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It can be both humbling and reassuring to consider one’s
own life in the greater context.
Earliest writing (Sumerian cuneiform clay tablets) around
5000 years
Earliest art/paintings, around 40-60,000 years
Voyager “Golden Record”, and the Pioneer Plaque, could
last millions of years
Long
Now Foundation - planning for at least 10,000 years
Nuclear waste geological repositories- need to consider,
perhaps >100,000 years
We humans, we’ve been around perhaps 300,000 years.
What information medium can we use for *really* long
term data, resilient for hundreds of thousands of years,
in
a reasonably expected combination of environmental
and
social conditions?
We have extensive writings from Roman and Greek
civilisations, and carving text into rock seems pretty
durable. But there’s a selection bias in that: we
only see the texts that have survived- we don’t know
what
percentage of the initial population that is.
An engraved golden plaque will resist corrosion almost
indefinitely, but because (in a cultural context) the
material is valuable, its prone to looting, melting down,
and re-use.
Stone inscriptions, exposed to weathering, might only
survive a few hundred years (visit a graveyard).
A recorded CD, perhaps a hundred years, but some
future
person will need the technology to read and interpret
the
data.
So, having pondered this for some time, I’m suggesting a
long term data storage solution: sintered tungsten
carbide
letters embedded in stainless steel mesh-reinforced clay
tablets, encapsulated in borosilicate glass.
For digital data, perhaps carbide beads bonded to a
stainless steel ribbon.
Glass disc for long term data storage
https://hardware.sl...turistic-glass-disc
The piece of silica glass storing the 1978 "Superman" movie, measures 7.5 cm x 7.5 cm x 2 mm. The glass contains 75.6 GB of data plus error redundancy codes. [xaviergisz, Nov 06 2019]
Rosetta Cemetery
Rosetta_20Cemetery
[theircompetitor, Nov 06 2019]
Pi
https://en.wikipedi.../Pi#Infinite_series
and how to cook it. [neutrinos_shadow, Nov 07 2019]
US Study on how to label long term (nuclear) waste storage.
https://www.osti.gov/biblio/10117359
Circa 45MB if you *are* interested enough to download. I imagine it's as much about the symbology of any structure that you build over the site as the language (if any) you use to warn. [st3f, Nov 07 2019]
Rosetta Project
https://rosettaproject.org/about/
Text in multiple languages, so someone might be able to understand it [Frankx, Nov 07 2019]
Digits of Pi
https://www.askamat...n-the-digits-of-pi/
Some discussion [Frankx, Nov 11 2019]
Pi doesn't repeat
https://www.askamat...ly-start-repeating/
Pi is irrational [Loris, Nov 12 2019]
[link]
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// "sintered tungsten carbide letters embedded in stainless steel mesh-
reinforced clay tablets, encapsulated in borosilicate glass." // |
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A member of LongNow here. Just wondering, can you elaborate on this
chcoices? They certainly do make sense, just what you were optimizing
for -- as there do exist other tough materials. Resistance to erosion?
Price? Difficulty to manufacture? Transparency? Performance in space?
Also, what kind
of overall structure are you considering for highest retention, as the size
not just materials, also matters -- take small grain-like sample of these
materials, and they'll get lost among others. Make a mountain of these
same materials, and it may stand for a few tens of millions of years.
(Apparently, mountains are not as old as we think.). |
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I think there is a problem with the idea of storing data or information for posterity or for future readers. Whatever you choose to store and record, is not necessarily what the future readers want to read. Think of the amount of second or third-rate fiction lovingly preserved by our great libraries in deep storage in salt-mines in Cheshire. My guess is that no-one will ever read the majority of this stuff. |
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Thinking of very old texts, think of the poetry of Psappho. We only have fragments, but many of them are fairly recently discovered from archaeological excavations of a rubbish dump. If only we had the complete text of all her poems! But this is an endless question. If we had the complete text of all her poems, we might wish that we could see her jotters where she made rough drafts. Even if we had those jotters, we might wish to have her letters written to other poets and contemporaries. If we had the letters, we would wish that we knew what the replies said! Imagine we had all that heaving pile of original text surmounted by towering mountains of scholarship and exegesis, some plucky professor might suggest how much more we could learn if we had her diaries. And once they too had been excavated from the rubbish dump, and we could read her daily thought processes, imagine what we would miss out by not having the rough drafts of her daily journal instead of just relying on the neat, redacted version of record. And even then, we don't get an impartial look at her life. Suppose we also had the daily journal of her housekeeper, giving us a candid opinion of what kind of a person she was, with all her foibles and idiosyncracies. And to be honest, there would still be questions even if all of this was extant. What did she look like? What did she wear? How did she move? How did her voice sound? What did she have for breakfast? In the end, nothing short of a total immersive continuous video and audio recording stream from multiple cameras and microphones will do. And so yes, we could all install constantly recording cameras and microphones into every room of our houses, and carry recording rigs with us whenever we go out, generating huge data streams to be captured, archived and stored in ever increasing servers, burned to glass disks and stored in amazingly organised automated warehouses all over the world. Not only would this use up a significant portion of world GDP but it would be far too much information for humans to read or view, which suggests that the main use of this data recording and storage exercise is to feed the exponentially growing AI so that the machines can find out everything about us use that knowledge to take over the world. |
