Cryptocurrencies as Money

A free economy can be compared to statistical physics. There are many actors. Independent comparisons, information processing, produce local transactions, but level out into a collective valuation, collective prices, until a global market establishes in time (more or less stable) and space (over countries, continents and the planet), until the number of transaction are maximal, i.e. fulfill all needs in all remote corners of the planet. Maximum entropy is maximum information (processing) is maximum energy consumption. Limits/setbacks of growth are reached with energy limitation/exhaustion, but new sources, automation and finally AI help out.

Cryptocurrencies (short crypto, fungible and non-fungible tokens) are a very accessible interface and infrastructure for the bookkeeping of real assets by humans and/or trading bots. Cryptos can be the money of the future. What is missing yet, is the widespread adoption, which would make valuation statistical and thus stable.

Introduction

If you have a key to a lock (of a house), then you have access (to the house). The same key-lock principle is behind the private-public cryptographic key. Instead of a physical key-lock we deal with two sequences of bytes.

• The private part is the "key"
• The public part is the "lock" (but normally called "address")

In ECDSA keys, the public key can be generated from the private key. So by "key" mostly the private part is meant.

Having the key gives you ownership. Locks can be combined to produce shared ownership, where more keys are needed to unlock.

In general a token is a hash of some data. The hash of the public key(s) states ownership, either of an addable number (fungible) or of another token (non-fungible). The ownership can be redeemed using the private key(s), by creating a signature, that can be checked against the public key and thus verified by everybody.

In general a transaction has more inputs and more outputs.

Each node in the network has its own interpreter to check the signatures and do other tasks like executing smart contracts. This applies to EVM (Ethereum Virtual Machine), but also to bitcoin and its forks, like bitcoin-cash,

The private keys are stored in wallets. The wallet also cares to make new keys (HD Wallets).

The unspent transaction output (UTXO, Coin) is first created as the first transaction of a block (coinbase), as reward for mining the block. This numeric value is kept limited by network consensus thus can be used to temporarily replace other limited assets, i.e. it can function as money, as long as the network is online. To keep the network running, nodes are motivated to join and stay by block reward and fees.

A small change in data, and the hash is completely different. The network of miners accepts only blocks with a hash less than a certain number (difficulty). For that only (all) values nonce number is tried.

The difficulty avoids that one can provide all the blocks and thus have control over a chain.

Blocks are chained together by the previous block hash (hashPrevBlock). The blockchain forms a public decentralized ledger, secure, because it cannot be changed unless one is able to redo the difficulty of all blocks following the changed one and overtake the network.

The network nodes check that the difficulty is met and wouldn't accept a block otherwise. Nodes build on the longest chain.

The difficulty is adjusted regularly (every 14 days or $14*24*6 = 2016$ blocks for bitcoin) such that the network can produce no more than about one block per 10 minutes.

Money is a collective product. The consensus rules and validation are a collective product. The joint usage of the network are a collective product. Together they make a collective value, they make money (= fiat money).

Time = Value = Transaction

Value can mean:

• an element of a variable: most elementary
• a number: mostly the result of counting values in variables (information)
• human valuation/pricing: this considers human needs
• ethical value: considering human needs, but eluding pricing

The values of a variable are exclusive. The value implies the variable.

The values of the variable must occur for a variable to exist. Selection of values of the variable cycles. Every value takes time or better is a time step of the variable. One cycle is one variable, is one time.

Every variable is also an independent time.

Information is the number of values of a variable. As such information is a quantity characterizing a variable, not a value. But since variables are values for higher level, the information (extension) is an extensive value. It motivates addition and ultimately all other operations.

Most values consist of internal variables. Internal communication produces inertia, because a level has a more or less fixed speed of communication, with a maximum speed for the lowest level.

When one variable separates into more independent variables they also form independent times. The variables get out of sync without communication.

Independent times make their value combinations random. Such a system of independent variables forms an exponential number of value combinations. If $S$ is the number of identical and independent variables of size $n$, $n^S$ is the number of value combinations.

