This analysis is not quite fair. It takes into account locality (i.e. the speed of light) when designing UUID schemes but not when computing the odds of a collision. Collisions only matter if the colliding UUIDs actually come into causal contact with each other after being generated. So just as you have to take locality into account when designing UUID trees, you also have to take it into account when computing the odds of an actual local collision. So a naive application of the birthday paradox is not applicable because that ignores locality. So an actual fair calculation of the required size of a random UUID is going to be a lot smaller than the ~800 bits the article comes up with. I haven't done the math, but I'd be surprised if the actual answer is more than 256 bits.
(Gotta say here that I love HN. It's one of the very few places where a comment that geeky and pedantic can nonetheless be on point. :-)
This is the right critique. The whole article is a fun thought experiment but it massively overestimates the problem by ignoring causality. In practice, UUID collisions only matter within systems that actually talk to each other, and those systems are bounded by light cones. 128 bits is already overkill for anything humans will build in the next thousand years. 256 bits is overkill for anything that could physically exist in this universe.
And recent DESI data suggests that dark energy is not constant and the universe will experience a big crunch in a little more than double its current age, for a total lifespan of 33 billion years, no need to get wild with the orders of magnitude on years into the future. The infinite expansion to heat death over 10^100 years is looking less likely, 10^11 years should be plenty.
not obvious to me this makes things better as opposed to worse? sure, the time bound helps but in the runup to a crunch won't we get vastly more devices in causal range at an asymptotically increasing rate?
Protons can decay because the distinction between matter and energy isn't permanent.
Two quarks inside the proton interact via a massive messenger particle. This exchange flips their identity, turning the proton into a positron and a neutral pion. The pion then immediately converts into gamma rays.
If you go far beyond nanoseconds, energy becomes a limiting factor. You can only achieve ultra-fast processing if you dedicate vast amounts of matter to heat dissipation and energy generation. Think on a galactic scale: you cannot have even have molecular reaction speeds occurring at femtosecond or attosecond speeds constantly and everywhere without overheating everything.
Maybe. It's not clear whether these are fundamental limits or merely technological ones. Reversible (i.e. infinitely efficient) computing is theoretically possible.
We don't "make" universes in the MWI. The universal wavefunction evolves to include all reachable quantum states. It's deterministic, because it encompasses all allowed possibilities.
Protons (and mass and energy) could also potentially be created. If this happens, the heat death could be avoided.
Conservation of mass and energy is an empirical observation, there is no theoretical basis for it. We just don't know any process we can implement that violates it, but that doesn't mean it doesn't exist.
Time translation symmetry implies energy conservation, but time translation symmetry is only an empirical observation on a local scale and has not been shown to be true on a global universe scale.
I got a big laugh at the “only” part of that. I do have a sincere question about that number though, isn’t time relative? How would we know that number to be true or consistent? My incredibly naive assumption would be that with less matter time moves faster sort of accelerating; so, as matter “evaporates” the process accelerates and converges on that number (or close it)?
Times for things like "age of the universe" are usually given as "cosmic time" for this reason. If it's about a specific object (e.g. "how long until a day on Earth lasts 25 hours") it's usually given in "proper time" for that object. Other observers/reference frames may perceive time differently, but in the normal relativistic sense rather than a "it all needs to wind itself back up to be equal in the end" sense.
The local reference frame (which is what matters for proton decay) doesn't see an outside world moving slower or faster depending on how much mass is around it to any significant degree until you start adding a lot of mass very close around.
Would this take into account IDs generated by objects moving at relativistic speeds? It would be a right pain to travel for a year to another planet, arrive 10,000 years late, and have a bunch of id collisions.
Maybe the definitions are shifting, but in my experience “on point” is typically an endorsement in the area of “really/precisely good” — so I think what you mean is “on topic” or similar.
> A more reasonable upper limit might be to assume that every atom in the observable universe will get one ID (we assume atoms won’t be assigned multiple IDs throughout time, which is a concession). There are an estimated atoms in the universe. Using the same equation as above, we find that we need 532 bits to avoid (probabilistically) a collision up to that point.
This doesn't take into account that you will inevitably want to assign unique IDs to various groups of atoms (e.g. this microchip, that car, etc.). And don't even get me started on assigning unique IDs to each subatomic particle.
Even every possible permutation of every single subatomic element in the universe? Even if we just consider atoms, at 10^80 atoms in the entire universe, there are (10^80)! possible permutations, which is many, many, many orders of magnitude larger.
And this isn't even counting sets that include multiples of the same item; once you get into that territory, there really is no upper bound.
New atoms form all the time, either through fusion or fission. The latter is happening right now all around you- either from potassium in plants breaking down, to radon gas that sept up from the ground, to carbon itself. All of these have unstable isotopes with half lives short enough to have at least a little activity near you.