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Look at things from a different viewpoint. By far the majority of knowledge about human activity in the past comes not from reading ancient texts, but from archaeology. i.e. from raking through ancient rubbish. The science of archaeology is in its infancy, barely a couple of hundred years old, and I imagine that techniques and protocols will continue to develop fast. But an ancient decayed rubbish heap can tell us a huge amount of very detailed information about the lives of the humans who were responsible for its creation. Detailed and fine-grained patterns of resource use and behaviour are revealed by molecular-level analysis of dirt, dust, crumbs, slime, discarded fragments, poop, etc. Therefore, it seems to me that as a Human society, the best way for us to ensure long-term storage of information about us as communities and societies and also as individuals, is to consume more and waste more and be generally more profligate. Buy your daily coffee in a single-use plastic cup, and discard into the landfill waste stream. The more that human activities impact on the environment in as many different ways as possible, the more information about those activities will be preserved for the longest possible time. |
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How long, exactly, have you been stalking Sappho? |
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[pocmloc] - very interesting to think about what information should be preserved. And who will want to read it and why. I wasn't really thinking about that, just that *if* one wanted to preserve information (for whatever reason) to be accessed by a person in the far distant future, what physical medium would best support that. |
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So I'd generally argue against (exclusively) machine-readable formats, because they require specific technology to access. |
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[Mindey] - I'm impressed by Long Now's vision. |
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In terms of material choices: durability against corrosion/erosion, redundancy/fault-tolerance in construction, but the need to be useless in terms of materials. If you engraved text on stainless steel tablets, it's not unlikely that someone in the future would say "hey, that's a useful material, I'll make something else out of it", destroying the information.
So a material combination that's of little value, or that the effort of extracting useful materials is such that makes it pointless. |
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Clay tablets, of a convenient size (say A4) with stainless steel mesh, would be somewhat tolerant to breakage (the mesh would at least hold the fragments together). Carbide characters both form an erosion/chemical resistant text and emboss the text into the clay: extracting them is unlikely to yield a useful material - at best an abrasive. The glass envelope - transparent to allow the text to be read, but also providing further chemical/erosion resistance and structural cohesiveness - and also of little value other than the text it contains. |
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I was considering something that would survive exposure to open-air weathering or burial with (say) some moderately corrosive chemical/biological agents typical of landfill etc. - in readable form for as long as possible. |
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We suggest embedding the information within a featureless black monolith with sides in the ratio of 1:4:9. |
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After all, it worked last time around ... |
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I thought the point of a featureless monolith was that it
lacked features? |
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The smart way to do it would be (as Carl Sagan wrote
somewhere) to design the universe such that the information
is embedded in the digits of pi. |
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// thought the point of a featureless monolith was that it
lacked features?// |
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2100 -- the year we discovered the monolith is not
featureless |
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// the point of a featureless monolith was that it lacked features? // |
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No, like [xen], when you look at it closely it's got a really ugly side ... |
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//digits of pi//
But the digits of pi are dependent on the chosen base. So
that wouldn't really work. |
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Even if you stick to the same number base (we suggest 2 for simplicity ), what your species hasn't twigged yet is that Pi isn't the same everywhere. |
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You think it is, and it's an easy assumption to make, but that's wrong. |
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Once you grasp that fact, a lot of the puzzle around Dark Matter becomes explicable and even rational. |
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Given that there an infinite number of bases in
which you could calculate pi, every possible
message is already encoded. |
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You just have to identify which base has the
message you want encoded. And you’ll probably
have to invent a very large number of new
symbols. |
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//digits of pi are dependent on the chosen base// binary,
obviously. |
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Oh no. Given that the digits of pi are infinite, it
already encodes every finite message somewhere
among them, even in base-10 |
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I love the idea that Dark Matter is just an accounting error. I was suspecting uninformed fealty to outdated equations by Einstein, along with no real understanding of gravity, but this is for 8th to answer, whatever his real Dark Matter number may be. |
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[MaxwellBuchanan]; yeah. I tried to find a binary form of pi
to include in my last comment, trusting that the geeks of
the internet would have done so already; but alas, Google
failed me (OK, I only searched for a couple of minutes).
They (out in the internet wilds) keep trying to create the
binary version by converting the decimal version, and
failing. A better way to do it would be to use one of the pi-
generating algorithms (see linky) , but keep the output in
binary. |
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//Given that the digits of pi are infinite, it already
encodes every
finite message somewhere among them, even in base-
10// |
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Yes, but the trick to it is to encode the message before
you'd
expect it, statistically. |
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In the book, IIRC, there are two messages mentioned. The
first is a
few million digits in, in some base in the range 10..100,
and
encodes a relatively long message using a subset of the
digits.