The information speed comes into play when comparing to another variable. Information/Information = time/time = information/time = energy (see earlier blog). While information is conserved, energy is not. The information stays constant even if it spreads to more variables, in the same level or vertically in the hierarchy. $pV = ST + U$ becomes $pV=ST$, if the internal information (energy) $U$ is ignored, because locked up, anyway, i.e. not spreading vertically.

A transaction is the movement of a packet to new coordinates (value = location = selection = owner). In physics, the packet is internal physical information, internal variables/times. In human economy, it is valuated/priced considering human needs. The transactions by themselves form values, a variable, in the observed level. The packet is transacted based on a price agreement. As the transaction is also with information/price (food, gas, fee, VAT), the internal value of the packet (rest mass) is lower.

• Physics: For a variable to exist, the values must occur.
• Economics: For a valuation/price to exist and persist, transactions must occur.

Note

• A transaction is a time step of economy and it has a price.
• Transactions are needed to maintain value.
• The transactions of a product represent a cycle, a variable.
• A product has inner cycles (those of components).
• Products of higher level move slower and have a higher price (mass).
• The economic pricing hierarchy builds on top of basic living cost.

Money, Pricing

In human economics, transaction of physical resources are associated with a (numerical) value through the valuation/pricing process, that takes into account the demand/need of a resource and their limited availability specific to a person or a group of people.

Valuation of a product is a comparison with other products. If one person would do that, it would create its own valuation scale. The major products an individual compares to are due to its basic needs: food, housing, clothing, ... To compare, the person simulates having the product. A product needs to be personally used to have personal value. As the person has limited time values (.e.g seconds per life), a person's total valuation is limited.

Individuals averaged over a large population, or better a large number of transactions, produces money.

We don't use gold coins any more, we are on the verge of not using paper bills any more, either. We are left with only numbers. But the numbers have a value through the trust in each other that they will redeem the number with same valuation. Like, if you helped me for a day, I give you a bill or text you a message, which remembers you, that I Owe yoU (IOU) a day of help, too.

We collect such IOU's, so we don't need to stash food ourselves, because others do it for us. We can redeem our IOU's, when we are hungry.

Money is collective trust in the promises made by others, by the society. The valuation of money rises and falls with honorable and trustworthy behavior.

Valuation varies between people, space and time. Traders calculate with the valuation of other people, and especially use the valuation differences between people (arbitrage). In order to exploit the valuation difference, the trader relies on secrecy:

• that the valuation of one party stays unknown to the other party and
• that the calculations leading to the price offered by the trader stays secret

Secrecy and trust do not go well together,

• Valuation differences, i.e. lucrative business ideas, do not stay secret long, but attract competitors.
• Companies are short-lived, if their products that don't live up to the promises.
• Outright lies, fake it till you make it, regularly lead to gigantic crashes in the finances.

Secrecy exists, but it does actually not matter so much. Even without it there is division of labor (including mental work) due to the expertise necessary and the limited time of one to do all alone. Sharing information without limit, nowadays so easy, boosts the economy.

Traders are like Maxwell demons, like are biological cells, plants, herbivores, carnivores, ..., farmers, traders, engineers, businessmen, investors, ... They all process information in a successively higher level, and can have a positive energy balance from it. Energy is information/time, the higher the level, the slower. But the information packets matter. A scientist has a long curriculum on its shoulder, like a complex protein has a long chemical pathway.

An important criterion in valuation is the marginal profit/loss ($MP = MR-MC$), i.e. profit change by one more/less customer, product or whatever other unit, because it tells in which direction to go to maximize profit.

All this comparison in an economy creates stable prices (more global prices in space as well as time).

The collective comparison produces a common currency. Although just a number, that currency is limited, because also input channels, e.g. via work, is compared to the same scale.

Pricing is not solely based on calculations or statistics, though. Also power hierarchies or human relations play a role. Sometimes prices can even be dictated.

Comparing is work and many people don't spend too much effort on it, also because the effort very quickly surpasses the value of the product. Sharing information, the rating of other people, reduces the effort considerably.

