Four Years Remaining

The following is an expanded version of an explanatory comment I posted here.

Alice's Diary

Alice decided to keep a diary. For that she bought a notebook, and started filling it with lines like:

Alice did her best to keep a meticulous account of events, and whenever she had a discussion with friends about something that happened earlier, she would quickly resolve all arguments by taking out the notebook and demonstrating her records. One day she had a dispute with Bob about whether she lent him $250 earlier or not. Unfortunately, Alice did not have her notebook at hand at the time of the dispute, but she promised to bring it tomorrow to prove Bob owed her money.

Bob really did not want to return the money, so that night he got into Alice's house, found the notebook, found line 132 and carefully replaced it with "132. Kissed Dave". The next day, when Alice opened the notebook, she did not find any records about money being given to Bob, and had to apologize for making a mistake.

Alice's Blockchain

A year later Bob's conscience got to him and he confessed his crime to Alice. Alice forgave him, but decided to improve the way she kept the diary, to avoid the risk of forging records in the future. Here's what she came up with. The operating system Linups that she was using had a program named md5sum, which could convert any text to its hash - a strange sequence of 32 characters. Alice did not really understand what the program did with the text, it just seemed to produce a sufficiently random sequence. For example, if you entered "hello" into the program, it would output "b1946ac92492d2347c6235b4d2611184", and if you entered "hello " with a space at the end, the output would be "1a77a8341bddc4b45418f9c30e7102b4".

Alice scratched her head a bit and invented the following way of making record forging more complicated to people like Bob in the future: after each record she would insert the hash, obtained by feeding the md5sum program with the text of the record and the previous hash. The new diary now looked as follows:

Now each record was "confirmed" by a hash. If someone wanted to change the line 132 to something else, they would have to change the corresponding hash (it would not be 1010 anymore). This, in turn, would affect the hash of line 133 (which would not be 8204 anymore), and so on all the way until the end of the diary. In order to change one record Bob would have to rewrite confirmation hashes for all the following diary records, which is fairly time-consuming. This way, hashes "chain" all records together, and what was before a simple journal became now a chain of records or "blocks" - a blockchain.

Proof-of-Work Blockchain

Time passed, Alice opened a bank. She still kept her diary, which now included serious banking records like "Gave out a loan" or "Accepted a deposit". Every record was accompanied with a hash to make forging harder. Everything was fine, until one day a guy named Carl took a loan of $1000000. The next night a team of twelve elite Chinese diary hackers (hired by Carl, of course) got into Alice's room, found the journal and substituted in it the line "143313. Gave out a $1000000 loan to Carl" with a new version: "143313. Gave out a $10 loan to Carl". They then quickly recomputed all the necessary hashes for the following records. For a dozen of hackers armed with calculators this did not take too long.

Fortunately, Alice saw one of the hackers retreating and understood what happened. She needed a more secure system. Her new idea was the following: let us append a number (called "nonce") in brackets to each record, and choose this number so that the confirmation hash for the record would always start with two zeroes. Because hashes are rather unpredictable, the only way to do it is to simply try out different nonce values until one of them results in a proper hash:

To confirm each record one now needs to try, on average, about 50 different hashing operations for different nonce values, which makes it 50 times harder to add new records or forge them than previously. Hopefully even a team of hackers wouldn't manage in time. Because each confirmation now requires hard (and somewhat senseless) work, the resulting method is called a proof-of-work system.

Distributed Blockchain

Tired of having to search for matching nonces for every record, Alice hired five assistants to help her maintain the journal. Whenever a new record needed to be confirmed, the assistants would start to seek for a suitable nonce in parallel, until one of them completed the job. To motivate the assistants to work faster she allowed them to append the name of the person who found a valid nonce, and promised to give promotions to those who confirmed more records within a year. The journal now looked as follows:

A week before Christmas, two assistants came to Alice seeking for a Christmas bonus. Assistant Jack, showed a diary where he confirmed 140 records and Mary confirmed 130, while Mary showed a diary where she, reportedly, confirmed more records than Jack. Each of them was showing Alice a journal with all the valid hashes, but different entries! It turns out that ever since having found out about the promotion the two assistants were working hard to keep their own journals, such that all nonces would have their names. Since they had to maintain the journals individually they had to do all the work confirming records alone rather than splitting it among other assistants. This of course made them so busy that they eventually had to miss some important entries about Alice's bank loans.