[edit - wikipedia confirms it as over 10^20 places in - in base 11, using only '0'
and '1' values]
So, if you're looking for it, it sticks out like a sore thumb. |
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It's a cute idea, but I'm not convinced it would be easy to
monkey
with even low decimal places of any fundamental
constant, let
alone mathematical constants - and still get a usable
universe. |
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Hi [Loris] - I don't know which book? |
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I guess I was just noting that, in any base, all human knowledge, every message that could ever be sent, the code for a superintelligent AI, and the answer to every physics question - are all there in the digits of Pi. But obviously not in any useful way. |
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It would be possible to encode a specific message by noting where in the string of pi digits it occurs, but the digits to note the location (i.e. the address) is going to be longer than the actual message - so it's not useful. |
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I suspect that even if you searched pi in many different bases, the data needed to address the message would be larger than the message itself. |
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// I'm not convinced it would be easy to monkey with even low decimal places of any fundamental constant, let alone mathematical constants - and still get a usable universe. // |
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That is because you're just looking at it from your constrained viewpoint. |
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It is a "Black Swan". From your planet, with the information you have currently available and obtainable, with your current theoretical knowledge and mathematics, and your level of intelligence, it is a perfectly reasonable and logically consistent deduction; indeed it is the only one that fits the observed facts, or at least most of them. |
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But not all of them. Despite diligent application of the biggest theoretical hammers available, and resort to the desperate and very dubious practice much favoured by biologists of selectively discarding all data that doesn't fit the theory, some bits of data stubbornly refuse to fit. |
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This leads to the inescapable but uncomfortable realization that something, somewhere, is very badly wrong - either with the theory, or the Universe*. |
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Now, because the theory - such as it is - works very nicely in your local area, and is extremely useful for things like celestial mechanics, GPS, etc., you are understandably reluctant to discard it. |
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Newton was not "wrong". Newtonian mechanics, the laws of motion, are perfectly good even post-Einstein. They don't work at the quantum (very small) level, or at the relatavistic level (v -> C). But for throwing rocks at one another - allowing for air resistance - they're perfectly good. |
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Once you clamber off your squalid little lump of rock and get out and meet grown-ups, your view of the Universe will change - although that requires that you have developed FTL spacedrive, which demands that you have already worked out that a lot of your assumptions are wrong, because otherwise you can't build one. |
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*It would be wise to remain open to the distinct possibility that the Universe is, in fact, wrong. It can come as a bit of a shock to discover after many years that you have been using the wrong Universe all this time, a bit like finding out that a famously macho actor had a gay lover; so it's good to be sitting down when you do it. |
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I've always known that any cosmological theory that leaves
Milton Keynes unexplained simply must be wrong. |
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speaking of Pi didn't they just say that the universe is a
sphere after all? |
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We regret to inform you that in all the physical and cosmological theories known, the only explanation of Milton Keynes that can be agreed on is "Shit happens". |
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Just linked a 45 MB US Govt document about how to
label
long term nuclear waste storage. I believe that one
of the
options is to hide the fact that there is anything
buried at
all, on the premise that if your message is no longer
understood, leaving a marker might encourage
digging in
a spot that would otherwise be left alone. After all
having to
dig through a couple of hundred metres of reinforced
concrete and low-water-conduction clay might send a
message more effective that any sign would. |
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On the thought of language, the fact that few of us
can read
what was written in English just 1000 years ago
suggests that
the evolution of language brings about obstacles as
big as the
decay of the medium upon which you write. Not
insurmountable, just another challenge along the
way. |
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language is tough but at the same time we still read Latin,
Hebrew, Pharsi, the Khoran (which would be 1400 year old
Arabic) etc. |
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So the way to do it is to make the place of religious
significance. Which I think was already done in one of the
Planet of the Apes sequels |
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//English just 1000 years ago// |
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This was the thinking behind the Rosetta Project [link] - to preserve a body of text in multiple languages so that some future reader might be able to make sense of it. The Rosetta stone was a huge breakthrough in decoding ancient languages. |
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When the repository is opened to visitors as a museum a few millennia hence, the guide's speech to the tour group is going to be very amusing. |
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It's interesting to speculate on what the neolithic inhabitants of Wessex would think if they could look forward four thousand years and see coachloads of brightly clad Japanese tourists tramping all round Stonehenge, waving cameras and sipping beakers of Costa Coffee ... |
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Although ironically, being humans, the thing they're actually most likely to think is not "Our sacred site is being desecrated !" but "Oooh, durable weatherproof clothing not made from animal skins, and plentiful hot food and drink ... can we have some of that, please ?" |
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//The Rosetta stone was a huge breakthrough in decoding
ancient languages.// |
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learning something new every day |
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[8th]... it's a fair point. We have no idea what the world of any future reader of our texts would be like, or why/whether they would have any interest at all. |
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// learning something new// apologies [their], just the point that copies of the same text in multiple languages dramatically increases the chances of decoding it. |
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For long-term preservation, wouldn't you want to send
whatever it is to the moon? Send a few copies in case one
gets hit by a meteorite, and make sure it's either buried or at
least not degraded by light. |
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Of course, if part of the text consists of instructions on how to
build a spaceship, you could have problems with data
recovery. |
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Is there any chance of preserving Simon Cowell for eternity by that method ? |
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We'll be happy to assist, if enough humans want it ... |
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// why/whether they would have any interest at all. // |
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There is nothing, no matter how obscure, irrelevant, pointless, useless, trivial and dull that cannot be worked up into the starting point for a Ph.D. thesis and grant application. |
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But we defer to [MB] on that one, given his proven expertise ... |
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//Hi [Loris] - I don't know which book?//
It's what Max was referring to - "Contact", by Carl Sagan.