The scarcity (limited supply and demand) is an essential feature of money, just like of every other product.

Scarcity could be named stability of valuation in a statistical sense. It does not refer to one person or one product. It does not mean that an individual should suffer of scarcity. It just means that sudden collective changes of valuation through a change in trust or supply and demand brings some disruption, with winners and losers, and needs time to stabilize again.

For a (stable) valuation there need to be (many) transactions. Transactions need consensus of more people to use the currency. The currency needs to be well distributed over a large basis of users to maximize transactions.

Money, despite varying prices, still represents real resources. In accounting, the real resources are assets, while the money is equity+liability. Assets = money. But it is a local assumption, because the pricing changes. There need to be regular currency adaptations.

The price can change because of more demand of a real resource (assets), but it can also change because the money supply changes.

A sudden change in money supply will change the demand on assets, which will change their prices. The same happens when the asset supply changes. Also both supplies can change. After one-sided changes it takes some time for prices to stabilize again.

If a money supply change reflects the resource/asset supply change, then the price stays stable.

Often there is one currency but many assets. But more generally there are different types of assets, as well as different types of currencies. One can make a currency per product. The currencies have their exchange rates. To compare, one needs to convert to one currency (valuation/pricing). One common currency stays relatively stable, because averaged over many transactions.

A countries legal tender is kept stable by adapting the supply,

• either by issuing new money or
• by buying up money of its currency

A central organization has control by issuing or withholding money. The control is exerted via parameters like interest rate. More money will be issued,

• if the central bank interest is low
• if the state's public spending is high

It is not just the political authority that control the money supply. Basically, those who own, do control. So centrally owned money means central control of money supply, and so indirectly central control of average pricing of products, i.e. the inflation.

General inflation is not just due to money supply, but also by the change in pricing of important products, which are ingredients of a large portion of all products, like energy and work force.

• by central pricing agreements like that for work force
• by change of taxes
• by a change in supply, e.g. by deciding to get out of fossil energy supply
• by a change in demand

Every product is its own currency. A currency is a product like every other. But a central currency is a special product, because it is more centrally controlled than any other product.

Central control would need a lot of information to make a good control. Normally central control is associated with inadequate reaction to changes.

A transaction needs a compromise between the parties. First, the compromise was quite local to a transaction and was done through bargaining. But with more bookkeeping and calculations, larger chains of transactions are taken into account. They lead to narrower price ranges of buyers and sellers. Transactions happen if the price ranges overlap. The bookkeeping and other kind of communication over space and time, like collective price agreements or dictation, make prices more global in space and time, i.e. more stable.

Many local independent decisions normally produce a better stable result via the law of large numbers than by central control. A globally used independent, not centrally controlled, exchange currency would become stable after some time and stay stable unless disruptive events occur.

Note

• A currency is like every product.
• Transactions (supply and demand) are needed for valuation/pricing, of money as well as of real assets.
• Difference in valuation above fee produce transactions.
• Many transactions produce a stable currency in the absense of disruption.

Traditional Money Compared to Crypto

Crypto has all the qualities of traditional money:

• the paper bill number corresponds to a crypto key hash (number), but that bill/number is just the carrier of value and can be exchanged by another paper bill or crypto key (fungible)
• like the paper bill, a crypto-key has a value associated to it
• instead of putting the bill into your physical wallet, you put the crypto key into a digital wallet
• the crypto key is the record of your belonging, like the paper bill you own
• Your physical wallet or your bank account is your bookkeeping, just like the digital wallet is your bookkeeping. The wallet is like an account.

The role of money is to allow bookkeeping.

But for global/long-term bookkeeping, money needs to be stable, else one better considers it as an asset, a product.

Since crypto is not widely adopted yet, it is unstable, because not averaged over a large number of diverse transactions.

Wide adoption needs and produces stability.

Currently crypto is better considered an asset, like a physical product or like shares on a company.

Governments regard a crypto as an asset, like shares.

