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> required to use powerful and energy-hungry GPUs to solve a complex mathematical problem. No mathematical problem is getting "solved". It is much more akin t

> required to use powerful and energy-hungry GPUs to solve a complex mathematical problem. No mathematical problem is getting "solved". It is much more akin to playing the lottery: Entirely random numbers are being tried out, by sending them through an energy-intensive algorithm (being energy-intensive is the algorithm's only purpose in proof-of-work), until what comes out is less than another number. That other number is chosen according to the desired "difficulty", it has no significance beyond that. The algorithm is literally meant to spend energy, i.e. the outcome of the computation has no meaning by itself. This also means that proof-of-work cryptocurrencies actively counteract any advances to make the computation more efficient: The "difficulty" will just be adjusted up until the efficiency gain is canceled out. Proof-of-work cryptocurrencies are inefficient by design.

Banana699 4y ago
This is a lot of words to say that PoW involves an inverse-hash problem being solved. Inverse-hash is a mathematical problem. Finding the nonce is solving it.
- mondoveneziano 4y ago
  I was explaining in layman's terms.
  - khazhoux 4y ago
    Layman’s explanation: POW works by solving a complex mathematical problem. :-)
    - pavlov 4y ago
      It’s not the layman’s explanation because the average person doesn’t encounter mathematical problems being solved by a brute force lottery. In high school math, problems are solved by choosing the right formula and plugging in the right variables. Throwing the dice trillions of times isn’t what people imagine when they hear “solving a complex mathematical problem.” That framing is designed to make PoW more acceptable to laypersons, as it sounds like the computation is useful or at least clever rather than intentionally designed to waste energy.
      - khazhoux 4y ago
        The average person doesn’t encounter mathematical problems -- full stop. They have no reference point between one algorithm and the next. Heck, I understand well how POW works, and even I think of it as solving a "complex mathematical problem"... the inherently difficult problem of prime factorization. Anyways, potayto potahto.
        bawolff 4y ago
        > Heck, I understand well how POW works, and even I think of it as solving a "complex mathematical problem"... the inherently difficult problem of prime factorization. ??? Factoring is not a common problem for proof of work. In fact im not sure how you could even make that work in a way that ensures participants arent cheating.
        khazhoux 4y ago
        All cryptography exploits the inherent difficulty of factoring integers. POW requires brute force precisely because the underlying hashing algorithms are built around large primes. This is, actually, how I layperson-explain cryptography: there’s no fast or easy way to take any huge number and know what two numbers mutiplied to make it, and this mathematical property is what makes (good) passwords hard to crack.
        bawolff 4y ago
        This is very not true. Only RSA is built around factoring. I suppose if you consider discrete log to also be factoring related, some other public key & key agreement algs are also. Hash functions and symmetric algorithms are not based around factoring.
        tsimionescu 4y ago
        That is simply not how cryptographic hashes work. They have nothing to do with primes, and having a quick way to factor large numbers would do nothing to impact the security of the PoW part of Bitcoin (I believe it may affect the security of your wallet, though, but that is an entirely different attack). Note that even being able to quickly reverse the hash function for Bitcoin wouldn't do anything to the PoW security. The only thing that matters for PoW as implemented in Bitcoin is that there is no way to predict the value of the hash of a block + nonce faster than computing the hash. This doesn't rely on integer factorization difficulty in any way, it simply relies on a construction that uses many one-way functions.
  - bawolff 4y ago
    Why are we explaining in layman's terms on hacker news? Maybe i'm being pretensious, but surely we all know what sha256 is. Its used pretty constantly everywhere, long before bitcoin was a thing.
- osigurdson 4y ago