Consequently, Jacks and Mary's "own journals" ended up being shorter than the "real journal", which was, luckily, correctly maintained by the three other assistants. Alice was disappointed, and, of course, did not give neither Jack nor Mary a promotion. "I will only give promotions to assistants who confirm the most records in the valid journal", she said. And the valid journal is the one with the most entries, of course, because the most work has been put into it!

After this rule has been established, the assistants had no more motivation to cheat by working on their own journal alone - a collective honest effort always produced a longer journal in the end. This rule allowed assistants to work from home and completely without supervision. Alice only needed to check that the journal had the correct hashes in the end when distributing promotions. This way, Alice's blockchain became a distributed blockchain.

Bitcoin

Jack happened to be much more effective finding nonces than Mary and eventually became a Senior Assistant to Alice. He did not need any more promotions. "Could you transfer some of the promotion credits you got from confirming records to me?", Mary asked him one day. "I will pay you $100 for each!". "Wow", Jack thought, "apparently all the confirmations I did still have some value for me now!". They spoke with Alice and invented the following way to make "record confirmation achievements" transferable between parties.

Whenever an assistant found a matching nonce, they would not simply write their own name to indicate who did it. Instead, they would write their public key. The agreement with Alice was that the corresponding confirmation bonus would belong to whoever owned the matching private key:

To transfer confirmation bonuses between parties a special type of record would be added to the same diary. The record would state which confirmation bonus had to be transferred to which new public key owner, and would be signed using the private key of the original confirmation owner to prove it was really his decision:

In this example, record 284 transfers bonus for confirming record 132 from whoever it belonged to before (the owner of private key 6669, presumably Jack in our example) to a new party - the owner of private key 1111 (who could be Mary, for example). As it is still a record, there is also a usual bonus for having confirmed it, which went to owner of private key 4442 (who could be John, Carl, Jack, Mary or whoever else - it does not matter here). In effect, record 284 currently describes two different bonuses - one due to transfer, and another for confirmation. These, if necessary, can be further transferred to different parties later using the same procedure.

Once this system was implemented, it turned out that Alice's assistants and all their friends started actively using the "confirmation bonuses" as a kind of an internal currency, transferring them between each other's public keys, even exchanging for goods and actual money. Note that to buy a "confirmation bonus" one does not need to be Alice's assistant nor register anywhere. One just needs to provide a public key.

This confirmation bonus trading activity became so prominent that Alice stopped using the diary for her own purposes, and eventually all the records in the diary would only be about "who transferred which confirmation bonus to whom". This idea of a distributed proof-of-work-based blockchain with transferable confirmation bonuses is known as the Bitcoin.

Smart Contracts

But wait, we are not done yet. Note how Bitcoin is born from the idea of recording "transfer claims", cryptographically signed by the corresponding private key, into a blockchain-based journal. There is no reason we have to limit ourselves to this particular cryptographic protocol. For example, we could just as well make the following records:

This would be an example of a collective deposit, which may only be extracted by a pair of collaborating parties. We could generalize further and consider conditions of the form:

Here could be any predicate describing a "contract". For example, in Bitcoin the contract requires to be a valid signature, corresponding to a given public key (or several keys). It is thus a "contract", verifying the knowledge of a certain secret (the private key). However, could just as well be something like:

which would be a kind of a "future prediction" contract - it can only be evaluated in the future, once record 42000 becomes available. Alternatively, consider a "puzzle solving contract":

Finally, the first part of the contract, namely the phrase "Transfer bonus in record ..." could also be fairly arbitrary. Instead of transferring "bonuses" around we could just as well transfer arbitrary tokens of value:

The value and importance of such arbitrary tokens will, of course, be determined by how they are perceived by the community using the corresponding blockchain. It is not unreasonable to envision situations where being DA BOSS gives certain rights in the society, and having this fact recorded in an automatically-verifiable public record ledger makes it possible to include the this knowledge in various automated systems (e.g. consider a door lock which would only open to whoever is currently known as DA BOSS in the blockchain).

Honest Computing

As you see, we can use a distributed blockchain to keep journals, transfer "coins" and implement "smart contracts". These three applications are, however, all consequences of one general, core property. The participants of a distributed blockchain ("assistants" in the Alice example above, or "miners" in Bitcoin-speak) are motivated to precisely follow all rules necessary for confirming the blocks. If the rules say that a valid block is the one where all signatures and hashes are correct, the miners will make sure these indeed are. If the rules say that a valid block is the one where a contract function needs to be executed exactly as specified, the miners will make sure it is the case, etc. They all seek to get their confirmation bonuses, and they will only get them if they participate in building the longest honestly computed chain of blocks.