Shares do get quite independent from the company that issued them. Their price is rather dominated by supply and demand. Only occasionally good or bad news from the company change the behavior of traders. If the link to the company is removed then we basically are equivalent to a crypto, meaning that then both have no links to real assets other then through the valuation via supply and demand.

On the other hand many cryptos are driven by ads and influencers, with a company behind it that organizes that, and also controls the consensus centrally. This is very much like traditional shares.

Cryptos can replace traditional shares: Instead of issuing shares, a company can issue a crypto to finance itself.

• The manufacturer can have its own fungible token to express the market valuation (EIP-20) of its products.
• Or every product item can get its own non-fungible token (NFT, EIP-721, deed). It does not matter how the token is generated. It points to metadata via tokenURI that has more asset information. Ownership is not encoded in the token hash, but with separate addresses, like for fungible tokens.

Market

Market cap(italization) is coin supply times current price of one coin with respect to a FIAT currency.

Cryptos can be bought and sold in exchanges or privately.

The crypto's exchange rate, i.e. its price, depends on the limited supply and demand.

For the demand it must satisfy needs.

• Provide a money infrastructure easily usable via smartphones (or other computers)
• Keep the coin supply limited
• Serve as an exchange currency between other currencies over time or space
• Represent bookkeeping, possibly local for a product or a company
• Trade and exploit valuation differences

For supply, block reward and fee keep the network running:

• Crypto is created as reward for mining blocks: The coinbase is the first transaction of a block and it creates new output without input, i.e. new coin.
• The output can be sold for other currencies, which gives the coin a price.
• Transaction within the network do have a fee to account for the physical resources involved (electricity, computers) to reward the block miner and to avoid DoS attacks.
• Fee burning reduces the supply more, when demand is more, thus working against inflation, and possibly producing deflation.
• Buy back and burn by sending to an unusable address, is also used to reduce the supply.

All cryptos fulfill basically the same goal. That some are valued more than others is to some extend irrational speculation, to some extend limited support from wallets and crypto exchanges, to some extend lack of trust.

Currently, speculation is the major motive. This leads to unstable coins, if there are only big players, because big players decide slowly and keep a trend going, trying to drag others along and win from their movements. There are not enough independent actors to keep the coin stable.

A crypto cannot produce coin forever,

• because computers work with limited width numbers
• because any real resource is also limited
• because a unique consensus does not cover all needs
• because for scalability more networks are more efficient

Bitcoin, for example, reduces block subsidy gradually to 0. The assumption is that fee and valuation can keep the nodes online.

Scalability

The independent movements of a large population to fulfill their daily needs would make a crypto stable. That is the case for large fiat currencies.

No current crypto currency network can process that many transactions, therefore they rise the fee to keep away the masses.

Ethereum can process around 7-15 transactions per second, Bitcoin around 3-7. Second layer networks like Lightning for Bitcoin and Raiden for Ethereum, or sharding (partitioning of the database) are efforts to increase scalability, maintaining security and decentralization.

Second-layer networks reduce fees, because some communication is done off-chain.

Bitcoin has about 13000 listening nodes. A high node count produces more load for transactions, because every node needs to process them.

The fee is an important criterion to choose a crypto.

Exponential growth is a consequence of independent times/actors (Boltzmann statistics). Current exponential fees make the fee market "exponential-exponential". The fee rate should be constant. A fee competition between cryptos can help. But there is also the network competition for more hash power that asks for more reward.

Many different cryptos can be a remedy to the scalability problem. Each crypto can represent a local usage (can even be pegged to a local asset). The coins stabilize each other by exchange sites. Some exchange sites have a site-specific exchange coin as intermediary.

Trading bots can exploit valuation differences of various cryptos, level them out and thus produce a stable coin that can work as money.

Trust

A currency is an IOU. The amount of currency a person possesses, is a promise of society to redeem later with same assets.

A currency is stable if people trust in it, and they trust in it if it is stable.

You cannot trust anybody but the statistics of large number.

Individual decisions should not be made due to currency value, because it ruins statistics.