Given that constant change to the available combinations of sets, it would seem that a truly capable system would need to be practically infinite, no?
A more realistic estimate of the total number of addressable things should take into account that for anything to be addressable, its address should be stored somewhere at least once.
If it takes at least Npb particles to store one bit of information, then the number of addressable things would decrease with the number of bits of the address.
So let's call Nthg the number of addressable things, and assume the average number of bits per address grows with Nb = f(Ntng).
Then the maximum number of addressable things is the number that satisfies Nthg = Np/(Npb*f(Ntng)), where Np is the total number of particles.
One could take anything like a cell and split it into genes, molecules, atoms, sub-atomic wave functions (with infinite value range) and take time which can be split into another infinite entity say even within a finite interval. How does this analysis account for that?
I could split this object into 10^500 or 10^50^500^5000 etc., with imagination being the limit.
These values Id'd at whatever imaginable resolution are far from practically useful but at a cosmic scale, there is no telling what is a useful value?
So this framework seems to be more limiting because we define a resolution ?
Heh. I once had to make an argument that 256 bit randomly assigned identifiers are good enough without explicit collision checking. People wanted me to add complex and expensive collision checks.
My argument was the 2^256 actually approaches the number of atom in the observable universe (within 1 to 3 orders of magnitude), and that collisions are so unlikely that we'll have millions of datacenter meltdowns first (all assuming we have a good source of random numbers, of course). In the end I convinced everybody that even 128 bits are good enough, without any collision checking required.
I thought my arguments was clever, but this is so much better. :)
The total amount of computer data across all of humanity is less that 1 yottabyte. We're expected to reach 1 yottabyte within the next decade, and will probably do so before 2030. That's all data, everywhere, including nation-states.
The birthday paradox says that you'll reach a 50% chance of at least one collision (as a conservative first order approximation) at the square root of the domain size. sqrt(2^256) is 2^128.
Now, a 256 bit identifier takes up 32 bytes of storage. 2^128 * 32 bytes = 10^16 yottabytes. That's 10 quadrillion yottabytes just to store the keys. And it's even odds whether you'll have a collision or not.
And if the 50% number scares them, well, you'll have a 1% chance of a collision at around... 2^128 * 0.1. Yeah, so you don't reach a 1% over the whole life of the system until you get to a quadrillion yottabytes.
Because you're never getting anywhere near the square root of the size, the chances of any collision occurring are flatly astronomical.
I build a whole database around the idea of using the smallest plausible random identifiers, because that seems to be the only "golden disk" we have for universal communication, except for maybe some convergence property of latent spaces with large enough embodied foundation models.
It's weird that they are really under appreciated in the scientific data management and library science community, and many issues that require large organisations at the moment could just have been better identifiers.
To me the ship of Theseus question is about extrinsic (random / named) identifiers vs. intrinsic (hash / embedding) identifiers.
You should check out Vernor Vinge's A Fire Upon The Deep for more fun examples of how intra-galactic communication would be labeled, with routes & such.
From this book in particular, I love the scene with everyone sitting around talking about how horrifying the concept of cheese is. The rest of the quartet is wonderful, with the second book (A Closed and Common Orbit) being the MVP IMO.
The Dewey section and Elias omega encoding was fun, but it reminded me of Project Xanadu's tumblers[1] - a variable length dotted notion where each segment is unbounded.
Tumblers are modeled using transfinite numbers which makes me wonder: what are the similarities and differences between transfinite numbers and Elias omega encoding? I'm not well versed in either, so I expect it's either a question from ignorance or I may have a lot to learn. :)
I forget the context but the other day I also learned about Snowflake IDs [1] that are apparently used by Twitter, Discord, Instagram, and Mastodon.
Timestamp + random seems like it could be a good tradeoff to reduce the ID sizes and still get reasonable characteristics, I'm surprised the article didn't explore there (but then again "timestamps" are a lot more nebulous at universal scale I suppose). Just spitballing here but I wonder if it would be worthwhile to reclaim ten bits of the Snowflake timestamp and use the low 32 bits for a random number. Four billion IDs for each second.
There's a Tom Scott video [2] that describes Youtube video IDs as 11-digit base-64 random numbers, but I don't see any official documentation about that. At the end he says how many IDs are available but I don't think he considers collisions via the birthday paradox.
"Agreement" of time is probably nonsense, yeah. I realized after posting so I edited in the parenthetical, but as [3] notes, locality probably makes this less of a real issue.
Apparently with the birthday paradox 32 bit random IDs only allow some tens of thousands per second before collision chance passes 50%. Maybe that's acceptable?
From real life we know that people prefer to have multiple anonymous IDs, or self-selected handles, either makes fully deterministic generation schemes moot.
Also, network routing requires objects that have multiple addresses.
Physics side of whole thing is funny too, afaik quantum particles require fungibility, i.e. by doxxing atoms you unavoidably change the behavior of the system.