(The pi stuff is not in the film based
on the book, though, so don't bother with that.) |
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//I suspect that even if you searched pi in many different
bases, the data needed to address
the message would be larger than the message
itself.//
That's almost exactly the explanation of how you could
identify such a message to be 'real'
rather than noise. |
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//That is because you're just looking at it from your
constrained viewpoint.//
8th, I think you misunderstand my point - or to break it
down, two points.
In the first case, maths. It's precisely because maths is
based on abstractions that it should be
universally true.
The calculation of pi is fixed in Euclidean geometry, and
therefore outside your jurisdiction. |
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This leads to the second case, physical constants. The
most significant bits of these are
probably specified by the requirements of the simulation.
Universes which collapse to a
singularity in the first few cycles, or which never form up
into stuff are so boring.
You could fuck with the /measurement/ of e.g. pi by
making your universe non-Euclidean,
sure, but that's not going to be measurable from within-
universe with sufficient precision to
read any decent length of message. |
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//It would be wise to remain open to the distinct
possibility that the Universe is, in fact,
wrong.//
I posit that the universe is not /even/ wrong. |
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Have you ever investigated Euclidean geometry anywhere outside your galaxy ? |
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Euclidean geometry and the corresponding mathematical abstractions were developed in your environment. Therefore they are self-consistent. But it is a bold and, so far, unproven assertion that the postulates ate universally applicable, particularly since you have only partially observed the universe, and that as it was in your remote past. |
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The mathematics may well be correct, but the physics certainly isn't - hence the concept of "Dark Matter" was invented to account for the glaring discrepancies between theory and observation. |
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It's a weak analogy, but consider an observer who remaind in a room where the temperature varies between 283 and 305 K and watches through the window. The observer might see snow falling, but since the temperature in the room never drops below 283 K, ice is unknown. Thr observer then develops a "Theory of Falling White Stuff" based on known lical phenomena and behaviours of materials. |
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If the observer goes "outside" - and not very far outsude - the phenomena of snow, wind, and unstable muddy slush underfoot become apparent. The observer's first reaction will probably be to invent the overcoat, or equally, to go back inside where it's warm and dry and think about it for a bit. |
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I believe Einstein's equations for gravity in the Theory of General Relativity are based on a model of non-Euclidean geometry which happened to be hot at the time. |
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"There were three theories about this, and they all had the following important features in common: They were internally consistent, they completelyand and satisfactorily explained all the known facts, and they were entitely wrong ..
" |
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//Have you ever investigated Euclidean geometry anywhere
outside your galaxy ? // |
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Nice trolling, but I don't have to. Maths goes from axioms to
deductions; inferences are valid dependent only on the logic
and regardless of whether the axioms are true. |
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How does that reconcile with Russel's view that a correctly codified Formal Logic should not give rise to paradoxes, whereas Euclid's geometry does ? |
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If you wish to assert that mathematical logic is vallid under all circumstances, from the Big Bang through to Heat Death, or gravitational collapse, you need to be able to prove it. Russel couldn't, and he was regarded by his contemporaries as "pretty smart". |
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Einstein was deeply unhappy about having to bung in the "Cosmological Constant" to make his equations work in the "real" (allegedly) Universe - he referred to it as an "unsatisfactory fudge". So, while mathematics may appear to be "universal", there's still a lot you don't know. |
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//Have you ever investigated Euclidean geometry
anywhere outside your galaxy ? // |
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//If you wish to assert that mathematical logic is vallid under
all circumstances, [...] you need to be able to prove it.// |
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//...should not give rise to paradoxes, whereas Euclid's
geometry does...// |
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Come on then, let's hear it. |
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//Einstein was deeply unhappy about having to bung in the "Cosmological Constant" to
make his equations work in the "real" (allegedly) Universe - he referred to it as an
"unsatisfactory fudge". So, while mathematics may appear to be "universal", there's still a
lot you don't know.// |
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You're conflating maths and physics. That's a mistake. |
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Totally true. I suspect the challenge is to consider
whether Euclidean geometry is a valid
representation of “real space” on a large scale.
