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How to fit any dataset with a single parameter

arxiv.org

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Re: How to fit any dataset with a single parameter

#141

Post by michaelcampbell »

throwawaytemp27 wrote: post #53
michaelcampbell wrote: post #19

This reminds me of the "worst way to ask a user for a telephone number" UI, after one UI forced the user to select each digit in a 0-9 dropdown. The specific one I'm thinking of is just spit out a scrollable numeric string of Pi, and make the user scroll until their phone number was the digits of Pi that matched it. My (7 digit) phone number occurs after digit position 9_000_000, and occurs 21 times in the first 200_…

I wonder if you gave away your phone number there? Or how many 7 digit numbers match those criteria?

My phone number is already "out" in terms of being on the internet, and I can change it pretty easily if it became an ACTUAL security issue.

But it would be an interesting exercise to do, I guess.

Re: How to fit any dataset with a single parameter

#142

Post by dotancohen »

pveierland wrote: post #45
air7 wrote: post #17

This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick! Just encode the text as a ascii codes after the decimal dot of a zero. (0.656168.. etc). Then just mark that ratio of the sticks length and you're done...

My shot at the calculation for fun :-) Stick encoding with graphite resolution (0.335 * 10^-9 meter) [1]: "Uti" (31 bits -> 3 UTF8 characters) Stick encoding with Planck resolution (1.616255 * 10^-35 meter) [2]: "Utility ought " (115 bits -> 14 UTF8 characters) Complete first sentence: "Utility ought to be the principal intention of every publication." [3] It appears that this storage scheme may not be suited towards…

I would look more into the limitations of the read tech (how accurately can we measure the stick length and the mark location) rather than inherent limitations of the medium. Very few technologies reach the actual theoretical limitations of the materials they are made of.

Re: How to fit any dataset with a single parameter

#143

Post by hnlmorg »

amelius wrote: post #130
hnlmorg wrote: post #18

Earlier quoted context omitted.

This reminds me of the fun thought experiment of using /dev/random as storage. Given an infinite amount of time you'll find every file you need.

The index might need more bits than the file.

Considerably more in all probability :)

Re: How to fit any dataset with a single parameter

#144

Post by Radim »

mjburgess wrote: post #22
air7 wrote: post #17

This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick! Just encode the text as a ascii codes after the decimal dot of a zero. (0.656168.. etc). Then just mark that ratio of the sticks length and you're done...

I don't see this as a joke, but a radical and important point. Reality, in being geometrical, is infinitely informationally dense (with a discrete conception of information). This distinction between geometrical space and time, and discrete algorithmic computability is unbridgeable. And hence there is an extemely firm footing on which to reject: AI, brain scanning readers, teleporters, etc and most sci-fi computation…

Others already noted how shaky your assertion "Reality, in being geometrical, is infinitely informationally dense" is.

Instead, let me throw out another extreme (but fun) view in the opposite direction: Finitism [0].

These guys not only reject the existence of the continuum; they reject all infinities altogether! In finitism, even discrete things exist only as finite objects (that is further constructable – Ultrafinitism [1]).

So no infinite universe, no "set of all natural numbers", no "limits" and other ideals over infinite domains. Screw Platonism. Hello Wittgenstein (and Wolfram).

I don't know how far that theory can be taken in a practical sense – most body of science is built on Platonism [2] – but I have to say finitism does appeal to my CS heart and my earthly experience.

[0] https://en.wikipedia.org/wiki/Finitism

[1] https://en.wikipedia.org/wiki/Ultrafinitism

[2] https://en.wikipedia.org/wiki/Primitive_recursive_arithmetic

Re: How to fit any dataset with a single parameter

#145

Post by mjburgess »

Radim wrote: post #144
mjburgess wrote: post #22

Earlier quoted context omitted.

I don't see this as a joke, but a radical and important point. Reality, in being geometrical, is infinitely informationally dense (with a discrete conception of information). This distinction between geometrical space and time, and discrete algorithmic computability is unbridgeable. And hence there is an extemely firm footing on which to reject: AI, brain scanning readers, teleporters, etc and most sci-fi computation…

Others already noted how shaky your assertion "Reality, in being geometrical, is infinitely informationally dense" is. Instead, let me throw out another extreme (but fun) view in the opposite direction: Finitism [0]. These guys not only reject the existence of the continuum; they reject all infinities altogether! In finitism, even discrete things exist only as finite objects (that is further constructable – Ultrafini…

My view is indeed the opposite. It seems trivial to me that reality has actual infinities as seen from a discrete pov.

A trivial example: you can partition the environment into an infinite number of objects. And which partition scheme you choose is, in some sense, abitary.

Eg., "object: the edge of the glass", "composite: edges of glasses on the table", etc.

Reality admits an infinite number of such schemes, and also forcloses an infinite number (eg., if "pen"=pen, then "paper"!=pen).

I dont think one can meaningfully speak "of reality", ie., provide a discrete linguistic/propositional account, which avoids these infinities.

I also think there is no meta-scheme, so one cannot even order (in terms of fundamentality) which scheme is 'the really real' one.

It's my view that the reason for this issue is that cognition is discrete but reality continuous. Since discrete aggregations arent enough, likewise "aggregative models of atoms" arent enough for chemistry.

