Blockchainische Untersuchungen

Satoshi Nakamoto did not understand the "Byzantine Generals Problem," as is evidenced by the following: satoshi.nakamotoinstitute.org...

The proof-of-work chain is a solution to the Byzantine Generals' Problem.** I'll try to rephrase it in that context.

Let us first make it quite clear that, for 2n+1+m nodes (which vertices are simultaneously message-radiating "generals", message-reflecting or, in the case of faulty/malignant elements, transmitting or absorbing witnesses, and message-absorbing lieutenants), no "do gooder consensus", in the case interesting us to be understood as meaning that truth is what "good guys" *decide* it to be, can be ascertained unless the traitors/fomenters' contingent m isn't above n (the problem isn't a problem if n vanishes, because for evil to overcome good, it has to exist.)

Instead of a reductio ad absurdum we shall succinctly analyze i.e., slaughter the beast at hand and excise from within its innards, that is in the very question, its general solution.

We shall as well discover that substituting reason for faith, computation for trust, complicates, slows down, hampers, squanders, pollutes i.e., is, in a word, inefficient.

Imagine a multitude of nodes and let one of them, x, ask a question to some other, say y. Now if x were endowed with simple and despised faith it would accept y's answer confining annoying solicitations to a singleton, but this age is a haughty and voluble one, we ask for proofs even of axioms, blind as we are to the fact that we still are giving our credence to authorities or, as is the case for Bitcoin, to the hardware, to the software, to the network supporting it, if only they belittle faith. Such a x won't be satisfied with y's answer but will have to beg all the other nodes for what is it that y told them in response to x's question. Far from being done with it, taking a majority of the reports, it will have to, for the same reason, ask, for any z, all the remaining nodes what is it that z told them that x said. As you can judge, we have an infinite regress in the making, "fortunately" enough for infidels, they are to be held in the chains of finitude and therefore these sequences can be terminated. How deep such a pit need be? If it were to heap n "good" nodes t0, t1, ... tn-1 where t0 would be y, then if there still remained, in addition to x, taken as "good" for argument's sake, n other "good" nodes, and at most n "bad" ones, then lo, x would find itself in the pleasant position of agreeing with any of the n other remaining "good" nodes concerning tn-1's witness, this because tn-1 being "good" will send the same message to all the askers, and so will "reflect" x, mirror as it were, or the n remaining "do gooders." Hence when x will ask these n "good" nodes "what is it that tn-1 said that ... t1 said that t0 vomited?," it will find itself sprinkled with the same droplets of noisome diarrhea that tn-1 itself benefitted it with, and therefore whatever the no more than n "false witnesses" told x in regard to t0, ... tn-1, it will have a majority of n+1 equal votes vs. less than or equal to n diverging ones. Now that, if you take some time to think instead of indulging in prolefeed such as that ridiculous but nonetheless pernicious "Lucifer" TV show or some pr0n, belongs to the species of worse scenario and by that we mean that the maximum number of "goodies" is chained for n badies, beyond which disagreement among the nice vertices is not impossible. Now picture yourself tn-1 as "bad", shall the unchained n+2 "good" nodes agree on t0, ... tn-1? Not necessarily, as a counterexample shows: tn-1, being a contrarian, isn't bound to send the same datum to all nodes, let it report i to x, j to a "good" w and any random heterogeneous, all different from i and j, garbage to all the others, where i and j are different. Now x and w will ask all the remaining nodes, whether "good" or "bad" they have no inkling of, what tn-1 told that ... t0 said. The evil nodes may very well bombard x with i all the while assuring w of j. For x this state of affairs will result in his assigning i to t0, ... tn-1 seeing that it has a majority of n occurrences of i against n+1 votes, no n of which are equal but w will conclude j for the same t0, ... tn-1. And yet, although the "good" nodes will differ on t0, ... tn-1 with an evil tn-1 appendage, they still will agree on t0, ... tn-2, because they will value the well-ending t0, ... tn-1 equally which is, for each "goodie", n+1 identical decisions against n on bad-ending t0, ... tn-1. The cases where t0, ... tn-1 is mongrelous i.e., with both "good" and "evil" ti, i < n-1 are easier because there are fewer free fomenters. This procedure ensures hivemindeness on the "good" nodes' part: they'll decide on the same value for t0, ... tn-2, for t0, ... tn-3 and so on until they come to consensus on t0 that is y.