A Currency must be stable.

• A deflationary currency is bad, because it postpones transactions, and loses the link to real economy
• An inflationary currency is bad, because it prevents long-term planning.

Large fiat currencies are rather stable through the sheer amount of transactions. Stablecoin is normally pegged to to important fiat currencies like the Dollar (Tether), Euro or Yen.

Cryptos need to be trustworthy

• the network needs to be reliable and stay online all the time
• the link to real assets (NFT) must be correct
• The way programming decisions are made, whether centralized or via enhancement proposal publicly scrutinized

Trading Bot

Stability is relative, though. Just as intermediary to an exchange, a short term stability is already enough. A bot can quickly react on changes, exploit them and produce stability, for people to use.

For a valuation to be stable its supply must change according to its demand. The bot can swap falling cryptos with rising ones, leveling them out. This swapping is the result of many bots buying low and selling high, but for them small amounts already matter.

Note

speculation on trends

The principle of speculation is to act before others and gain from others.

If one is first to buy in an upward trend, and first to sell in a downward trend, one earns most. If one is first in the game, one earns most.

• By convincing others their behavior is a result and thus is of course later.
• Otherwise one observes and anticipates the actions of others before they actually happen. Predictable behavior is always losing in speculation.

Buy when price is minimum, sell when price is maximum.

With slow competition:

• buy, when the price starts to increase and
• sell, when it starts to decrease

But, with fast competition, a minimum in local time, is already beyond the minimum, when the exchange serializes independent requests. Then

• buying, when the price falls and
• sell when the price rises

Fast bot competition produces so small and fast vibrations that the currency seems stable for the human eye.

Let's envision a future time where every person has its own avatar bot and their are additional bots in several levels. The ultimate demand is from humans, though. The avatar must see the human demand. For that, currencies must be pegged to real assets.

• Let's assume a currency pegged to a local electricity power station (LOCTRO).
• The demand increases locally in space and time, due to cold weather and electric heating.
• The power station decides to increase the price of LOCTRO to gain on the demand.
• A local consumer bot on electricity (BOTTRO) sees changes in LOCTRO. It exchanges LOCTRO for FARTRO (farther away power station).
• The bot is fast and humans will actually see no change in price in BOTTRO. BOTTRO is a stable mix.
• When all use more electricity, because suddenly everybody charges its electric car, a personal consumption avatar can swap BOTTRO's for other cryptos, telling the person to reduce electricity consumption, to use the bike instead of the EV.
• Investors see BOTTRO increase, such that a larger local investments makes sense. They build a new power station and power storage.
• After the investment has been payed off, competition makes BOTTRO fall and become stable again.

Bots can help stabilize local changes. Speculative human changes are local changes. Bots can help to merge the many cryptos into a stable global money.

Note

• The role of money is to allow bookkeeping.
• A crypto is like money, but the public ledger/network brings along the full infrastructure for bookkeeping.
• More cryptos with (automatic) trading between them are a remedy to the scalability problem.

DEFI and DAO

DEFI: decentralized finance

DAO: decentralized autonomous organization

Cryptos are public ledgers. This does not yet make them decentralized finance, if the consensus rules are centrally dictated. Rather it also needs organizational decentralization that distribute control over the programming of the consensus rules.

The ledger only records transactions. For transactions to increase and become statistical the coin must be distributed. Only in combination with fair organizational rules, that care for a good distribution, transactions and thus valuation of the coin becomes decentralized.

Decentralized finance usually just refers to the public ledger, and the avoidance of a third person in transactions via smart contracts. It does not refer to a fair distribution. For fair distribution the participants in transactions must care for fairness. Fairness is an ethical value of humans, but often cannot unfold due to lack of information, centrally imposed to keep the advantage and power.

The distribution of information is the first step to fairness. The following crypto properties help towards fairness:

• The ledger is public.
• Smart contracts are programmed and can be reviewed before adoption.
• Neither can be modified afterwards.
• Smart contracts can be done without the need to trust a third party.