Specifying a CSPRNG as an entropy source to avoid collision is incorrect.
CSPRNGs make prediction of the next number difficult (cracking-AES difficulty) but do not add entropy and must be seeded uniquely otherwise they will output the same numbers. Unless the author is proposing having the same machine generate a single universe-scale list in one run.
Also “banning” ids that are all 1s or 0s is silly; they are just as valid and unique as any other number if you’re generating them properly. Although I might suggest purchasing a lottery ticket if you get an UUID with all settable bits as 1.
Banning 0s might be to avoid conflicts of with testing? Kind of like how you’d want to block logins with emails that have a domain example.com. Idk I’m grasping at straws
One upside of the deterministic schemes is they include provenance/lineage. Can literally "trace up" the path the history back to the original ID giver.
Kinda has me curious about how much information is required to represent any arbitrary provenance tree/graph on a network of N-nodes/objects (entirely via the self-described ID)?
(thinking in the comment: I guess if worst case linear chain, and you assume that the information of the full provenance should be accessible by the id, that scales as O(N x id_size), so its quite bad. But, assuming "best case" (that any node is expected to be log(N) steps from root, depth of log(N)) feels like global_id_size = log(N) x local_id_size is roughly the optimal limit? so effectively the size of the global_id grows as log(N)^2? Would that mean: from the 399 bit number, with lineage, would be a lower limit for a global_id_size be like (400 bit)^2 ~= 20 kB (because of carrying the ordered-local-id provenance information, and not relative to local shared knowledge)
The ATProto underlying BlueSky social network is similar. It uses a content-addressed DAG.
Each “post” has a CID, which is a cryptographic hash of the data. To “prove” ownership of the post, there’s a witness hash that is sent that can be proved all the way up the tree to the repo root hash, which is signed with the root key.
Neat way of having data say “here’s the data, and if you care to verify it, here’s an MST”.
Provenance is a DAG, so you get a partial order for free by topological sort. That can be extended to a compatible total order. Then provenance for a node is just its ordering. This kind of mapping from objects to the first N consecutive naturals is also a minimal perfect hash function, which have n log n overhead. We can't navigate the tree to track ancestry, but equality implies identical ancestry.
Alternatively, we could track the whole history in somewhat more bits with a succinct encoding, 2N if it's a binary tree.
In practice, deterministic IDs usually accept a 2^-N collision risk to get log n.
I’m going to vibe code an app that lets you register a computronium unique id (is that name taken?) I’ll corner the market.
I’m also going to devise a standard that arbitrarily breaks it into groups of hexadecimal digits of arbitrary length in the spirit of UUIDs, and reserve a prefix space for Planck-unit timestamps (computronium-ID-7) so that you can lexicographically sort your COMPID7s.
The practical punchline buried in this analysis: at human scale, the real tradeoff isn't uniqueness vs collision risk — it's uniqueness vs legibility.
Pure random IDs are theoretically optimal but operationally hostile. When something breaks at 3am, you want the ID to whisper where it came from. That's why ULIDs embed timestamps, DNS is hierarchical, and git hashes are content-addressed. You're trading a negligible increase in collision probability for debuggability.
The article's proof that deterministic schemes can't beat linear worst-case growth is elegant. But at any scale where humans are in the loop, it doesn't matter — you're generating maybe 10^12 IDs total, not 10^120. The interesting design space is the middle: enough randomness for uniqueness, enough structure for humans.
Chiming in from the decentralized world - there’s an adversarial / cooperative dynamic in the assignment of these IDs - and the selection of parents, not discussed in the original. I think you could possibly get to sub linear by allowing a small number of cooperative nodes to assign new IDs.
On the contrary, having the right to assign IDs is powerful; on balance, to my mind the right thing to do is some sort of a ZK verifiable random function, e.g. sunspot-based transformations combined with some proof of ‘fair’ random choice. In that case, I think the 800 bit number seems like plenty. You could also do some sort of epoch-based variable length, where for the next billion years or so, we use 1/256 of the ID space, (forced first bit to 0), and so on.
The obvious solution is a system like IP addresses. Every system has an address like
universe.galaxy.region.system or whatever, then the system is subdivided in whatever way is logical for that system.
That way you can route ships or data or whatever to a specific system in a logical way. Each system decides how to allocate addresses. Since most systems won’t have anything or anyone to care, something like NASA or registrars would just allocate a block to the system and give large things like planets an address.
Quite offtopic, but: I found UUIDs being overused in many cases. People then abused them to store data, making them effectively "speaking IDs" or "multi column indices".
Unless it's a key that needs to be sortable (e.g. insertion order) or a metric/descriptor of some kind, I'm not sure why UUID would be overused or inappropriate for use.