An aqueous solution, just like a society, is much more than merely the sum of the properties of its members. When we partition the world with a discrete scheme, we introduce "emergent properties" which are only the "leftovers from our reductive failure".

The only problem infinity poses is to being realised by a discrete sequential process. That can never be actually infinite. But everything else can!

Re: How to fit any dataset with a single parameter

#146

Post by bopbeepboop »

mjburgess wrote: post #145
Radim wrote: post #144

Earlier quoted context omitted.

Others already noted how shaky your assertion "Reality, in being geometrical, is infinitely informationally dense" is. Instead, let me throw out another extreme (but fun) view in the opposite direction: Finitism [0]. These guys not only reject the existence of the continuum; they reject all infinities altogether! In finitism, even discrete things exist only as finite objects (that is further constructable – Ultrafini…

My view is indeed the opposite. It seems trivial to me that reality has actual infinities as seen from a discrete pov. A trivial example: you can partition the environment into an infinite number of objects. And which partition scheme you choose is, in some sense, abitary. Eg., "object: the edge of the glass", "composite: edges of glasses on the table", etc. Reality admits an infinite number of such schemes, and also…

The point is that number is large, but 0% of infinity.

I’ll bet $1000 you can’t name more than 10^1000^1000 possibilities — a far cry from an actual infinity.

Not that I disagree, but you’re using “infinity” in the sense of “a really large, unknowable so number” — when it’s actually infinitely larger than that.

There’s an open question of whether reality is infinitely fine grained or finitely grained — and even if infinitely grained, how much so. (And more broadly, what the topology/geometry is.)

Eg, can you have a particle at a Chaitan coordinate, or do they have to be computable? — classic Euclidean? — origami coordinates? Etc.

Re: How to fit any dataset with a single parameter

#147

Post by alisonkisk »

air7 wrote: post #17

This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick! Just encode the text as a ascii codes after the decimal dot of a zero. (0.656168.. etc). Then just mark that ratio of the sticks length and you're done...

That's πfs

https://github.com/philipl/pifs

Re: How to fit any dataset with a single parameter

#148

Post by alisonkisk »

idiotsecant wrote: post #9

First, this is a fun implementation and I love it. Second, you could as easily embed an infinite size dataset into an infinitely long binary string and say that you've reproduced your dataset with a 'single' parameter! That's sort of what this is doing, with some extra steps.

πfs

https://github.com/philipl/pifs

Re: How to fit any dataset with a single parameter

#149

Post by adrian_b »

dotancohen wrote: post #142
pveierland wrote: post #45

Earlier quoted context omitted.

My shot at the calculation for fun :-) Stick encoding with graphite resolution (0.335 * 10^-9 meter) [1]: "Uti" (31 bits -> 3 UTF8 characters) Stick encoding with Planck resolution (1.616255 * 10^-35 meter) [2]: "Utility ought " (115 bits -> 14 UTF8 characters) Complete first sentence: "Utility ought to be the principal intention of every publication." [3] It appears that this storage scheme may not be suited towards…

I would look more into the limitations of the read tech (how accurately can we measure the stick length and the mark location) rather than inherent limitations of the medium. Very few technologies reach the actual theoretical limitations of the materials they are made of.

Straightforward length measurement (by interferometry) has a resolution limited by the wavelength of light that can be generated with lasers, so up to the near ultraviolet, at a few hundred nanometers.

Resolution smaller than a wavelength can be achieved with vernier techniques (like in a caliper), but those require a pair of light sources with precise frequency/phase relationships between themselves, which are difficult to make at such high frequencies, so it is hard to improve much the resolution.

I have not looked to see if there have been any progresses in recent years, but I would guess that a very approximate limit for the resolution of length measurement would be around 100 nm. So measuring the length of an 1 meter stick might provide up to log_2(10^7) bits, so about 23 ... 24 bits.

Of course, any temperature fluctuation would change the length of the stick by much more than the resolution.

However that can be avoided by encoding the information not in the absolute length, but in the ratio between the lengths of 2 segments marked on the stick.

No matter what, it is possible to write much more bit symbols on any stick than it is possible to encode in the measurements of one or a few lengths marked on the stick.

That is due to the fact that halving the size of a bit symbol doubles the quantity of information written on the stick, while halving the length corresponding to the measurement resolution provides just 1 single bit of extra stored information.

Re: How to fit any dataset with a single parameter

#150

Post by fouc »

air7 wrote: post #17

This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick! Just encode the text as a ascii codes after the decimal dot of a zero. (0.656168.. etc). Then just mark that ratio of the sticks length and you're done...

You reminded me of https://en.wikipedia.org/wiki/Gödel_numbering

> Each letter of the message is represented in order by the natural order of prime numbers—that is, the first letter is represented by the base 2, the second by the base 3, the third by the base 5, then by 7, 11, 13, 17, etc. The identity of the letter occupying that position in the message is given by the exponent, simply: the exponent 1 meaning that the letter in that position is an A, the exponent 2 meaning that it is a B, 3 a C, 4 a D, up to 26 as the exponent for a Z. The message as a whole is then rendered as the product of all the bases and exponents. Examples. The word 'cab' can thus be represented as 2^3 x 3^1 x 5^2, or 600.

Excerpt From: Frederik Pohl. “Starburst.”

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