Mathematical axioms are, by definition,
assumptions. They will produce the same self-
consistent mathematical constructs wherever they
are applied. |
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[8th], I suspect that Russel also identifies some
paradoxes that ultimately defeat the idea of (even
an internally) self-consistent set of logical
statements. Perhaps your culture has found a
solution to that? |
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We do, but we're not telling. |
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So far, [Frankx], you're doing extremely well, way ahead of [Loris]; you are in line to be awarded the Galactic Institute's Prize for Supreme Cleverness, then taken out the back and beaten to death (because nobody loves a smartass). |
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Ouch!
<runs away to hide/> |
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//I suspect that Russel also identifies some paradoxes that
ultimately defeat the idea of (even an internally) self-
consistent set of logical statements.// |
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Hang on a sec - a "self-consistent set of logical statements"
is
entirely possible - it's just that such a mathematical system
can't be both self-consistent and complete. see: Gödel's
incompleteness theorems. |
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Waiting for Gödel's is fruitless. He never shows. |
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I saw part of a documentary about mathematicians who ended up in asylums. Many of them were trying to spring Gödel. |
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//You're conflating maths and physics. That's a mistake.//
Physics will do whatever maths tells it to do; the only
limitations are that (a) there are many different maths and
(b) physics isn't always fast enough to keep up with the maths,
hence all this quantum wibble. |
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I don't know if I agree with this math/physics comparison. Perhaps you've heard the claim that all science starts with physics? No doubt it's contentious, but the impression is that quantum and related string theories are being inflicted on us by the readiness of mathematicians to spin themselves into abstraction instead of engaging in observational physics. |
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//the readiness of mathematicians to spin themselves into
abstraction instead of engaging in observational physics//
The problem with that argument is that a lot of observational
physics starts from the maths. The maths tells you that such-
and-so a particle can exist; then you spend your billions
building the equipment to make/find said particle. So far,
the mathematicians haven't been doing too badly. |
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Yes, but they're rubbish at finding their own car keys. Oh yes, tbey can find keys(i) in a set m of {keys (1... n)} but they still end up standing in the rain by a locked car* and late for their meeting. |
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* or a car(i) in a set c of {cars(1 ... n)}. |
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To take a recent example: the "proof" for gravity waves. Admittedly, the lab experiment was probably devised by a physicist, but using measures of statistical significance produces a kind of tautology. Yes, the later tests produced unexpected anomalies, but with no corresponding proof of the underlying mechanism, real or imagined. I can point you to a physicist forum which was replete with studied misgivings regarding the statistics, after the first few results were reported. |
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That's good; science requires that everything must be rigorously questioned. |
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When the outcomes become consistent and predictable, then the confidence factor improves. But it is still not "proof". |
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Lasers were shot across the length of the U.S. If they did not arrive at precisely expected times, the scientists proclaimed "It must be gravity waves and nothing else!" Perhaps the mirrors were produced by the same company which produced the Hubble telescope, or possibly cats with advanced understanding of kinesthetics jumped the gun somewhere. |
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Noting the archeology of garbage middens approach, if they replaced 1% of those mysterious op-art appearing printer's registration marks with equations and cellular automata seeds of big pictures it might come in handy for people. |
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Probably better to design your media to suit superevolved cockroaches, though ... |
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[st3f], thanks for the link. It's not often you see a
team of
anthropologists, astronomers, linguists and
materials
scientists! |
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It's a fascinating and oddly beautiful document;
expressing
the care of humans today for the welfare of those
in 10,000
years time. |
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[Loris]...incompleteness theorems - yes, my error.
Can't be
self-consistent and complete, me. |
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Use DNA. Let me be clear, DNA is a _really_ bad way to
encode information in general, and it's not particularly long-
lasting on a molecule-by-molecule basis. However, if all
you want is longevity, you can make trillions of trillions of
identical molecules. Put the DNA in a dry, light-proof
robust container (maybe filled with argon). The DNA will be
far, far better preserved than (for instance) Neanderthal
DNA, and can sustain a lot of damage before it becomes
unsequenceable. 100,000yr-old fossils are easy enough to
sequence from, despite abysmal preservation conditions.