That's the problem with address type of systems is that they expect the object at that location to always be at that location. How do you encode the orbital speed, radius of orbit for not just the object, but also the object it is orbiting will need the same info as it is also in motion, then that object's parent galaxy's motion. Ugh, now I need a nap to calm down a bit.
It is interesting how much of our infrastructure relies on the assumption that 'close enough' is actually 'good enough' for uniqueness. When we move from UUIDs to things like ULIDs or Snowflake IDs, we are really just trading off coordination cost for a slightly higher collision risk that we will likely never hit in several lifetimes. Thinking about it on a 'cosmological' scale makes you realize how much of a luxury local generation is without needing a central authority. It is that tiny bit of entropy that keeps the whole distributed system from grinding to a halt.
We will probably end up with something like each planet has its own local addressing, and the big router in the sky does NAT, each solar system has a router and so on.
It's observable universe, and that's the only thing that matters. Events outside the observable universe are causally disconnected. We will never interact with anything outside the observable universe. For all practical purposes, it's the same thing.
The best way to solve this is not to, and just giving up on the idea of identification.
If you have an infinite multiverse of infinite universes, and perhaps layers on that, with different physics, etc., you can’t have identity outside of all existence.
In Judaism, one/the name of God is translated as “I am”. I believe this is because God’s existence is all,
transcending whatever concepts you have of existence or of IDs. That ID is the only ID.
So, the cosmic solution to IDs is the name of God.
This analysis is not quite fair. It takes into account locality (i.e. the speed of light) when designing UUID schemes but not when computing the odds of a collision. Collisions only matter if the colliding UUIDs actually come into causal contact with each other after being generated. So just as you have to take locality into account when designing UUID trees, you also have to take it into account when computing the odds of an actual local collision. So a naive application of the birthday paradox is not applicable because that ignores locality. So an actual fair calculation of the required size of a random UUID is going to be a lot smaller than the ~800 bits the article comes up with. I haven't done the math, but I'd be surprised if the actual answer is more than 256 bits.
(Gotta say here that I love HN. It's one of the very few places where a comment that geeky and pedantic can nonetheless be on point. :-)
Reminds me of a time many years ago when I received a whole case of Intel NICs all with the same MAC address.
It was an interesting couple of days before we figured it out.
This is the right critique. The whole article is a fun thought experiment but it massively overestimates the problem by ignoring causality. In practice, UUID collisions only matter within systems that actually talk to each other, and those systems are bounded by light cones. 128 bits is already overkill for anything humans will build in the next thousand years. 256 bits is overkill for anything that could physically exist in this universe.
You must consider both time and locality.
From now until protons decay and matter does not exist anymore is only 10^56 nanoseconds.
If protons decay. There isn't really any reason to believe they're not stable.
And recent DESI data suggests that dark energy is not constant and the universe will experience a big crunch in a little more than double its current age, for a total lifespan of 33 billion years, no need to get wild with the orders of magnitude on years into the future. The infinite expansion to heat death over 10^100 years is looking less likely, 10^11 years should be plenty.
https://www.sciencedaily.com/releases/2026/02/260215225537.h...
not obvious to me this makes things better as opposed to worse? sure, the time bound helps but in the runup to a crunch won't we get vastly more devices in causal range at an asymptotically increasing rate?
Protons can decay because the distinction between matter and energy isn't permanent.
Two quarks inside the proton interact via a massive messenger particle. This exchange flips their identity, turning the proton into a positron and a neutral pion. The pion then immediately converts into gamma rays.
Proton decayed!
This destroys a baryon, an operation which is prohibited by the standard model.
That's such an odd way to use units. Why would you do 10^56 * 10^-9 seconds?
This was my thought. Nanoseconds are an eternity. You want to be using Planck units for your worst-case analysis.
If you go far beyond nanoseconds, energy becomes a limiting factor. You can only achieve ultra-fast processing if you dedicate vast amounts of matter to heat dissipation and energy generation. Think on a galactic scale: you cannot have even have molecular reaction speeds occurring at femtosecond or attosecond speeds constantly and everywhere without overheating everything.
Maybe. It's not clear whether these are fundamental limits or merely technological ones. Reversible (i.e. infinitely efficient) computing is theoretically possible.
If you have a black hole as an infinite heat sink this helps a great deal.
Black holes have a maximum growth rate
By infinite I mean a black hole gets COLDER as you add mass and energy to it.
Planck units are a mathematical convenience, not a physical limit. For instance, the Planck mass is on the order of an eyelash or grain of sand.
Planck units are physical limits. The Planck mass is the limit of the mass of an elementary particle before it would form a black hole.
"Plank units are not physical limits on reality itself" is what I should have said. We can obviously have larger or smaller masses.
The plank time is a limit on a measurement process, not the smallest unit of time.
> Plank units are not physical limits on reality itself
We don't actually know that. They might be. Planck units are what happens when GR meets QM and we just don't know yet what happens there.
