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According to Wikipedia, solipsism is the philosophical idea that only one's own mind is sure to exist. In 1993, Cynthia Dwork and Moni Naor proposed the idea that one could use proof-of-work to combat spam e-mail. The same concept was later adopted by Bitcoin.

The idea behind proof-of-work is simple. Using a cryptographic hash function (in Bitcoin's case SHA-256) we have to find an input that produces an SHA-256 hash with some agreed special property. Since SHA-256 is presumed to be a one-way function there's no better way to find such an input than to use brute force to generate inputs and see if their SHA-256 hash satisfies the given property. The expected amount of trial-and-error required to produce a hash with the desired property is inversely proportional to the proportion of hashes satisfying the property.

In Bitcoin's case the desired property is that the calculated hash, interpreted as an integer in little-endian byte order, is below some given threshold. In the case of Bitcoin the number of SHA-256 calculations required to generate such hashes has been more than 10^26 in some cases. For example, if you take the number 98468625188936598445757615969686194678278100228635623545838523999870405803634, represent it in big-endian binary format, calculate the SHA-256 and reverse the bytes, you get the 256-bit hexadecimal number 00000000000000000000011246f099d94f91628d71c9d75ad2f9a06e2beb7e92, which has 87 leading zero bits. With a high probability, finding this number has taken more than 2^87 ≈ 1.5*10^26 SHA-256 computations.

You can find a Python script and a few more examples here.

What has all this to do with solipsism? The fact that we can name such numbers shows that there are computational resources capable of producing them (i.e. calculating more than 10^26 SHA-256 hashes). On the other hand such extreme amounts of computation are beyond the capability of human mind by about 20 orders of magnitude. Even if all 7.5 billion humans on Earth were to compute SHA-256 hashes at the rate of 1 per second (1 per day is more realistic), it would still have taken more than 400 million years to produce the number above. Thus we can conclude that vast computational resources must exist outside one's mind and that solipsism is false.

About assumptions: It is not rigorously known that SHA-256 is computationally hard to invert. In particular, proving that one-way functions exists would show that P!=NP.

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    Your argument seems circular. If the basis for refuting solipsism is that vast computational resources must exist outside one's mind because it would take 7.5 billion humans on Earth with minds, such as we take them to be, too long, then we are concluding existence of other minds from assuming... their existence, and much more about them besides. A solipsist need not take seriously any conclusions about limitations of her own mind inferred from observing illusory "other humans". – Conifold Nov 17 '17 at 19:35
  • I'm not actually trying to prove the existence of other minds, but rather the existence of computational resources that are able to produce Bitcoin blocks (that are really just numbers satisfying certain conditions). – Ville Hakulinen Nov 17 '17 at 19:45
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    Ok, but according to a solipsist the entire universe is a creation of her mind, so why would adding to that Bitcoin's computational resources make any difference? – Conifold Nov 17 '17 at 20:01
  • If you watch some Youtube videos put out by the Bitcoin traders, you'll see that solipsism is quite common. – user4894 Nov 17 '17 at 21:53
  • Here's a guy who computed SHA-256 by hand. In theory humans could mine bitcoin with pencil and paper. Just slowly. righto.com/2014/09/mining-bitcoin-with-pencil-and-paper.html – user4894 Dec 19 '17 at 20:19
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Solipsism is the theory that only I exist - not that only my mind is sure to exist.

The question assumes the falsity of solipsism in order to refute it. The solipsist does not grant that there are 7.5 billion other people - or even that there is one other person. S/he can hold that the scenario, possibilities and impossibilities envisaged are merely your own conceptions - or rather his or hers since only he or she exists. Or, strictly, mine since only I exist and this exchange is taking place purely in my own mind or head.

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The problem here is the concept of existence.

If existence means "occupation of space" you don't need a proof of work. You can just use any proof of occupation to validate existence. If existence means working (as in cogito ergo sum) then you can use a proof of work. Anyway, there are trivial proofs of work that can overcome services using proof of work validations like greylisting, then proof of work is not a perfect test. So, a deeper problem exists with defining existence for different types of things: you cannot apply the same test to a rock, a galaxy, an atom, an idea, a software application, etc. In consequence, commonly there are several different concepts of existence.

The solipsist concept of existence is related to the systems theory (didn't existed before 1900). Systems are a wide concept that describes the mechanics of all imaginable groups of related parts. Systems are the supra-group of things, concepts, ideas, objects, entities, beings, etc. A cell is a system and has certain similarities to an equation, like having inputs, outputs, and a mechanism of causality that gives a sequence to inputs and then outputs. You interact with them if you provide an input and receive a different output. There's not so much written about generic/systemic interaction, this is a growing discipline, but you can take a look to my book for some ideas and references, check my profile.

So, for solipsists, something exists if you can interact with it (esse est percipi). This is a better definition of existence, since it does not apply only to physical objects: it applies to all imaginable things, that is, systems. In consequence, we don't have different concepts of existence, depending on the domain of the term. So, for solipsists, a cell exists if you can interact with it in some way (for example, by discussing it with your teacher). We know that Einstein existed because he interacted with some people who interacted with others who interact with us (that's out of the scope of a proof of work). The center of the earth started existing since we got aware that the earth is a sphere. An idea exists if you can think about it, examinate it, correlate it with other ideas, etc. A planet does not exist until someone interacts with it in some way. And we interact in some way with that guy. If there are living beings of alternative dimensions walking on our planet, they will not exist until we find some way to interact with them. A box of chocolates can simultaneously exist and don't for two different people depending on how do they interact with it: if it's empty, some could tell that it doesn't exist. If you think on it, this means that existence is subjective, and even if shocking, that has sense.

Of course, the theory of systems didn't existed when Berkeley stated that esse est percipi. His ideas didn't belong to his time. In fact, even today, solipsism is usually qualified under pejorative terms.

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The pricing function says you can have the resource if you do the work.

Your question/argument says that solipsism is false because of computationally infeasible resources for bitcoin transactions.

That really has nothing to do with the definition of solipsism.

But I could agree with you, given a definition of self, that extended beyond the mind; If world were mind for the solipsist. Which is contrary to the accepted definition of solipsism as it exists today.

I would file your question as a research question. This site is not "for" research. It is "about" accepted facts in the literature; So you can get a quick answer that is verified. I hope you can appreciate that for what it is. I'm new to this site, and find it hard to distinguish between research and accepted fact for a variety of reasons; most notably the concept of progress.

  • If solipsism is true why care about the Earth? It is after all just a figment. And solipsism does not entail that one can do anything one wants, mere absence of the external world does not bring about complete control over one's own self. – Conifold Nov 17 '17 at 20:57
  • How do you know that "mere absence of the external world does not bring about complete control over one's own self."? By the definition of solipism you can't. I care about the Earth because it is my home. – user66136 Nov 17 '17 at 22:06
  • I do not need to know. I do not see any logical connection between the two, and I am not aware of a plausible argument to that effect. – Conifold Nov 17 '17 at 22:08
  • I don't see your point. – user66136 Nov 17 '17 at 22:39
  • @Conifold In the spirit of discussion, Can I ask your opinion about how solipsism views the world if it is only consisting of figments? I mean does it relate the world and mind using an argument similar along the lines of plausibe deniability – user66136 Nov 18 '17 at 16:57

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