyclopedia+on+a+toothpick) & there's a lot of debate as to whether it's possible or not. If you're interested in Data Compression you might want to check out the Million Random Digit Challenge here (http://marknelson.us/2006/06/20/million-digit-challenge).

[zak]

thanks matthew for the valuable links, i like especialy The Stick of Jan Sloot (http://ticc.uvt.nl/~pspronck/sloot.html) it reminds me of the current unlimited detail technology of the Euclideon from Australia (http://www.euclideon.com/) which are discussed recently in the thread the Polygon is dead (http://www.thinbasic.com/community/showthread.php?11304-The-Polygon-is-dead&p=84281)
i hope the Euclideon (http://www.euclideon.com/) are not going the same road and fate.

[matthew]

There's no-denying that the work Euclideon are doing will be useful in the future. But I think the reason people are doubting them is because they've basically had to over-hype their technology in order to secure funding.

[Charles Pegge]

By making a ratio mark on hi magic rod, Dr. Zeta could only encode the first three letters of the encyclopaedia. (I'm assuming his rod is made of atoms which have a minimum spacing of 1.5E-10 metres, and that his rod is about 1 metre in length)

But Dr. Arcturus has a better system. He has a small notebook with pages made of graphene. They are only 1 atom thick. With his his neutron pen, he is able to scan the encyclopaedia, then he makes a tiny dot with the pen on one of the pages of his notebook. Within this dot, the neutron pen has created a binary encoding by converting Carbon12 atoms to carbon13.



http://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Graphen.jpg/300px-Graphen.jpg


http://en.wikipedia.org/wiki/Graphene


(http://en.wikipedia.org/wiki/Graphene)

[danbaron]

From,

http://en.wikipedia.org/wiki/Wikipedia:Size_comparisons

the online version of the Encyclopedia Britannica has 300,000,000 characters.

Each character is encoded into 3 digits, so, we need a total of 900,000,000 digits.

Let's say that the rod is one meter long.

To show what's going on, let's first pretend that what we want to encode is much shorter, and that we need only 4 digits.

Then, say, for instance, the fraction is 0.3947.

In that case, we would need to be able to divide the 1 meter rod into 10,000 equal parts, i.e., into 10^4 equal parts.

Each part would be 10^(-4) meters long, i.e., 1/10th of a millimeter long.

http://www.engineeringtoolbox.com/length-units-converter-d_1033.html

We would count the first 3947 of them on the rod, for our measurement.

However, if you think about it, in the actual case, we need to be able to divide the rod into 10^900,000,000 equal parts.

So, each part would be 10^(-900,000,000) meters long.

I think, the smallest objects posited to exist in the universe are super-strings.

They are approximately 10^(-35) meters long.

http://physics.about.com/od/quantumphysics/f/stringtheory.htm

As far as anyone is aware, (if they exist) there is nothing smaller than a super-string.

But, let's say that someday a particle is found that is one trillionth-trillionth the size of a super-string.

Then, that particle would be 10^(-59) meters long.

So, in my opinion, the idea that any measurement will ever be made within "light years" of 10^(-900,000,000) meters, is, and will remain, dreaming.

[danbaron]

How about for Charles' way?

We have 3*10^8 characters.

If we are generous, and allow 10 bits for each character, then we need,

3*10^9 bits.

So, we would need a sheet of carbon,

sqrt(3*10^9) * 1.42*10^(-10) = 7.778*10^(-6) meters x 7.778*10^(-6) meters.

Or,

7.778 micrometers x 7.778 micrometers.

[Charles Pegge]

I agree Dan, I get an estimate of similar magnitude.

How powerful would Dr. Arcturus neutron pen need to be?

Assuming the pen creates neutrons from pure energy, we can use Einstein's equation E=MC^2

The mass of a neutron is about 1.7E-27 Kilos. The speed of light C is about 3E8 meters per second, which gives an embodied energy of about 1.5E-10 joules per neutron. (ie setting 1 bit of data). So it takes less than a Joule to encode the Encyclopaedia.

The pen only needs a small battery :D

Charles

[danbaron]

I fixed the calculation.

I'm tired.

I hope it is correct now.

That means that on a carbon sheet 1 meter by 1 meter, you could fit an amount of information equivalent to 1/(7.778*10(-6))^2 = 16.53 billion online Encyclopedia Britannicas.

From the graphene article, http://en.wikipedia.org/wiki/Graphene, the in-plane atomic spacing is 1.42*10^(-10) meters, and the inter-plane atomic spacing is 3.35*10^(-10) meters.

So, in a cubic centimeter of carbon, you could fit approximately,

1/(1.42*10^(-8 )^2 * 1/(3.35*10^(-8 ) = 1.480*10^23 bits of information.

(http://en.wikipedia.org/wiki/Graphene)That would be approximately equivalent to 1.480*10^23 / 3*10^9 = 49.3 trillion online Encyclopedia Britannicas.
(http://en.wikipedia.org/wiki/Graphene)
I'll bet that is much more much than all of the world's current data.

(But, let me know when they start selling 1 atom thick graphene sheeting, by the roll.)

[danbaron]

I don't know anything about chemistry (or is this physics?).

Can you make graphene from a mix of carbon 12 and carbon 13?

Will it work if you try to shoot a neutron into the nucleus of a carbon 12 atom, will it "stick"?

Would you be able to instantaneously read whether an atom was carbon 12 or carbon 13?

It seems that in 3 dimensions, things would be much harder.

I'd like to see the technology that can fire a neutron into the nucleus of a particular atom in a lattice.

And, I'd like to see the technology that can locate and read the state of particular atom in a lattice.

I imagine that the reverse process, of changing carbon 13 to carbon 12, would also be much harder. Even if you could knock a neutron out of the nucleus, how could you prevent it from sticking to a neighboring nucleus? And, what would you knock it out with, a proton?

[Charles Pegge]

Carbon 13 is very close to Carbon 12 in is characteristics but organisms have a bias towards taking in C12. C13 can be detected because it has a Nuclear Magnetic Resonance signature whereas C12 does not.

Creating neutrons is a bit more tricky. Destroying them or creating them from scratch requires very intense energies - as in the first few seconds of the Big-Bang. :)

Might be easier to swap existing c12s and c13s in the graphene lattice, since it is only necessary to break a few covalent bonds.

Charles

[danbaron]

I never thought about this topic.

I wasn't thinking about creating neutrons, or any other particle.

I guess I assumed you could get them from somewhere else.

For instance, if you dismantled a hydrogen atom, you would get 1 proton, 1 neutron, and 1 electron.

But, I have no memory of how difficult that would be to do, how much energy would be required.

I guess you would be struggling against the strong nuclear force.

So, my intuition is that removing protons and neutrons from an atomic nucleus, would not be a trivial task.

Now, I'll look at what Wikipedia says about fission.

I looked a little bit.

"Research reactors produce neutrons that are used in various ways, with the heat of fission being treated as an unavoidable waste product."

So far, I don't think nuclear reactors are small enough to put inside PCs, but to create ROM in a laboratory, who knows?

[kryton9]

Cool topic guys, enjoyed reading the posts.