But as a heuristic, they probably put pretty good bounds on what we can reasonably expect to be technologically achievable before humans go extinct.
Nanoseconds is a natural unit for processors operating around a GHz, as it's roughly the time of a clock cycle.
If a CPU takes 4 cycles to generate a UUID and the CPU runs at 4 GHz it churns out one every nanosecond.
If we think of the many worlds interpretation, how many universes will we be making every time we assign a CCUID to something?
> many worlds interpretation
These are only namespaces. Many worlds can have all the same (many) random numbers and they will never conflict with each other!
In that interpretation the total number of worlds does not change.
We don't "make" universes in the MWI. The universal wavefunction evolves to include all reachable quantum states. It's deterministic, because it encompasses all allowed possibilities.
Humpf…
You just had to collapse my wave function here…
Protons (and mass and energy) could also potentially be created. If this happens, the heat death could be avoided.
Conservation of mass and energy is an empirical observation, there is no theoretical basis for it. We just don't know any process we can implement that violates it, but that doesn't mean it doesn't exist.
Conservation laws result from continuous symmetries in the laws of physics, as proven by Noether's theorem.
Time translation symmetry implies energy conservation, but time translation symmetry is only an empirical observation on a local scale and has not been shown to be true on a global universe scale.
Proton decay is hypothetical.
So is the need for cosmologically unique IDs. We're having fun.
I got a big laugh at the “only” part of that. I do have a sincere question about that number though, isn’t time relative? How would we know that number to be true or consistent? My incredibly naive assumption would be that with less matter time moves faster sort of accelerating; so, as matter “evaporates” the process accelerates and converges on that number (or close it)?
Times for things like "age of the universe" are usually given as "cosmic time" for this reason. If it's about a specific object (e.g. "how long until a day on Earth lasts 25 hours") it's usually given in "proper time" for that object. Other observers/reference frames may perceive time differently, but in the normal relativistic sense rather than a "it all needs to wind itself back up to be equal in the end" sense.
The local reference frame (which is what matters for proton decay) doesn't see an outside world moving slower or faster depending on how much mass is around it to any significant degree until you start adding a lot of mass very close around.
Would this take into account IDs generated by objects moving at relativistic speeds? It would be a right pain to travel for a year to another planet, arrive 10,000 years late, and have a bunch of id collisions.
I have to confess I have not actually done the math.
Oh no! We should immediately commence work on a new UUID version that addresses this use case.
Maybe the definitions are shifting, but in my experience “on point” is typically an endorsement in the area of “really/precisely good” — so I think what you mean is “on topic” or similar.
Pedantry ftw.
:-)
The answer is 42. Have it from good source!
Hanson's Grabby Aliens actually fits really well here if you're looking for some math to base off of.
> A more reasonable upper limit might be to assume that every atom in the observable universe will get one ID (we assume atoms won’t be assigned multiple IDs throughout time, which is a concession). There are an estimated atoms in the universe. Using the same equation as above, we find that we need 532 bits to avoid (probabilistically) a collision up to that point.
This doesn't take into account that you will inevitably want to assign unique IDs to various groups of atoms (e.g. this microchip, that car, etc.). And don't even get me started on assigning unique IDs to each subatomic particle.
> This doesn't take into account that you will inevitably want to assign unique IDs to various groups of atoms (e.g. this microchip, that car, etc.).
Sure it does. Those are not going to add up to a single extra bit.
Even every possible permutation of every single subatomic element in the universe? Even if we just consider atoms, at 10^80 atoms in the entire universe, there are (10^80)! possible permutations, which is many, many, many orders of magnitude larger.
And this isn't even counting sets that include multiples of the same item; once you get into that territory, there really is no upper bound.
New atoms form all the time, either through fusion or fission. The latter is happening right now all around you- either from potassium in plants breaking down, to radon gas that sept up from the ground, to carbon itself. All of these have unstable isotopes with half lives short enough to have at least a little activity near you.
Given that constant change to the available combinations of sets, it would seem that a truly capable system would need to be practically infinite, no?
So UUIDv∞ will be at least 536 bit long?
And with group IDs, timestamp, etc. - 1024 bit long?
>And don't even get me started on assigning unique IDs to each subatomic particle.
If a neutrino oscillates between flavors, does it get 3 IDs? Or does it get a new ID with each oscillation?
Thankfully, we only need one electron ID at all.
For the uninitiated: https://en.wikipedia.org/wiki/One-electron_universe
A more realistic estimate of the total number of addressable things should take into account that for anything to be addressable, its address should be stored somewhere at least once.
If it takes at least Npb particles to store one bit of information, then the number of addressable things would decrease with the number of bits of the address.
So let's call Nthg the number of addressable things, and assume the average number of bits per address grows with Nb = f(Ntng).