Because of that, we can envision blockchain designs where a "block confirmation" requires running arbitrary computational algorithms, provided by the users, and the greedy miners will still execute them exactly as stated. This general idea lies behind the Ethereum blockchain project.

There is just one place in the description provided above, where miners have some motivational freedom to not be perfectly honest. It is the decision about which records to include in the next block to be confirmed (or which algorithms to execute, if we consider the Ethereum blockchain). Nothing really prevents a miner to refuse to ever confirm a record "John is DA BOSS", ignoring it as if it never existed at all. This problem is overcome in modern blockchains by having users offer additional "tip money" reward for each record included in the confirmed block (or for every algorithmic step executed on the Ethereum blockchain). This aligns the motivation of the network towards maximizing the number of records included, making sure none is lost or ignored. Even if some miners had something against John being DA BOSS, there would probably be enough other participants who would not turn down the opportunity of getting an additional tip.

Consequently, the whole system is economically incentivised to follow the protocol, and the term "honest computing" seems appropriate to me.

Collecting large amounts of data and then using it to "teach" computers to automatically recognize patterns is pretty much standard practice nowadays. It seems that, given enough data and the right methods, computers can get quite precise at detecting or predicting nearly anything, whether it is face recognition, fraud detection or movie recommendations.

Whenever a new classification system is created, it is taken for granted that the system should be as precise as possible. Of course, classifiers that never make mistakes are rare, but if it possible, we should strive to have them make as few mistakes as possible, right? Here is a fun example, where things are not as obvious.

Consider a bank, which, as is normal for a bank, makes money by giving loans to its customers. Of course, there is always a risk that a customer will default (i.e. not repay the loan). To account for that, the bank has a risk scoring system which, for a given loan application, assesses the probability that the corresponding customer may default. This probability is later used to compute the interest rate offered for the customer. To simplify a bit, the issued interest on a loan might be computed as the sum of customer's predicted default risk probability and a fixed profit margin. For example, if a customer is expected to default with probability 10% and the bank wants 5% profit on its loans on average, the loan might be issued at slightly above 15% interest. This would cover both the expected losses due to non-repayments as well as the profit margin.

Now, suppose the bank managed to develop a perfect scoring algorithm. That is, each application gets a rating of either having 0% or 100% risk. Suppose as well that within a month the bank processes 1000 applications, half of which are predicted to be perfectly good, and half - perfectly bad. This means that 500 loans get issued with a 5% interest rate, while 500 do not get issued at all.

Think what would happen, if the system would not do such a great job and confused 50 of the bad applications with the good ones? In this case 450 applications would be classified as "100%" risk, while 550 would be assigned a risk score of "9.1%" (we still require the system to provide valid risk probability estimates). In this case the bank would issue a total of 550 loans at 15%. Of course, 50 of those would not get repaid, yet this loss would be covered from the increased interest paid by the honest lenders. The financial returns are thus exactly the same as with the perfect classifier. However, the bank now has more clients. More applications were signed, and more contract fees were received.

True, the clients might be a bit less happy for getting a higher interest rate, but assuming they were ready to pay it anyway, the bank does not care. In fact, the bank would be more than happy to segment its customers by offering higher interest rates to low-risk customers anyway. It cannot do it openly, though. The established practices usually constrain banks to make use of "reasonable" scorecards and offer better interest rates to low-risk customers.

Hence, at least in this particular example, a "worse" classifier is in fact better for business. Perfect precision is not really the ultimately desired feature. Instead, the system is much more useful when it provides a relevant and "smooth" distribution of predicted risk scores, making sure the scores themselves are decently precise estimates for the probability of a default.

Probability theory is often used as a sound mathematical foundation to formalize and derive solutions to the real-life problems in fields such as game theory, decision theory or theoretical economics. However, it often turns out that the somewhat simplistic "traditional" probabilistic approach is insufficient to formalize the real world, and this results in a large number of rather curious paradoxes.

One of my favourite examples is the Ellsberg's paradox, which goes as follows. Imagine that you are presented with an urn, containing 3 white balls and 5 other balls, that can be gray or black (but you don't know how many of these 5 exactly are gray, and how many are black). You will now draw one ball from the urn at random, and you have to choose between one of the two gambles:

1A)

You win if you draw a white ball.

1B)

You win if you draw a black ball.

Which one would you prefer to play? Next, imagine the same urn with the same balls, but the following choice of gambles:

2A)

You win if you draw either a white or a gray ball.