CaseOP1=node+1+*=flagx1+star@++ or0

Yes?

The belabored *digression* that follows S. Nakamoto's d'entrée de jeu conclusion, for such it proves to be as far as the object of the exchange is concerned, and which is purported to cast the Blockchain into the BG's framework, is not even coherent viz.:

"It has been decided that anyone who feels like it will announce a time, and whatever time is heard first will be the official attack time.

**The problem is that the network is not instantaneous, and if two generals announce different attack times at close to the same time, some may hear one first and others hear the other first.**" continued with "**They use a proof-of-work chain to solve the problem.**"

How? "Once each general **receives whatever attack time he hears first**, he sets his computer to **solve an extremely difficult proof-of-work problem** that includes the attack time in its hash."

This to my mind looks like a rather silly petitio principii.

"The proof-of-work is so difficult, it's **expected to take 10 minutes of them all working at once before one of them finds a solution.**"

So, for them to solve the problem of agreeing on a concerted-attack time against the King's WiFi password, they find no better than duplicating that same problem (only postponing it and risking the attack's failure).

"Once one of the generals finds a proof-of-work, he broadcasts it to the network, **and everyone changes their current proof-of-work computation to include that proof-of-work in the hash they're working on.

** If anyone was working on a different attack time, they switch to this one, because its proof-of-work chain is now longer."

He who wrote the above doesn't have a clear idea of what a Blockchain is (or else is willingly obfuscating it for evident reasons), let alone the BGP: why should the less lucky, or as is often the case in practice, not as powerful as the de facto general, lieutenants decide to prolong said general's already hashed and received block thereby having to restart hashing their own, now altered blocks because of their overwriting the parent block's "address" i.e., hash field? (And of course, a node can still receive a more recently solved block, and not on the same branch, than an much older one.) Why should the would be generals not compete against one another instead, growing parallel block branches? After all it is significantly a matter of luck for one to bump into an adequate block-hash. The BGP's solution doesn't define "good" as "most powerful", but demands that the good nodes be more than twice as numerous as the bad ones. The Blockchain is an euphemism for "Strength is Law", the Law of the Jungle.

The Blockchain is an interesting *antisolution* to the BGP, a minority of nodes (i.e., violating the indispensable to any solution minimum ratio of 2n+1:n of "goodies" to "badies") can very well "speak" a longest branch of the Blockchain tree (for it is a *tree*, not a sequence as it appears to be presenting itself) and thereby impose their truth, their history, their law.

It is not difficult in the least to graft and grow a longest "bad future" on the Timechain: www.wingclips.com...

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a reply to: Sheshbazzar

This is one of those threads I seriously think twice about responding to.

A 51% attack becomes easier as the computation resources are concentrated.

Proof of Work is dead in the water and doesn't scale as it currently exists. Even Ethereum is suffering from massive gas fees at it's current level of use. BTC was an incredible achievement, just like the telegraph. Bigger things are coming.

Distributed ledgers and concensus networks are already faster, cheaper, and less energy intensive than BTC. Crypto still has limited adoption, but it's coming.

a reply to: Sheshbazzar


Where to begin....

The 4 hours window having been exceeded, I have to "edit" the OP here:

"Such a x won't be satisfied with y's answer but will have to beg all the other nodes, [call them z], what is it that y told them in response to x's question. Far from being done with it, taking a majority of the reports, x will have to, for the same reason, ask, [for any such z, all the remaining nodes what is it that z told them that y said it that it said to x]".

I'm sorry, the truth is, the solution of the BGP, its proof of correctness, is difficult to formulate.

a reply to: Sheshbazzar

It doesn't matter. Bitcoin doesn't have to depend on millions of transactions a second.

Unless they upgrade to smartchain , they'll never fix the problem using their code.

Projects utilizing sidechain and wrappable tokens have already solved the issue.

Now they can just wrap whatever they want and voila....million transactions/sec...and the bonus of dApps and deFi to boot.

F2pool practically governs BTC right now. Go look at the pump and dumps....outdated.

PoS

The tech is about to explode...

a reply to: MykeNukem

The Blockchain is the work of a genius. It is evil, it devours real goods (GPUs, electricity hence coal, wood, rivers, rare earth el. etc.) for nothing. David Kleiman, its inventor I suspect, paid with his life.

Worthy of death is him who invests in cryptocurrencies: www.pcmag.com...