Then the maximum number of addressable things is the number that satisfies Nthg = Np/(Npb*f(Ntng)), where Np is the total number of particles.
One could take anything like a cell and split it into genes, molecules, atoms, sub-atomic wave functions (with infinite value range) and take time which can be split into another infinite entity say even within a finite interval. How does this analysis account for that?
I could split this object into 10^500 or 10^50^500^5000 etc., with imagination being the limit.
These values Id'd at whatever imaginable resolution are far from practically useful but at a cosmic scale, there is no telling what is a useful value?
So this framework seems to be more limiting because we define a resolution ?
Heh. I once had to make an argument that 256 bit randomly assigned identifiers are good enough without explicit collision checking. People wanted me to add complex and expensive collision checks.
My argument was the 2^256 actually approaches the number of atom in the observable universe (within 1 to 3 orders of magnitude), and that collisions are so unlikely that we'll have millions of datacenter meltdowns first (all assuming we have a good source of random numbers, of course). In the end I convinced everybody that even 128 bits are good enough, without any collision checking required.
I thought my arguments was clever, but this is so much better. :)
Nah, it's much easier than that.
The total amount of computer data across all of humanity is less that 1 yottabyte. We're expected to reach 1 yottabyte within the next decade, and will probably do so before 2030. That's all data, everywhere, including nation-states.
The birthday paradox says that you'll reach a 50% chance of at least one collision (as a conservative first order approximation) at the square root of the domain size. sqrt(2^256) is 2^128.
Now, a 256 bit identifier takes up 32 bytes of storage. 2^128 * 32 bytes = 10^16 yottabytes. That's 10 quadrillion yottabytes just to store the keys. And it's even odds whether you'll have a collision or not.
And if the 50% number scares them, well, you'll have a 1% chance of a collision at around... 2^128 * 0.1. Yeah, so you don't reach a 1% over the whole life of the system until you get to a quadrillion yottabytes.
Because you're never getting anywhere near the square root of the size, the chances of any collision occurring are flatly astronomical.
Great insights and visualisations!
I build a whole database around the idea of using the smallest plausible random identifiers, because that seems to be the only "golden disk" we have for universal communication, except for maybe some convergence property of latent spaces with large enough embodied foundation models.
It's weird that they are really under appreciated in the scientific data management and library science community, and many issues that require large organisations at the moment could just have been better identifiers.
To me the ship of Theseus question is about extrinsic (random / named) identifiers vs. intrinsic (hash / embedding) identifiers.
https://triblespace.github.io/triblespace-rs/deep-dive/ident...
https://triblespace.github.io/triblespace-rs/deep-dive/tribl...
Entity identity can be intrinsic. Why not consistency contracts?
Just past page 281 of Becky Chambers's delightful "the galaxy, and the ground within".
Man I love the series.Looks like this multispecies universe has centrally-agreed-upon path addressing system.
You should check out Vernor Vinge's A Fire Upon The Deep for more fun examples of how intra-galactic communication would be labeled, with routes & such.
In fact, it is right here in my stack of to-reads! Picking it up now due to your recommendation. Cheers!
From this book in particular, I love the scene with everyone sitting around talking about how horrifying the concept of cheese is. The rest of the quartet is wonderful, with the second book (A Closed and Common Orbit) being the MVP IMO.
The Dewey section and Elias omega encoding was fun, but it reminded me of Project Xanadu's tumblers[1] - a variable length dotted notion where each segment is unbounded.
Tumblers are modeled using transfinite numbers which makes me wonder: what are the similarities and differences between transfinite numbers and Elias omega encoding? I'm not well versed in either, so I expect it's either a question from ignorance or I may have a lot to learn. :)
1. https://www.artandpopularculture.com/Tumbler_%28Project_Xana...
I forget the context but the other day I also learned about Snowflake IDs [1] that are apparently used by Twitter, Discord, Instagram, and Mastodon.
Timestamp + random seems like it could be a good tradeoff to reduce the ID sizes and still get reasonable characteristics, I'm surprised the article didn't explore there (but then again "timestamps" are a lot more nebulous at universal scale I suppose). Just spitballing here but I wonder if it would be worthwhile to reclaim ten bits of the Snowflake timestamp and use the low 32 bits for a random number. Four billion IDs for each second.
There's a Tom Scott video [2] that describes Youtube video IDs as 11-digit base-64 random numbers, but I don't see any official documentation about that. At the end he says how many IDs are available but I don't think he considers collisions via the birthday paradox.
[1]: https://en.wikipedia.org/wiki/Snowflake_ID
[2]: https://youtu.be/gocwRvLhDf8
There also DRUUID: https://gist.github.com/bricss/53e5babedf44bf3ab71334c15102e...
> [1]: https://en.wikipedia.org/wiki/Snowflake_ID
Isn't this just the same scheme as version 1 UUID, except with half the bits? I guess they didn't want to dedicate 128 bits to their IDs.