Extra fairness effort on top of the public ledger is still needed, though. The DAO needs its own purpose, its own constitution, local consensus rules, The data for a specific DAO needs to be made conveniently manageable for its members according to the DAO's constitution.

Bitcoin is a public ledger, but it is yet mostly used by rich people that have money to speculate on ups and downs of its exchange rate. The bitcoin capital is in the hands of a few and therefore not stable.

Everything develops by proposal and acceptance/adoption. So someone needs to (centrally) develop a proposition. If others accept the proposal a consensus has been reached.

A new crypto/blockchain/DAO needs someone to start it. If it gets adopted a consensus has been reached.

But people should also verify that the further governance is decentralized else their investment is laid into the hands of a few, which is not decentralized finance any more.

Source Code

bitcoin-core was the first and is now reference implementation to many forks. The forks, like bitcoin-cash-node, share much code with bitcoin-core and regularly take over changes from bitcoin-core.

Here some central identifiers. Initial v means vector, i.e. many:

CBlock(Header): vtx (nVersion hashPrevBlock hashMerkleRoot nTime nBits nNonce)
CTransaction: vin vout nVersion nLockTime hash
CTxIn: prevout scriptSig nSequence
CTxOut: nValue scriptPubKey
COutPoint: txid n
CChain: vChain of CBlockIndex
CScriptCheck: scriptPubKey amount ptxTo nIn nFlags cacheStore txdata pTxLimitSigChecks pBlockLimitSigChecks
CTxMemPool: mapTx
CConnMan: vNodes
CNode: hSocket, vRecvMsg

Note

hash

Hashes are used for

• transactions (txid)
• public key (Pay-to-PubKey Hash = P2PKH)
• signatures (content according SigHashType + private key)
• blocks (hashPrevBlock)
• proof-of-work (POW): find a nonce that makes the block hash smaller than nBits

While POW's smaller-than task is hard, finding the data exactly hashing to a given hash is almost impossible. Hashing is a trapdoor.

Node

A bitcoin node is a bitcoind daemon running on a computer. Each node is its own time. Parallel times means parallel independent information.

To manage to maintain the consistency of many transactions, transactions are divided into blocks.

A mining node creates blocks (CBlock) that are filled with transactions (vtx) from the mempool of transactions (addTxs). The block is like a page in a ledger.

To make a common ledger, a common time, more mining nodes need to find a way to choose, who contributes the next block with transactions to the chain.

The first mining node that fulfills the proof-of-work, adds a block to to the longest chain. The frequency of blocks is controlled by the difficulty.

CBlockHeader::hashPrevBlock of each block fixes content of the previous block, because changing the content would produce a different hash that would not fit any more to hashPrevBlock of the next block. The hash brings the blocks into a sequence, a chain (vChain).

This ledger is replicated in all full nodes.

CBlock is derived from CBlockHeader and contains the transactions (vtx).

The hashPrevBlock that fulfills the nBits difficulty is based on data in the header (hashMerkleRoot, nTime, nNonce). The transactions are included in the hash indirectly via the hashMerkleRoot field.

The block chain is like its own time. The many different times of all the nodes create one common time.

The result of hashing is random. To find hashPrevBlock that meets the difficulty the hashes per second matter. Whether they are achieved in parallel or sequentially does not matter. This way many slow machines can be as fast as one fast machine. The fastest machine must not be more than 50% of the hash frequency of the whole network, else that fast machine could tamper with a block and then rebuild the chain and produce a longest chain, that would be accepted by the network.

Network

The network has a documented protocol.

Nodes in the network are characterized by permission flags like PF_MEMPOOL,...

The nodes exchange NetMsgType messages:

CConnMan::ThreadMessageHandler
    PeerLogicValidation::ProcessMessages
        ::ProcessMessage
            ::RelayTransaction
            ::ProcessGetData
            ::Process...
                CInv//ventory

A PeerLogicValidation implements the NetEventsInterface interface with SendMessages and ProcessMessages.