2B)

You win if you draw either a black or a gray ball.

The paradox lies in the fact, that most people would strictly prefer 1A to 1B, and 2B to 2A, which seems illogical. Indeed, let the number of white balls be W=3, the number of gray balls be G and the number of black balls - B. If you prefer 1A to 1B, you seem to be presuming that W > B. But then W+G > B+G and you should necessarily also be preferring 2A to 2B.

What is the problem here? Of course, the problem lies in the uncertainty behind the number of black balls. We know absolutely nothing about it, and we have to guess. Putting it in Bayesian terms, in order to make a decision we have specify our prior belief in what is the probability that there would be 0, 1, 2, 3, 4 or 5 black balls in the urn. The classical way of modeling the "complete uncertainty" would be to state that all the options are equiprobable. In this case the probability of having more black balls in the urn than the white balls is only 2/6 (this can happen when there are 4 or 5 black balls, each option having probability 1/6), and it is therefore reasonable to bet on the whites. We should therefore prefer 1A to 1B and 2A to 2B.

The real life, however, demonstrates that the above logic does not adequately describe how most people decide in practice. The reason is that we would not assign equal probabilities to the presumed number of black balls in the urn. Moreover, in the two situations our prior beliefs would differ, and there is a good reason for that.

If the whole game were real, there would be someone who had proposed it to us in the first place. This someone was also responsible for the number of black balls in the urn. If we knew who this person was, we could base our prior belief on our knowledge of that person's motives and character traits. Is he a kindhearted person who wants us to win, or is he an evil adversary who would do everything to make us lose? In our situation we don't know, and we have to guess. Would it be natural to presume the uncertainty to be a kindhearted friend? No, for at least the following reasons:

• If the initiator of the game is not a complete idiot, he would aim at gaining something from it, or why would he arrange the game in the first place?
• If we bet on the kindness of the opponent we can lose a lot when mistaken. If, on the contrary, we presume the opponent to be evil rather than kind, we are choosing a more robust solution: it will also work fine for the kind opponent.

Therefore, it is natural to regard any such game as being played against an adversary and skew our prior beliefs to the safer, more robust side. The statement of the problem does not clearly require the adversary to select the same number of black balls for the two situations. Thus, depending on the setting, the safe side may be different. Now it becomes clear why in the first case it is reasonable to presume that the number of black balls is probably less than the number of white balls: this is the only way the adversary can make our life more difficult. In the second case, the adversary would prefer the contrary: a larger number of black balls. Therefore, we would be better off reversing our preferences. This, it seems to me, explains the above paradox and also nicely illustrates how the popular way of modeling total uncertainty using a uniform prior irrespective of the context fails to consider the real-life common sense biases.

The somewhat strange issue remains, however. If you now rephrase the original problem more precisely and define that the number of black balls is uniformly distributed, many people will still intuitively tend to prefer 2B over 2A. One reason for that is philosophical: we might believe that the game with a uniform prior on the black balls is so unrealistic, that we shall never really have the chance to take a decision in such a setting. Thus, there is nothing wrong in providing a "wrong" answer for this case, and it is still reasonable to prefer the "wrong" decision because in practice it is more robust. Secondly, I think most people never really grasp the notion of true uniform randomness. Intuitively, the odds are always against us.

Appendix

There are still a pair of subtleties behind the Ellsberg's problem, which might be of limited interest to you, but I find the discussion somewhat incomplete without them. Read on if really want to get bored.

Namely, what if we especially stress, that you have to play both games, and both of them from the same urn? Note that in this case the paradox is not that obvious any more: you will probably think twice before betting on white and black simultaneously. In fact, you'd probably base your decision on whether you wish to win at least one or rather both of the games. Secondly, what if we say that you play both games simultaneously by picking just one ball? This would provide an additional twist, as we shall see in a moment.

I. Two independent games

So first of all, consider the setting where you have one urn, and you play two games by drawing two balls with replacement. Consider two goals: winning at least one of the two games, and winning both.

I-a) Winning at least one game

To undestand the problem we compute the probabilities of winning game 1A, 1B, 2A, 2B for different numbers of black balls, and then the probabilities of winning at least one of two games for our different choices:

Now the problem can be regarded as a classical game between us and "the odds": we want to maximize our probabilities by choosing the gamble correctly, and "the odds" wants to minimize our chances by providing us with a bad number of black balls. The game presented above has no Nash equilibrium, but it seems that the choice of 3 black balls is the worst for us on average. And if we follow this pessimistic assumption, we see that the correct choice would be to pick consistently either both "A" or both "B" gambles (a further look suggests that both "A"-s is probably the better choice of the two).