That also looks like the widely used BSON ids, to anyone else interested
Getting the entire universe to agree on a single clock for creating timestamps sounds absurdly difficult. Probably impossible?
You don't need the universe to agree. You need your ID system to agree within a reasonable margin of error.
"Agreement" of time is probably nonsense, yeah. I realized after posting so I edited in the parenthetical, but as [3] notes, locality probably makes this less of a real issue.
Apparently with the birthday paradox 32 bit random IDs only allow some tens of thousands per second before collision chance passes 50%. Maybe that's acceptable?
[3]: https://news.ycombinator.com/item?id=47065241
The temperature of the cosmic microwave background can be used as a universal clock.
So can neutron star spin rates
Neutron star spins collectively can be used as a pretty accurate clock.
From real life we know that people prefer to have multiple anonymous IDs, or self-selected handles, either makes fully deterministic generation schemes moot.
Also, network routing requires objects that have multiple addresses.
Physics side of whole thing is funny too, afaik quantum particles require fungibility, i.e. by doxxing atoms you unavoidably change the behavior of the system.
> From real life we know that people prefer to have multiple anonymous IDs
There's nothing stopping a entity from requesting multiple IDs from one of the "devices"!
Specifying a CSPRNG as an entropy source to avoid collision is incorrect.
CSPRNGs make prediction of the next number difficult (cracking-AES difficulty) but do not add entropy and must be seeded uniquely otherwise they will output the same numbers. Unless the author is proposing having the same machine generate a single universe-scale list in one run.
Also “banning” ids that are all 1s or 0s is silly; they are just as valid and unique as any other number if you’re generating them properly. Although I might suggest purchasing a lottery ticket if you get an UUID with all settable bits as 1.
Banning 0s might be to avoid conflicts of with testing? Kind of like how you’d want to block logins with emails that have a domain example.com. Idk I’m grasping at straws
Fun read.
One upside of the deterministic schemes is they include provenance/lineage. Can literally "trace up" the path the history back to the original ID giver.
Kinda has me curious about how much information is required to represent any arbitrary provenance tree/graph on a network of N-nodes/objects (entirely via the self-described ID)?
(thinking in the comment: I guess if worst case linear chain, and you assume that the information of the full provenance should be accessible by the id, that scales as O(N x id_size), so its quite bad. But, assuming "best case" (that any node is expected to be log(N) steps from root, depth of log(N)) feels like global_id_size = log(N) x local_id_size is roughly the optimal limit? so effectively the size of the global_id grows as log(N)^2? Would that mean: from the 399 bit number, with lineage, would be a lower limit for a global_id_size be like (400 bit)^2 ~= 20 kB (because of carrying the ordered-local-id provenance information, and not relative to local shared knowledge)
The ATProto underlying BlueSky social network is similar. It uses a content-addressed DAG.
Each “post” has a CID, which is a cryptographic hash of the data. To “prove” ownership of the post, there’s a witness hash that is sent that can be proved all the way up the tree to the repo root hash, which is signed with the root key.
Neat way of having data say “here’s the data, and if you care to verify it, here’s an MST”.
Two ways to frame it:
Provenance is a DAG, so you get a partial order for free by topological sort. That can be extended to a compatible total order. Then provenance for a node is just its ordering. This kind of mapping from objects to the first N consecutive naturals is also a minimal perfect hash function, which have n log n overhead. We can't navigate the tree to track ancestry, but equality implies identical ancestry.
Alternatively, we could track the whole history in somewhat more bits with a succinct encoding, 2N if it's a binary tree.
In practice, deterministic IDs usually accept a 2^-N collision risk to get log n.
I’m going to vibe code an app that lets you register a computronium unique id (is that name taken?) I’ll corner the market.
I’m also going to devise a standard that arbitrarily breaks it into groups of hexadecimal digits of arbitrary length in the spirit of UUIDs, and reserve a prefix space for Planck-unit timestamps (computronium-ID-7) so that you can lexicographically sort your COMPID7s.
Man I got to get out in front of this.
The practical punchline buried in this analysis: at human scale, the real tradeoff isn't uniqueness vs collision risk — it's uniqueness vs legibility.
Pure random IDs are theoretically optimal but operationally hostile. When something breaks at 3am, you want the ID to whisper where it came from. That's why ULIDs embed timestamps, DNS is hierarchical, and git hashes are content-addressed. You're trading a negligible increase in collision probability for debuggability.
The article's proof that deterministic schemes can't beat linear worst-case growth is elegant. But at any scale where humans are in the loop, it doesn't matter — you're generating maybe 10^12 IDs total, not 10^120. The interesting design space is the middle: enough randomness for uniqueness, enough structure for humans.