DNA in these sealed containers would be sequenceable after
at least a million years, probably ten. |
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In from Venus, space is pretty clear of debris. Why not get a small nickel-iron asteroid, maybe 10 km across, and trim it into a platonic solid, then set it in an orbit between Venus and Mercury but at right angles to the plane of the ecliptic ? |
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Obvious a Cube would be best but a tetrahedron would work just as well. Polish the faces and set it spinning; it'll produce a mathematically predictable flash pattern totally different from any natural phenomenon. |
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Then just chisel your message on the sides in binary. |
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It'll last until your primary burns all irs hydrogen, which is a fairly long time, and it'll surely attract attention. |
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I like the idea that all irrational numbers are simply documents on different topics such that you can read them from some logical fundamental beginning out perpetually, each an endless tale, produced by the act of the process of translation. Pi might be a very important story of set of observations but that each and every irrational number can be translated into a different narrative. |
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I suspect the most valuable bits of knowledge we
will leave behind will be repair manuals for the
scrap heap societies of the future to keep their
recovered junk working in a post-apocalyptic
future. I’m optimistic like that, I know. |
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Beyond that, gasoline, oil, water, lithium, copper,
and such. |
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Somewhere in the digits of pi might be the answer
to life, the universe, and everything. |
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Yep, there it is, 42, in place #92 and 93... |
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Hello, [WcW] - I haven't seen you here in ages! |
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If you consider "The Sentinel", and the range of possible motives for an inrelligence that might plant such a device, don't forget to factor in the worst-case i.e. human reasons ... |
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"Hey Boss, we've got a ping from 45812249." |
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"Oh, interesting ... right, I'll order out the extermination team." |
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After all, if you're the dominant species in the galaxy, you need to make sure you stay that way. No chance of a Prime Directive there ... |
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//[Frankx] Given that the digits of pi are infinite, it already encodes every finite message somewhere among them//
No it doesn't. Just because a series of digits is infinite, it does *not* mean that it includes every possible finite series of digits. |
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Correct. 22/7 divides out as 3.142 recurring, which is infinite but does not contain all possible finite sequences. |
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To contain all possible finite sequences it must be both infinite and random. |
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//To contain all possible finite sequences it must be both infinite and random//
No - an infinite, random series is *not* guaranteed to contain every possible finite sequence. |
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Don't make us do math at you ... |
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(Please. But only because the HB's text format lacks the ability to express formal mathematical notation, particularly the integral symbol, and even support for sub- and superscripts is poor). |
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//No - an infinite, random series is *not* guaranteed to contain every possible finite sequence.// |
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HE'S BEHIND YOU!
Sorry, wrong cue. |
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//Is pi random?//
Nice awkward question. |
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For the purposes of this conversation I would like to specify an operation: 'mung'. Each digit of a
munged sequence is defined as half that of the equivalent digit of the unmunged sequence,
rounded down.
original value-> munged value
0 -> 0
1 -> 0
2 -> 1
3 -> 1
4 -> 2
5 -> 2
6 -> 3
7 -> 3
8 -> 4
9 -> 4
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This operation on a single random digit will remove one bit of information, but leave the
remainder intact. So if it was random, it is still random, just a bit smaller. |
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For example, to 10 significant figures, Pimung is 1.020241321 |
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If you consider Pi to be random, Pimung is therefore a transcendental number supplying an
infinite series of random digits, but not carrying any of the one-digit series '5', '6', '7', '8' or '9'. |
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If on the other hand Pi is not random enough for you, feel free to use a Chaitin constant instead,
generating a Chaitinmung. |
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//Pimung is therefore a transcendental number supplying an
infinite series of random digits, but not carrying any of the
one-digit series '5', '6', '7', '8' or '9'// But pimung is not
random, since 50% of all digits are missing completely. You
might as well say that "11111111..." is completely random. |
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Now that’s getting really interesting. [link]
discussing exactly this. |
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[pocmloc], I think the digits of pi couldn’t be truly
called random as they’re the product of a
function, but they seem to be statistically random. |
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// But pimung is not random, since 50% of all digits are
missing completely.// |
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Any digit of a munged sequence cannot be determined
without knowing the equivalent digit of the original
sequence.