Only full mining nodes create new blocks. They need and others can fetch all accumulated unconfirmed transactions (NetMsgType::MEMPOOL/[GET]BLOCKTXN). Other nodes RelayTransaction one-by-one (NetMsgType::TX), so after some time all nodes will have all relevant transactions.

CInv types correspond to NetMsgType commands:

MSG_TX: NetMsgType::TX
MSG_BLOCK: NetMsgType::BLOCK
MSG_FILTERED_BLOCK: NetMsgType::MERKLEBLOCK
MSG_CMPCT_BLOCK: NetMsgType::CMPCTBLOCK
MSG_DOUBLESPENDPROOF: NetMsgType::DSPROOF

Each node constantly communicates with other nodes:

• connman->PushMessage(pfrom, msgMaker.Make(NetMsgType::TX, ...)), ...
• ProcessMessage according to the protocol, especially:
  • fetch new blocks and determine ChainActive (longest chain) (ActivateBestChain/FindMostWorkChain)
  • fetch new transactions as they need to be in the block before the block hash is created

ZeroMQ or zmq is an additional optional protocol to broadcast transactions and blocks.

Transactions

Each of the transactions vtx in a CBlock have

• many inputs (vin)
• many outputs (vout)

A transaction can

• split the vin[i] to more vout[j], to take only part of a vout[n].nValue addressed by vin[i] and keep the rest via one's own change address, or it can
• combine more vin[i] (previous vout[k].nValue) to one new vout[j].nValue.
• or mix otherwise

vin is the n'th vout of another transaction (txid), referenced via prevout:COutPoint{txid;n}.

The unspent coin is important for validation.

cacheCoins:CCoinsMap is a map from vin[m].prevout to Coin{TxOut{nValue,scriptPubKey}} (CCoinsViewCache::FetchCoin()). This map is also stored in a leveldb .lvl database (CDBWrapper). The CBlockTreeDB is also stored in a leveldb database.

The Coin can be fetched from a CTxMemPool with mempool.get(txid).vout[n]. mempool holds enough transactions to check yet unstable blocks (COINBASE_MATURITY) against double spending.

Older transactions are secured in blocks by hashPrevBlock. Many blocks are serialized into one .blk file.

The sum of all vout[].nValue, i.e. GetValueOut(), minus the sum of all the vout[vin[].prevout], i.e. GetValueIn(), is fee.

Fee

The fee of a transaction is Σoutput - Σinput. The fees of all transactions mined into a block contribute to the coinbase, together with the subsidy. The fees are not linked to its original transaction via address keys. The coinbase has no input, but its output is subsidy+fee.

When mining a block the transactions are ordered high fee first. With more transaction available than fitting into a block those with higher fee are chosen, while the others wait for the next block.

There is a blockMinFeeRate(DEFAULT_BLOCK_MIN_TX_FEE_PER_KB) to accept to block and a GetMinFee() to accept a transaction into the transaction pool (g_mempool). The latter is influenced by the maxMemPoolSize configuration. The largest fee of the transaction falling out becomes the minimum of those allowed in. GetMinFee() gets exponentially smaller with a half life of 12 hours (or 6 or 3 depending on how fast the traffic goes down).

The users decide on the fees, but it is a guess, because if too low the transaction will not get into a block. A stuck transaction can be manually prioritisetransaction'ed, thus circumventing currently higher fees. But for that you need RPC access to a node.

The number of blocks in the network are kept at a constant rate (e.g. 1 / 10 min). With constant block size, even a larger network cannot serve more transactions. A larger network only produces more load for transactions.

In nature exponential behavior comes from independent times. The resource usage of a transaction can be considered constant (proportional to the number of network nodes). But those doing transactions are independent and thus produce an exponential memory usage. In the presence or constant memory, the fee will have an exponential behavior, shutting out an exponentially growing number of smaller fee transactions.

getmempoolinfo informs about the current GetMinFee().

GetMinFee() is a rate per KB. The actual fee is GetMinFee().GetFee(<transaction size in bytes>).