Chiming in from the decentralized world - there’s an adversarial / cooperative dynamic in the assignment of these IDs - and the selection of parents, not discussed in the original. I think you could possibly get to sub linear by allowing a small number of cooperative nodes to assign new IDs.
On the contrary, having the right to assign IDs is powerful; on balance, to my mind the right thing to do is some sort of a ZK verifiable random function, e.g. sunspot-based transformations combined with some proof of ‘fair’ random choice. In that case, I think the 800 bit number seems like plenty. You could also do some sort of epoch-based variable length, where for the next billion years or so, we use 1/256 of the ID space, (forced first bit to 0), and so on.
The obvious solution is a system like IP addresses. Every system has an address like universe.galaxy.region.system or whatever, then the system is subdivided in whatever way is logical for that system.
That way you can route ships or data or whatever to a specific system in a logical way. Each system decides how to allocate addresses. Since most systems won’t have anything or anyone to care, something like NASA or registrars would just allocate a block to the system and give large things like planets an address.
> In order to fix this, we might start sending out satellites in every direction
Minor correction: Satellites don't go in every direction; they orbit. Probes or spaceships are more appropriate terms.
Maybe they meant at every inclination. ;)
Quite offtopic, but: I found UUIDs being overused in many cases. People then abused them to store data, making them effectively "speaking IDs" or "multi column indices".
Unless it's a key that needs to be sortable (e.g. insertion order) or a metric/descriptor of some kind, I'm not sure why UUID would be overused or inappropriate for use.
Random UUIDs are not compressible. They are also frequently stored as 38-character strings.
800 bits is an incomprehensible number of possibilities…yet tiny in comparison to the number of .gifs that could be drawn.
I'd propose using our current view of physical reality to own a subset of the UIID + version field if new physics is discovered.
10-20 bits: version/epoch
10-20 bits: cosmic region
40 bits: galaxy ID
40 bits: stellar/planetary address
64 bits: local timestamp
This avoids the potentially pathological long chain of provenance, and also encodes coordinates into it.
Every billion years or so it probably makes sense to re-partion.
As for coordinates, don’t forget galaxies are clouds of stars flowing around and interacting with each other.
That's the problem with address type of systems is that they expect the object at that location to always be at that location. How do you encode the orbital speed, radius of orbit for not just the object, but also the object it is orbiting will need the same info as it is also in motion, then that object's parent galaxy's motion. Ugh, now I need a nap to calm down a bit.
You could estimate when the object was labelled by the coordinates used.
But where is the Greenwich meridian for the Milky Way?
offset length
Total: 128bytesIt is interesting how much of our infrastructure relies on the assumption that 'close enough' is actually 'good enough' for uniqueness. When we move from UUIDs to things like ULIDs or Snowflake IDs, we are really just trading off coordination cost for a slightly higher collision risk that we will likely never hit in several lifetimes. Thinking about it on a 'cosmological' scale makes you realize how much of a luxury local generation is without needing a central authority. It is that tiny bit of entropy that keeps the whole distributed system from grinding to a halt.
>the assumption that 'close enough' is actually 'good enough' for uniqueness
i'm pretty sure it's "far enough" that makes it "good enough"
We will probably end up with something like each planet has its own local addressing, and the big router in the sky does NAT, each solar system has a router and so on.
I really love everything related to Cosmology but I always struggle with two contrary concepts that lead to paradox (for me) :
- Infinity : from school, we learn our universe is infinite.
- We often do calculation with upper limit like this one : 10^240. This is a big number butttttt it's not infinite you know. 10^240+1, 10^240+2...
So :
1. if it's infinite, why doing upper limit calculation ?
2. if it's limited, what is there outside that limit ?
Extremly paradoxal
but can you have an id for every id?
Note that they almost immediately contract from 'the universe' to 'the visible universe', which isn't the same thing at all.
It's observable universe, and that's the only thing that matters. Events outside the observable universe are causally disconnected. We will never interact with anything outside the observable universe. For all practical purposes, it's the same thing.
xhxxhxhxhxhxhxhx
I was going to read this, but it starts with an AI slop header image for no purpose, so I intuited that the article was similarly ill constructed.
Another blow to the "all electrons are the same electron" theory. Why have only 1 electron with so many possible ids /s
The best way to solve this is not to, and just giving up on the idea of identification.
If you have an infinite multiverse of infinite universes, and perhaps layers on that, with different physics, etc., you can’t have identity outside of all existence.
In Judaism, one/the name of God is translated as “I am”. I believe this is because God’s existence is all, transcending whatever concepts you have of existence or of IDs. That ID is the only ID.
So, the cosmic solution to IDs is the name of God.
which name of god though - there are hundreds, and were right back at the same place of struggling to come up with a unique identifier.
gotta be careful:
https://hex.ooo/library/nine_billion_names_of_god.html
So we need to be careful. We do not know what happens after we assign all UUIDs.