The Blockchain is an altar, it sacrifices reality, the ascending smoke of which is its virtualization. The cloud.

The Saint Covid vaccine means Smart Dust chain shackles: patentscope.wipo.int...

666.

Interesting...

This is definitely one very informative thread to a complete ignoramus in the field of so-called crypto-"currencies".

If I got it right... Bitcoin was invented (by the NSA, would be my guess) to solve the problem of distributed searching for all the prime numbers in the given interval (of roughly 21 million of them being expected to be found in that interval), while Etherium was invented (again by the NSA) when they started receiving fake solutions invented by hackers who figured out how to fake such "solutions" in order to sell them (to any idiot on the crypto market) as genuine ones?

That same problem (of trust and verification), that Etherium was supposed to solve, is now being exacerbated by the fact that other state actors (Russia, China) have joined in all the fun by trying to both replicate NSA's initial success (the actual, genuine prime numbers the NSA managed to get their hands on before the whole thing went to sh*t), and also trip the NSA all over itself by introducing increasingly genuine-looking fake solutions for the NSA to incorporate into its encryption schemes, thus making the NSA create weak, easily-crackable engrams.

More or less something like that? I'd really appreciate if somebody corrected any misunderstandings on my part.

As for the Byzantine's General Problem... this is definitely the first time I've heard about it, but I can see... the problem with that problem.

Actually, I can also see that the problem is not solvable even in its simplest form of the most basic 2-node graph, where one of the nodes is you, and the other node is... not you, and therefore, not trustworthy, regardless of whether that node is designed to returns true or false answers, or worse, a random distribution of both, because it is not (even in theory) possible to determine which it is without actually verifying each and every answer by oneself (i.e. it may have given you just enough true answers to deceive you into declaring it trustworthy).

So, if the goal is to distribute a job between two nodes (one being you, and the other being not-you), the only way to be absolutely certain that each and every answer is true is by verifying each and every answer by oneself... which is not the same as doubling the whole work (doubling the time needed to finish the work), but actually worse than merely doubling the work (due to the time overhead involved in communicating and handling/verifying all those untrustworthy answers).

Introducing more than 2 nodes in the above example graph merely unnecessarily complicates the problem, because any given graph, of any arbitrary complexity, in regards to this particular problem can be reduced to an (the only possible) equivalent 2-node graph (of you and not-you nodes).

Again, I'd very much appreciate if somebody corrected any misunderstandings on my part.

originally posted by: Sheshbazzar
a reply to: MykeNukem

The Blockchain is the work of a genius. It is evil, it devours real goods (GPUs, electricity hence coal, wood, rivers, rare earth el. etc.) for nothing. David Kleiman, its inventor I suspect, paid with his life.

Worthy of death is him who invests in cryptocurrencies: www.pcmag.com...

The Blockchain is an altar, it sacrifices reality, the ascending smoke of which is its virtualization. The cloud.

The Saint Covid vaccine means Smart Dust chain shackles: patentscope.wipo.int...

666.

It may in fact be what the Beast system is built on.

It has all the properties that are required.

It will definitely replace the internet in the next 20 years.

I just do the tech and code.

People are evil, not things.

originally posted by: Sheshbazzar
The Blockchain is the work of a genius. It is evil, it devours real goods (GPUs, electricity hence coal, wood, rivers, rare earth el. etc.) for nothing. David Kleiman, its inventor I suspect, paid with his life.

After giving it some thought, and having been a software designer myself (a dying profession in a world where uneducated coding monkeys are valued more than people with university degrees), I will have to partially agree with these observations.

The inventor of Bitcoin was definitely either:

a) An Evil Genius who intended to do exactly what crypto "currencies" are doing right now (wasting unimaginable amounts of irreplaceable resources and energy, swallowing them all into a black hole of nothingness), or

b) A complete moron (or a math monkey in this case) who thought that because he wrote a program that spat random numbers between 0 and 99, and which was supposed to stop when it spat every single number in that range, the program would end its execution in exactly 100 steps

As any programmer who's ever worked with random functions knows very well, such programs are actually unbounded in time, and can (with an extremely low probability) take literally forever to finish.

If Bitcoin was designed to distribute the search for prime numbers in the given range by having all those bazillions of crypto "miners" actually test exactly the same numbers in that range over and over again (with some numbers possibly being repeatedly tested even millions of times), then such a search may take (now with not-so-extremely-low probability) literally forever to finish.

