ScaleDebate 
People in the cryptography currency eco debate about this issue again and again. On one hand people hope the cryptography currency to be a trustful store of value, on the other hand they hope it to be a vehicle of all transactions of typical daily life although both factions claim they care the security. This conflict leaded to the "civil war" of bitcoin in 2015. However, it can be avoided if people have the following understanding. Once again, it shows that a sole understanding of computer science without physics and some (non mainstream) economics is never good to cryptography currency in the sense that one would propose a wrong proposal about scaling or fail in the analysis of the security beyond computer science. Since real money in fact represents energy (to boil 100 gram water requires the same energy amount thousand years in the past or future, but not the same "fiat money" amount due to inflation), we can reason in energy term to have a clear whole picture across time and space. Suppose these notations:
Therefore, take BTC in 2015 as example:
We know that the new mined coins (if any) and F is to support the block generators' energy activity. We also know that NTD shall be equal to some proper percentile (not higher percentile like top 1) of network propagation speed otherwise we are going for a centralized highspeedconnected miners and it would be simpler and better and no bother by using a centralized Oracle(tm) database to keep people's coins amount; a fiat currency is conceptually a blockchain with only a single miner. So you can treat NTD as a constant about the current internet; you may think it 2M or 3M or whatever you justify by some reports from ISP. To get cheap fee, there is one way people can do by simply put F=0. But there are only NT transactions for a block and block generators will include higher fee transactions and people are facing prisonerdilemma and therefore this approach is impractical. Therefore we rule out the possibility of lowering fee by lowering F. Further, the 25 will eventually become zero and the transaction fee energy will be simply K / N which is irrelevant to F. Therefore, the only way to lower the transaction fee is to increase N or decrease K. For K, it can not grow always, it must be stable sometime in the future because the energy influx to the Earth is constant and we don't expect block generating is the major activity demanding energy on Earth. So many whatif:
Given NTD and K are bounded. Just playing the formula around and an elementary math can understand that it is impossible for any specific cryptography currency to have the following goals at the same time:
If the cryptocurrency's volume will be infinite, for example with alltime constant block reward 25 coins, then eventually, it will be worthless because the F will tends to infinity. If the cryptocurrency's volume is capped, after all the coins are mined, the only way to cope with economic growth (if any) is a bigger and bigger KT/F. In fact, at that time, all prices shall be lower in term of that cryptocurrency (aka appreciation) and constant in real energy term. People without net debt become wealthy, just like new money are issued and distributed based on the proportional law where money does not appreciate and depreciate. Physically, economic growth means the disposable energy becomes more. Therefore, given the constant volume of money, the money is in appreciation if the economy is growing. We can imagine a counter part where we use gold (BTC) and the paper money (LTC). A fast food restaurant hardly accepts gold for transactions, but the staff always finds some counterfeit currency money in monthly revenue review and this is the unavoidable evil to have a large throughput. "Different cryptography currencies of different goals" is the only way to go. What people shall really debate is the goal. If people emphasize the first (or the second) goal for a specific cryptography currency, then there must be some other cryptography currency emerging to fill the goal left behind and there are always the needs to exchange the two cryptography currencies occasionally for the designate purpose. In fact, we are already here: real estates and many other real stuff and BTC serve the first goal and the fiat currency which is maintained in some database we have no control serves the second goal. Both serve the defined goals very well. First Law of Crypto CurrencyThe higher is the price, the higher is the transaction fee unless only allowing players with higher internet capacity to be the nodes. Define the symbols below:
Then it follows: Therefore, say, a requirement of e < 0.01 is equivalent to Note that this law has nothing to do with crypto and in fact is a First Law of Currency; the communication speed M can be the database speed as well. As long as the M is much higher than a typical economic agent can afford, it must be sort of centralization in some parts. As long as people hope to have high price and low fee and decentralization, the only way is technology advance so that a larger M can be enjoyed by majority of economic agents. Impact of network propagation speed on trust levelWith the above math, it is also possible to quantify the impact of network propagation speed on the block chain. Suppose the network speed is infinite. Then each new found block broadcast by the finding node is known by all other nodes at zero time, therefore these nodes can stop mining and relaunch a new mining task to find the next block on top of this block. In other words, the whole network wastes no energy in the mining tasks. Suppose there is a finite network propagation speed so that ratio of propagation time to the block interval time T is nonzero e. When a mining node finds a new block, all other nodes keep wasting energy mining a block for time Te among the time interval T + Te, therefore a loss of energy power ratio e/(1+e) for all other miners; not only the immediate waste of energy but also the potential future blocks reorgs so that previous blocks become orphans whose committed energy being the accumulation of energy power of the onceuponcorrect chain is wasted. Suppose the average hashing ratio of a miner is h, so the overall average energy loss of the network during block time across time and space is e/(1+e)(1h)KT. Therefore the value of a coin is in fact reduced to
When e is zero, the P is just like normal estimation of proofofwork as above. When e is infinite, miners are separated from each other forever and all other miners' effort are waste to any specific miner who is just like working for a single miner blockchain:
The reason to have a low e is to reorg the blocks less likely and to allow people's confidence of the data buried in the block chain and the P can be calculated directly in the mining process without concerning the externality of orphan blocks. In case of large e, people can think an imaginary "nblock block" as "n blocks of the original chain as a set" to gain confidence. For example, suppose the total propagation time is a+B/M instead of B/M therefore
With the help of the imaginary block mindset to get a lower e
and "deals are confirmed" are defined at an nblock block. Someday when people use bitcoin both on Mars and Earth, they can decide the number of block for confirmation by this formula where a is 14 minutes.