  Here is how I explain it to people: Imagine a page of a book, for each letter a-z, assign a number to it (a=1, b=2, .. , z=26). Compute the sum of all of the letters on the page but reset back to zero when 100 is reached (i.e. 97 + 5 = 2). The resulting number is a kind of signature for the page. Changing a letter would result in a different sum. At this point, people usually understand the utility and irreversible nature of it but quickly realize that many pages could have the resulting signature. It is a fairly easy leap of faith for most people to accept that there could be much more sophisticated algorithms that 1) use a bigger number for the signature and 2) take position into account and 3) result in very different signatures with tiny changes in input. This is usually sufficient for anyone to understand what is meant by a hash. Finally explain that the hash must have a certain pattern to it (like end in a zero for example). If the hash of our "page" does not have this pattern, add another small gibberish word to the end and try it again. Keep trying until a hash with the expected pattern is found (and there is your Bitcoin). The suggestion that a mathematical problem is being solved (while not completely inaccurate) sounds a bit more elegant in my opinion than what is really going on. It is really more like guessing (not that it really matters).
  - jrm4 4y ago
    I definitely think it matters. The metaphor of "some moron pulling a slot machine over and over and over" (which is what I use) is more accurate and I think better represents what's actually happening than something like "solving," which evokes the image of smart person (or machine) sitting down and using their brain to discover useful information. When you say "solve" it implies that the information that is produced by the process is inherently valuable.
    - NiloCK 4y ago
      A lot of textbook exercises begin with a prompt like "solve for x", where x has no existence outside the scope of each given exercise. The information that is produced has no inherent value, but I'd be surprised to hear many people object to this usage of "solve".
    - hunter-gatherer 4y ago
simonebrunozzi 4y ago
You're nitpicking. Poster was trying to explain things in a simple way. Side question: what about your username? I live in Venezia and I'm curious now.
- pixelbro 4y ago
  It's not nit-picking. A layman presented with this explanation might get the impression that a "problem" is being "solved", which implies there is some utility to the PoW algorithm, rather than energy being wasted for the sole purpose of proving that energy has been wasted. In fact, even the word "Work" in "Proof of Work" implies the same. Proof of Waste would be a much more apt description of what is actually happening.
WFHRenaissance 4y ago
Eh, a mathematical puzzle is being solved via brute-force. My intent was to explain briefly that the problem/puzzle is by nature computationally-intensive to the extent that brute-force is the most efficient way to solve/complete it.
- dodomodo 4y ago
  But the whole usage of the math puzzle is that you have to solve it using brute force, If there was a better way it won't be useful. So yeah the whole point is just guessing numbers not solving the puzzle.
- lottin 4y ago
  It's a guessing game. Referring to a guessing game as a complex mathematical problem is misleading.
  - shukantpal 4y ago
    False. The problem is so complex we have to resort to guessing / brute force to solve it; if it's so easy, give me a closed-form solution so I can become rich.
    - Josde 4y ago
      While that is true, I think the point that other users are trying to make is that wording it as "a complex mathematical problem being solved" makes it look like that work is doing something useful when it really is not.
      - lottin 4y ago
        It's worse than that, they're aren't solving anything at all. They're taking part in a lottery, in which participants have to guess a number, and the winner gets to update the ledger. Nobody is solving complex mathematical problems.
        4y ago
jxi 4y ago
that’s like saying doing algebra problems isn’t “solving” any real world problems. it is solving in the mathematical sense.
tromp 4y ago
What you describe is just one particular (although by far the most common) Proof-of-Work algorithm called HashCash. There are several others, such as Cuckoo Cycle, in which one must find a fixed length cycle in a huge random graph, an obvious mathematical (graph theory) problem [1]. [1] https://cryptorials.io/beyond-hashcash-proof-work-theres-mining-hashing/ https://cryptorials.io/beyond-hashcash-proof-work-theres-min...