I do concede that it carries less randomness, per digit,
than the original series. However if the original is infinite,
and random, the munged series still embodies an infinite
amount of random. |
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//You might as well say that "11111111..." is completely
random.// |
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Well it might be. You can never be sure. |
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//Any digit of a munged sequence cannot be determined//
No, but I can say that the probability of the next digit being a
3 is 0.2, which is higher than 0.1 (the probability of its being a
3 in a random string of digits 0-9). |
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// No, but I can say that the probability of the next digit
being a 3 is 0.2, which is higher than 0.1// |
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My point is that a series can only be random for the
elements
it contains, and by definition it cannot contain any string
that
includes elements not present in the series. So, a truly
random sequence of the digits 0-4 will indeed contain all
possible strings of digits 0-4; but it won't contain any string
which includes a 5, or an A, or a champagne cork. |
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So, to return briefly to the bedside of sanity, does the
decimal representation of pi contain all possible sequences
of digits 0-9? As far as I can see, mathematicians believe it
does but have not proven this to be the case. But, equally,
pi is not a truly random number, since its digits can be
generated algorithmically. A truly random, infinite string of
digits 0-9 would contain all possible sequences of digits. |
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//they seem to be statistically random// That seems a bit vague! |
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//You might as well say that "11111111..." is completely random.// |
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It can be. Random coin-toss probability, remember ? |
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Since each event is unique and the probability is exactly 0.5, an infinite series of heads or tails is exactly as likely as getting exactly alternating heads/tails. So your infinite stream of 1's is exactly as likely (0.5) as your infinite stream of 0's. |
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But then, a firm grasp of mathematics and statistics have never been a given for biochemists. In fact, a firm grasp of a spoon is asking rather a lot of them ... don't worry, nurse will bring a napkin and wipe your chin for you. We'll put it in a non-spill mug for you next time. Do you want your blanket tucked round your legs ? No, that's not Mr. Chamberlain on the TV ... TV ... like the cinema newsreels, yes. Yes, the colour's very good ... yes, quite a new thing ... no, you don't have a ration book, the war ended ... no, Kaiser Wilhelm was the previous war ... yes, you're having your tea now, look, soup, yes? Oh dear ... |
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There are more things we don't know about pi than things we
do know about it. It's quite embarrassing. |
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To return briefly to the original idea, how about encoding
information in the distribution of layers in carbon, and then
storing billions of tons of this information-rich material
underground? It would survive for millions of years, and
almost the only way the information would be lost is if future
generations were stupid enough to dig it up and burn it as
fuel. |
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Yes indeed, but then you and your family have so many things to be embarrased about ... |
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//My point is that a series can only be random for the elements it contains, and by definition it cannot
contain any string that includes elements not present in the series. So, a truly random sequence of the
digits 0-4 will indeed contain all possible strings of digits 0-4; but it won't contain any string which
includes a 5, or an A, or a champagne cork.// |
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You're moving the goal-posts. A mungseries of an infinite 'true random' series is infinite, and it is random.
The fact that doesn't have an even distribution of digits is kind of irrelevant. It is trivial to massage the
output to cover that requirement - one way would be to add 5 to every other digit. |
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//So, to return briefly to the bedside of sanity, does the decimal representation of pi contain all possible
sequences of digits 0-9? As far as I can see, mathematicians believe it does but have not proven this to
be the case. But, equally, pi is not a truly random number, since its digits can be generated
algorithmically.// |
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Don't get hung up on using Pi. I did mention an alternative. |
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// A truly random, infinite string of digits 0-9 would contain all possible sequences of digits.// |
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That's a brave claim indeed, since you've forgotten to include the word 'finite'. |
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Well, if I'm wrong it'll take an infinitely long time to prove me
so. |
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Psst, [8th of 7], your calculator is truncating again. 22/7 is
3.142857 (entire decimal part recurring). |
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//Well, if I'm wrong it'll take an infinitely long time to prove me
so// |
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Nope, significantly less. |
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A transcendental number cannot list the full sequence of more
than one other transcendental number. |
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Even a "truly random, infinite string of digits 0-9" cannot contain all
decimal places of both pi and e, for example. |
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Ah, I understand now. We don’t know, although it
looks unlikely, that at some very distant but finite
point in the sequence of digits of pi, that it
doesn’t go ...31415926536... and repeat the whole
sequence cyclically. If it did, it would be infinite,
but not include every finite sequence. If it doesn’t
cycle, then it does include every finite sequence.
But we could never know because we would have
to search infinitely far into the digits to be sure it
doesn’t cycle. |
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I think it has been shown that pi does not repeat. |
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//a bit vague//... as I read it, the digits of pi
match a random distribution, in the same way a
“truly random” number would. But because it’s the
result of a calculable algorithm, I don’t think you
could call “pi” itself random. |
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Dunno, that vegetarian cottage pie you served up last month repeated something awful ... beans, leaks, onions and courgettes, wasn't it ? Diabolical... |
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//leaks// - apparently , there are quite discreet products you can insert into your pants to help with that problem |
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Yes, we've explained this to him ... not sure what had leaked into the "pie" but it didn't taste quite right .... |
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// Even a "truly random, infinite string of digits 0-9" cannot
contain all decimal places of both pi and e, for example. // |
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Yes it can—if it so happens that pi so contains e, or vice
versa, in the digits we haven't discovered yet. |
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//Even a "truly random, infinite string of digits 0-9" cannot
contain all decimal places of both pi and e// If you're
suggesting that an infinite series cannot contain two infinite
series, you're wrong. The infinities of:
(a) Digits of pi
(b) Digits of e and
(c) (a)+(b) |
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are all the same size. Since an infinite string can contain (a),
it follows that it can also contain (b) and (c). |
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These two pints are the same size, and one of them fits in a
pint glass, therefore they definitely
will fit nicely together in this pint glass. |
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//Yes it can—if it so happens that pi so contains e, or vice versa, in the
digits we
haven't discovered yet.// |
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Yeah, that occurred to me today as well. One could include the other as an
infinite
tail.
But we do know that it can't happen both ways (i.e. if pi tail-codes e, then
e can't
tail-code pi), since that would mean that they would repeat.