I-b) Winning two games
Next, assume that we really need to win both of the games. The following table summarizes our options:

This game actually has a Nash equilibrium, realized when we select options 1A and 2B. Remarkably, it corresponds exactly to the claim of the paradox: when we need to win both games and are pessimistic about the odds, we should prefer the options with the least amount of uncertainty.

II. Two dependent games
Finally, what if both games are played simultaneously by taking just one ball from the urn. In this case we also have two versions: aiming to win at least one, or aiming to win both games.

II-a) Winning at least one game
The solution here is to choose either the 1A-2B or the 1B-2A version, which always guarantees exactly one win. Indeed, if you pick a white ball, you win 1A, and otherwise you win 2B. The game matrix is the following:

II-b) Winning both games
The game matrix looks as follows:

The situation here is contrary to the previous: if you win 1A, you necessarily lose 2B, so here you have to bet both "A"-s to achieve a Nash equilibrium.

Summary
If you managed to read to this point, then I hope you've got the main idea, but let me summarize it once more: the main "problem" with the Ellsberg's paradox (as well as a number of other similar paradoxes) can be in part due to the fact that pure "uniform-prior" probability theory is not the correct way to approach game-theoretical problems, as it tends to hide from view a number of aspects that we, as humans, usually handle nearly subconsciously.

Money is something we take for granted and we usually don't think too much into what it actually is. As a result, when it comes up as a discussion topic, one may easily discover that nearly everyone has a personal twist on the understanding of what exactly is "money", and how this notion should be interpreted. At least that is the case within the circle of people, who are far from economics; and computer science people most often are. Last week this fact got itself another confirmation, when Swen came up with some fiscal policy-related problem, which didn't seem like a problem to me at all. After a long round of discussion we found out that when we said "money" we meant different things. So I thought I'd put down my understanding of this notion in words, so that next time I could point here and say: look, that's what I mean.

Of course, I don't pretend to be even a bit authoritative. After all, I don't know anything about economics (although I did take the elementary course, as any computer science student should). But I do find my understanding quite consistent with observation and common knowledge.

The Ideal Case

It's easy to start by imagining a country, call it "Veggieland", where people are completely inactive. They don't eat, work or play. Don't shop, produce or consume. Just lie around like vegetables, enjoy the sun and somehow manage to stay alive nonetheless. It is clear, that in this world, no money is needed: there is simply nothing to do with it.

Next, imagine that suddenly one veggielander Adam started longing for a glass of water, but he had no idea where to get it. At the same time another veggielander Betty saw Adam's problem and said: "Hey Adam, I can give you a glass of water, but you have to scratch my back for that", because Betty really liked when someone scratched her back. They exchanged services and were happy. Still no money was needed in Veggieland.

After that day Adam discovered that he was really good at scratching Betty's back, and he even liked it. So next time he came to Betty and proposed to scratch her back even though he didn't want water. What he asked in return was a promise that she would get him a glass of water next time he would ask. After a month or so of scratching Betty's back he collected 100 water glass promises, each written with Betty's hand on a nice pink piece of paper, and he found out that this was much more water than he would need until the end of his life. But he had to do something with these promises, because he couldn't "unscratch" Betty's back, right? So he went to that other guy Carl and said: "Hey, Betty has promised me a glass of water, and I can pass this promise to you, if you give me that shiny glass bead that you have, because I adore glass beads". Carl always trusted Betty's promises so he agreed. Now Adam had a bead and 99 water promises, Carl had one water promise. Carl then went to Betty, showed her the pink piece of paper, Betty exchanged it for a glass of water and burned it. Now there were just 99 promises left in circulation in Veggieland.

A month has passed and veggielanders understood that they could actually pass Betty's promises around, and give out their own promises in exchange for services. They wrote promises on pink pieces of paper and picked the "water glass promise" as a universal measure: now Daffy was providing floozies in exchange for 2 water glass promises, and Ewan was selling tiddlybums at a price 3 water glasses per portion. The system worked, because it satisfied two simple conditions:

1. Firstly, at any given moment the number of undone work was equal the number of these pink paper promises in circulation.
2. Secondly, the number of promised work was always feasible.

These conditions were easy to satisfy in Veggieland, because veggielanders were all honest and friendly people. They decided that any time someone fulfills his own promise, she should destroy one pink paper, and any time someone gives a promise, she should write a new pink paper, but no one should give a promise he can't hold.