In other words, if the non-distributed version of the task should've taken only 6 months to complete with a centralized, trustworthy hardware, we really shouldn't be surprised to find that same task, in a distributed (and unbelievably crappy) form, still running 120 months later... and with its end nowhere in sight.

... which gives me an interesting idea to ponder on.

Since whoever invented Bitcoin must verify each and every answer for correctness (by either repeating the same process of testing, or by comparing every received answer to all the previously verified and memorized answers), is it possible to crash the whole crypto "currency" system (Bitcoins, Etherium, and all the rest of that garbage) by flooding it with intentionally false "solutions"?

It would be like printing fake money bills on a home printer, but infinitely easier, since 0s and 1s cost virtually nothing. And the whole thing would not even be about spending any of that fake "money" (and getting filthy rich in the process), but about crushing the system by making it waste all that processing power and time on literally nothing... or, more like, nothing^2 (squared).

a reply to: clusterfok

NSA? Perhaps the CIA, but I don't think so. Dave Kleiman/Craig Wright are perhaps mere frontmen, but they who chose them, if flesh and and blood, would have to have received incorporeal suggestions (demons) because the scheme behind the Blockchain, how it views the world from the coins' perspective, the tree like structure of both the manifold of blocks (i.e., the Blockchain) and of each coin, and the very choice of the "frontmen" Kleinman/Jesus and Wright/Satan is very well thought. (A coin is a tree of "steps", a step is a user having owned said coin, if the coin's tree isn't degenerate i.e., has branches, then the coin has been double spent. The blocks gather such "steps" from coins and serve to prevent double spending. More technically, a coin's step is a "signature" as understood in asymmetric key cryptography, for user "x" to give user "y" a coin "z", x takes a step from the tree of steps z, one saying that x received the coin, adds a public key of y, fuses these data by hashing them and "decrypts" the hash with x's private key. Then, because the system is decentralized, it broadcasts the step it just built to all the users. Meanwhile, all the users, if we're not lying about our being decentralized, should be accumulating such steps in blocks, carefully avoiding to to put in the same block steps with a common source but different destinations: this is the double spending countermeasure. How are blocks closed? They are closed by finding a hash of theirs i.e., a numeral, a n-bit sequence, satisfying a certain criterion which is the length of its zero prefix. This prefix grows with time, and thus valid hashes are rarefied because all hashes are of length n: there are twice as many valid hashes with a i-bit zero prefix than there are with a i+1-bit one. When an user manages to close/baptize a block with a valid hash, it broadcasts it to all the users. How is a block node connected to its parent node in the Blockchain tree? Each block contains the name or number i.e., hash of its parent. There aren't, in practice, so many blocks for there occurring hash collisions.)

You are right, decentralization replicates entities, each one being the whole world except at a lower resolution in general (processors for example, they are miniature computers, with their memory i.e., registers and cache etc.). Leibnizian Monadology, they need no windows, they have their images.

Faith is the antithesis of reason (computation), it despises/doesn't rely on verification.

(A ledger is a longest branch of a Blockchain tree of blocks, a longest neck of a dendral hydra. And each user has his own variant, there is no Ledger nor Blockchain, only hopefully similar enough ledgers. The blochains are teraphim, each one monad's household idol.)

a reply to: Sheshbazzar

Well you lost me at 2n+1+m nodes.

Nonetheless seems interesting.

Whats "the Byzantine Generals' Problem"?

Edit: Googled it, i knew it rang a bell somehow.

a reply to: clusterfok

Concerning prime numbers, I think those in the know can decide very quickly, and economically, whether any integer is a prime or not. Cryptography is for the lewd masses.

What is searched for are not even pretty primes, much worse: mere hashes with n leading 0s. And yes, officially one brute forces the task: it is an exhaustive search. Centralized cliques are of course tacitly encouraged to divide the range of the search among the members, each one having a smaller one to look into.

The blockchain can be disrupted by a user able to spit blocks/find admissible hashes faster than the other users, growing a longest branch of the Blockchain tree.

a reply to: clusterfok

Exactly, there is no solution to the 2-node problem, nor to the 3-node one.

Here, perhaps counter intuitively, you have to add nodes to make it work: the 4-node problem is solvable provided that there is at most one "ill behaved" node. (Generally, for a n-node BGP problem to be solvable, there must be strictly less than n/3 "evil nodes" that is n must be >= than 3m+1, m being the number of evil nodes.)