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But regardless. I don't think that matters. 1/9 (0.1 recurring) is an infinite
sequence, as is 1/3 (0.3 recurring) and 2/9 (0.2 recurring). None of these
tail-code
each another.
I might accept the claim that two of these could be encoded in a number
which
was infinitely large as well as infinitely precise (i.e. ...22222.1111... - all
positions
2 up to infinitely large; all fractional places 1 down to infinitely small). I'm
not sure
whether a proper mathematician would.
Nevertheless, there's nowhere for the third (or a pi-e composite, or
whatever) to
go. |
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To reiterate: the infinities of [digits of pi], [digits of e] and
[digits of pi plus digits of e] are all the same size of infinities.
Therefore, any one of them can be (and will be, if the digits
are "random") contained in the other. |
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// To reiterate: the infinities of [digits of pi], [digits of e] and [digits of pi plus digits of e]
are
all the same size of infinities. Therefore, any one of them can be (and will be, if the digits are
"random") contained in the other.// |
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// A truly random, infinite string of digits 0-9 would contain all possible sequences of digits.// |
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Can you see how that's not the same?
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Because infinite 1s, infinite 2s and infinite 3s are all possible sequences of digits, and you
don't
get to have all of them. |
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Also, your reiteration is even wronger, because if pi 'contains' e, and e 'contains' pi, then pi
would repeat, and you've already said: |
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//I think it has been shown that pi does not repeat// |
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And I've previously posted a link to that effect.
We can of course accept that the digits of e, pi, and other components of minus one are not
random.
But that's never really been the issue here. |
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"Why take two infinite irrational numbers into the shower ... ?" |
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// infinite 1s, infinite 2s and infinite 3s are all possible
sequences of digits, and you don't get to have all of them.//
I disagree. Start with an infinitely long string of random
digits. Now take the first half of that string - it still has
infinite length, and that infinity is the same as the first
infinity (ie, neither infinity is larger than the other; just as
the number of odd integers is the same infinity as the
number of all integers). |
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By the same reasoning, you can cut the original string into
any number of equal-sized sub-strings, and each of them is
will still be infinitely large. One of those substrings will be
an infinity of 1s, or an infinity of 2's. |
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I think the "cutting in half" is misleading - to make the cut you have to get to half-way, which is impossible. |
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Better to select every second, or third, digit of pi. That creates a new sequence which is equally as long as the original. |
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It's possible that selecting (for example) every 43,279th digit of pi might give e
OK, it doesn't, but that's a matter of happenstance rather than size-of-infinity logical impossibility. |
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Has it been proven that taking every xth digit of pi does not give pi for all values of x greater than 1? |
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Are you talking about the fractional part ? Pi has to start with a "3" ... |
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If you start with the first digit, 3, and the fractional part is infinite in length and random, then yes, there must be a value of x where digit x, 2x, 3x comes out as ".141 ..." |
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But x is probably also infinite ... |
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//I disagree. Start with an infinitely long string of random
digits. Now take the
first half of that
string - it still has infinite length, and that infinity is the
same as the first infinity
(ie, neither
infinity is larger than the other; just as the number of odd
integers is the same
infinity as the
number of all integers).// |
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On the one hand, I do see what you mean. (I don't think I'm sure enough of the maths to comment on
the legitimacy of that as an argument.)
But - having thought about it overnight - on the other, I
don't think that works,
because diagonal
argument.
You're dealing with a larger infinity - the
length of the random
string is Aleph-naught infinite, but the number of infinite
strings is Aleph-one infinite. |
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(although admittedly I might have got that wrong.) |
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I'll take the first hand. |
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Right! This has got way beyond my understanding. |
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1) a random, infinite, non-repeating sequence of
digits (of, for instance 0..9) does contain every
finite sequence of those digits, and therefore
every finite message (encoded via some arbitrary
message-to-digit means) |
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2) pi (and other mathematical functions, such as e)
produce an infinite (probably random) (and
possibly proven non-repeating) sequence as
required for 1 |
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3) an infinite, random, non-repeating sequence of
digits can (and does) actually contain every other
infinite, random, non-repeating sequence of digits,
because of the weirdness of infinite sequences? |
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...which would mean that the infinite digits of pi
include the infinite digits of e, and simultaneously
the infinite digits of e would contain the infinite
digits of pi? |
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1) Yes. This is uncontroversial, although it does have the
slightly disturbing implication that even long
apparently non-random sequences (like a string of
10^^^10 '1'
digits in a row) are represented. [see - up-arrow
notation].
2) Qualified yes. It's probably safest not to call the digits
of Pi etc. random, since that leads to disagreements
about what 'random' means.
3) No. The 'other hand' in my comment above describes
why not. In essence it invokes Cantor's diagonal
argument.
...) I previously pointed out that is incompatible with the
proven fact that Pi doesn't repeat. |
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//it invokes Cantor's diagonal argument// Yes, but that only
works if you allow castling; otherwise he's open to attack by
either a rook, a knight or an okapi. |
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