As a result the people of Veggieland ended up with a perfect monetary system, driving its economics, and allowing citizens to trade services and goods. The analogy of this system with the real monetary systems around is straightforward, yet it is much easier to understand its properties, and thus the properties of the real-world money. The following are the important observations:

• Money itself is just an abstract promise, it has no form or inherent value. As long conditions 1 and 2 are satisfied, there is really no difference whether the function of money is performed using pink papers, glass beads, or even word-of-mouth promises. Money is not a resource, don't be misled by the idea of the gold standard times, that money equals gold. The point of the gold standard was just that, at the time, gold could somewhy satisfy properties 1 and 2 better than printed money and checks. Otherwise, you don't really need to "support" money with goods for no purpose, but to provide an illusion to people that money is indeed worth it's promise.
• The amount of money in circulation does not equal the amount of natural resources of the land. It is equal to the amount of economic activity, i.e., the number of unfulfilled promises. If someone discovers a gold mine, or simply brings in a lot of gold into the country, this will begin having impact only when people start actually demanding this resource and giving out promises in exchange.
• Who makes money? Well, ideally, each person that gives a reasonable promise in exchange for a real service increases the amount of money in circulation, and the person that fulfills a promise - decreases. Of course, real people are not honest and therefore real monetary systems are a crude approximation, with banks being in response of this dynamic money emission process.
• The choice of currency does make a difference. If someone comes to Veggieland with a bunch of euros (which are, in a sense, promises given by the europeans), the veggielanders won't be inclined to exchange them for their own promises, because although the newcomer can easily make use of the veggielanders' services, the contrary is not true: Veggielanders just never leave their country! A corollary of this observation is that the larger is the geographical span of a particular currency, the further away from the ideal trade unit it will be.

The Real Life

Now let's look at how monetary system is implemented in real countries. There are two main aspects to this implementation.

First issue is the choice and social support for the base monetary unit. Each country typically figures out its favourite name and denomination for the unit and calls it its "currency". A social contract is then made among the citizens, that all promises in the country are to be measured in this unit, and everyone should accept this unit in return for services. Note that this social contract guarantees the absolute liquidity of the currency and puts it strictly aside from anything else you might imagine to be a "close analogue" for money - be it gold, government bonds or securities. The latter are just not liquid enough to work as a general promise-container.

Secondly, the process of emission and subtraction of money from circulation. This certainly cannot be trusted to people, like it was in Veggieland. A banking system serves the purpose. The idea is that a single central trusted party is chosen, which emits and discards money. A person comes to the bank asking for a loan, the bank confirms that the person is trustworthy enough to keep his promises and gives him some money: money has just been emitted into circulation. Note that in our digital world most money is emitted in digital form, no paper money needs to be printed for that. In other words, the number you see on your account is actually larger than the number of paper money stored "behind" it. This is very natural, because otherwise the bank would have to keep paper-money-printing and destroying machines in it, which would be dangerous.

Most real monetary systems are just a bit more complicated, having a two-level banking system. The central bank crudely regulates money supply by emitting paper money, giving loans to commercial banks and instructing them to as to how much "more" money they may emit via the reserve requirements. The commercial banks then provide actual banking services to the people. With this distributed system people have a choice of several banks to trust their finances to, not just one. And if it turns out that one bank emits too much (i.e. gives too many loans), so that the emitted promises cannot be met, only the people trusting this bank (i.e. holding "this bank's" money) will suffer.

Final Questions

Despite the fact that the above theory seems consistent to me, it is not without complications. As I believe you've already tired of reading this post, I'll avoid spilling too much further thought upon you and just list the three points I find most confusing briefly.

• Despite being an abstract trade unit, money actually has value: it can bring interests. How do these interests "earned from nowhere" correspond to money emission? Why should owing lots of abstract promises necessarily generate more abstract promises?
• Internet banks take a fee for transfers, which makes digital money somewhat less liquid than paper money. I find it incorrect. Why should I pay to pay? I understand that banks need resources to support their services, but the amount of resources should not be proportional to the number of operations performed.
• If all the customers of a bank one day come to claim their savings in cash, the bank won't have enough cash and it will be perceived as a collapse for the bank. Considering the fact that digital money is, in fact, still real money, I see this as a certain drawback of the current two-level banking system. Or is it a necessary condition to distribute trust among the commercial banks?

If you think I'm completely wrong with all that, you are welcome to state your opinion in the comments.