Banana699 4y ago

This is a lot of words to say that PoW involves an inverse-hash problem being solved. Inverse-hash is a mathematical problem. Finding the nonce is solving it.

mondoveneziano 4y ago
I was explaining in layman's terms.
- khazhoux 4y ago
  Layman’s explanation: POW works by solving a complex mathematical problem. :-)
  - pavlov 4y ago
    It’s not the layman’s explanation because the average person doesn’t encounter mathematical problems being solved by a brute force lottery. In high school math, problems are solved by choosing the right formula and plugging in the right variables. Throwing the dice trillions of times isn’t what people imagine when they hear “solving a complex mathematical problem.” That framing is designed to make PoW more acceptable to laypersons, as it sounds like the computation is useful or at least clever rather than intentionally designed to waste energy.
    - khazhoux 4y ago
      The average person doesn’t encounter mathematical problems -- full stop. They have no reference point between one algorithm and the next. Heck, I understand well how POW works, and even I think of it as solving a "complex mathematical problem"... the inherently difficult problem of prime factorization. Anyways, potayto potahto.
      - bawolff 4y ago
        > Heck, I understand well how POW works, and even I think of it as solving a "complex mathematical problem"... the inherently difficult problem of prime factorization. ??? Factoring is not a common problem for proof of work. In fact im not sure how you could even make that work in a way that ensures participants arent cheating.
        khazhoux 4y ago
        All cryptography exploits the inherent difficulty of factoring integers. POW requires brute force precisely because the underlying hashing algorithms are built around large primes. This is, actually, how I layperson-explain cryptography: there’s no fast or easy way to take any huge number and know what two numbers mutiplied to make it, and this mathematical property is what makes (good) passwords hard to crack.
        bawolff 4y ago
        This is very not true. Only RSA is built around factoring. I suppose if you consider discrete log to also be factoring related, some other public key & key agreement algs are also. Hash functions and symmetric algorithms are not based around factoring.
        tsimionescu 4y ago
        That is simply not how cryptographic hashes work. They have nothing to do with primes, and having a quick way to factor large numbers would do nothing to impact the security of the PoW part of Bitcoin (I believe it may affect the security of your wallet, though, but that is an entirely different attack). Note that even being able to quickly reverse the hash function for Bitcoin wouldn't do anything to the PoW security. The only thing that matters for PoW as implemented in Bitcoin is that there is no way to predict the value of the hash of a block + nonce faster than computing the hash. This doesn't rely on integer factorization difficulty in any way, it simply relies on a construction that uses many one-way functions.
- bawolff 4y ago
  Why are we explaining in layman's terms on hacker news? Maybe i'm being pretensious, but surely we all know what sha256 is. Its used pretty constantly everywhere, long before bitcoin was a thing.
osigurdson 4y ago
Here is how I explain it to people: Imagine a page of a book, for each letter a-z, assign a number to it (a=1, b=2, .. , z=26). Compute the sum of all of the letters on the page but reset back to zero when 100 is reached (i.e. 97 + 5 = 2). The resulting number is a kind of signature for the page. Changing a letter would result in a different sum. At this point, people usually understand the utility and irreversible nature of it but quickly realize that many pages could have the resulting signature. It is a fairly easy leap of faith for most people to accept that there could be much more sophisticated algorithms that 1) use a bigger number for the signature and 2) take position into account and 3) result in very different signatures with tiny changes in input. This is usually sufficient for anyone to understand what is meant by a hash. Finally explain that the hash must have a certain pattern to it (like end in a zero for example). If the hash of our "page" does not have this pattern, add another small gibberish word to the end and try it again. Keep trying until a hash with the expected pattern is found (and there is your Bitcoin). The suggestion that a mathematical problem is being solved (while not completely inaccurate) sounds a bit more elegant in my opinion than what is really going on. It is really more like guessing (not that it really matters).
- jrm4 4y ago
  I definitely think it matters. The metaphor of "some moron pulling a slot machine over and over and over" (which is what I use) is more accurate and I think better represents what's actually happening than something like "solving," which evokes the image of smart person (or machine) sitting down and using their brain to discover useful information. When you say "solve" it implies that the information that is produced by the process is inherently valuable.
  - NiloCK 4y ago
    A lot of textbook exercises begin with a prompt like "solve for x", where x has no existence outside the scope of each given exercise. The information that is produced has no inherent value, but I'd be surprised to hear many people object to this usage of "solve".
  - hunter-gatherer 4y ago

simonebrunozzi 4y ago

You're nitpicking. Poster was trying to explain things in a simple way. Side question: what about your username? I live in Venezia and I'm curious now.

pixelbro 4y ago
It's not nit-picking. A layman presented with this explanation might get the impression that a "problem" is being "solved", which implies there is some utility to the PoW algorithm, rather than energy being wasted for the sole purpose of proving that energy has been wasted. In fact, even the word "Work" in "Proof of Work" implies the same. Proof of Waste would be a much more apt description of what is actually happening.

WFHRenaissance 4y ago

Eh, a mathematical puzzle is being solved via brute-force. My intent was to explain briefly that the problem/puzzle is by nature computationally-intensive to the extent that brute-force is the most efficient way to solve/complete it.

dodomodo 4y ago
But the whole usage of the math puzzle is that you have to solve it using brute force, If there was a better way it won't be useful. So yeah the whole point is just guessing numbers not solving the puzzle.
lottin 4y ago
It's a guessing game. Referring to a guessing game as a complex mathematical problem is misleading.
- shukantpal 4y ago
  False. The problem is so complex we have to resort to guessing / brute force to solve it; if it's so easy, give me a closed-form solution so I can become rich.
  - Josde 4y ago
    While that is true, I think the point that other users are trying to make is that wording it as "a complex mathematical problem being solved" makes it look like that work is doing something useful when it really is not.
    - lottin 4y ago
      It's worse than that, they're aren't solving anything at all. They're taking part in a lottery, in which participants have to guess a number, and the winner gets to update the ledger. Nobody is solving complex mathematical problems.
      - 4y ago

jxi 4y ago

that’s like saying doing algebra problems isn’t “solving” any real world problems. it is solving in the mathematical sense.

tromp 4y ago

What you describe is just one particular (although by far the most common) Proof-of-Work algorithm called HashCash. There are several others, such as Cuckoo Cycle, in which one must find a fixed length cycle in a huge random graph, an obvious mathematical (graph theory) problem [1]. [1] https://cryptorials.io/beyond-hashcash-proof-work-theres-mining-hashing/ https://cryptorials.io/beyond-hashcash-proof-work-theres-min...