On Ethereum the fee required to make transaction go through is called gas. EIP-1559 burns a base fee. Miners only get the difference to the base fee. The base fee changes with the traffic. Burning the base fee means more is burned the more traffic. The supply becomes smaller, when the demand becomes higher. This increases the price of the coin (deflationary coin/token).

Script

Bitcoin has no fields for addresses one spends money to or from. The addresses are buried in a script indirectly addressing public keys as hashes. To redeem a vout[i]->vin[j] from one transaction to another, the following script composition must evaluate to true (done by CScriptCheck):

[ <vin[j].scriptSig> ]  [ <vout[i].scriptPubKey> ]

The first part comes from the later transaction's vin[j].

There are more variants, the most frequent one is P2PKH.

P2PK:

[ <signature> ]    [ <public key> OP_CHECKSIG ]

P2PKH:

[ <Signature> <Public Key> ] [ OP_DUP OP_HASH160 <public key hash> OP_EQUAL OP_CHECKSIG ]

P2SH allows to provide the public keys (or locks) in a script only when actually spending:

[ <only push data to stack> <script> ] [ OP_HASH160 <script hash> OP_EQUAL ]

e.g.:

[ <signature> {<pubkey> OP_CHECKSIG} ] [ OP_HASH160 <hash of {<pubkey> OP_CHECKSIG>}> OP_EQUAL ]

The hash prevents linking an UTXO to the public key and avoids that future more powerful computers can infer the private key from the public. Hashes are also smaller and thus easier to be communicated on paper or screen printout, either via binary-to-text encoding like base58 or a QR code.

ECDSA cryptography (secp256k1 for Bitcoin) allows to recover the public key from the private key. So only the private key needs to be saved.

The public key can also be recovered from a signature and the message/hash that was signed. This is actually how <signature> <public key> OP_CHECKSIG works. To redeem, OP_CHECKSIG needs to have access to the private key. How the hash for the signature is created is known by SigHashType. The last byte of the signature encodes sigHashType for SignatureHash(), VerifySignature(). SignatureHash in script/interpreter.cpp shows what is signed. sigHashType can decide that more of the transaction than just vout[i]->vin[j] is signed, normally sigHashType=SIGHASH_ALL, i.e. the whole transaction is signed in each vout[i]->vin[j] link.

Everybody can recreate the same hash using the same data in the same order, but only the owner of the private key can make a signature of the hash fitting to he public key it contains.

When redeeming, the signature can be published, so that everybody can verify that the token was redeemed righteously (scriptSig).

SignSignature can be used to fill vin[i].scriptSig, i.e. to redeem a transaction.

The sigHashType used in scriptSig does not depend on scripPubKey, i.e. OP_CHECKSIG will succeed if the public key fits to the signature, independent of the content that was signed.

Token

In general the hash of some data is called token. For example, in pay-to-public-key-hash (P2PKH), the public key is the essential part in scriptPubKey. It is thus an ownership token.

EIP-20 (ERC-20) is a specification of fungible tokens on the ethereum network. Coins are fungible tokens: They don't identify an asset. 200000 compatible tokens exist. They are all traded on the Ethereum network, and can thus be exchanged against each other. UNI from uniswap is such a ERC-20 token.

EIP-721 specifies non-fungible token (NFT, deed). The value of NFT's is in its links to physical assets or other non-copyable items like contracts (mortgages and the like).

It is interesting that NFT's are used for images and other things that have no link to real assets, but that consist of data only, and can be copied easily.

OpenSea is a marketplace for NFT's.

Wallet

Coins is an unspent output of transactions (UTXO, COutPoint). To use coins one needs to have

• the private key fitting to the public key hash in scriptPubKey (for P2PKH)
• the transaction hash (txid)
• the index n into vout of txid

The public bitcoin site one can queried with a key hash, i.e. with an address, e.g.:

https://www.blockchain.com/btc/address/1EwpnNBdFJykwxp6X8v9AfZnup9bgmrLE1

Wallets can find transactions with importprivkey.

ScanForWalletTransactions allows to find the COutPoint{txid,n} for the private keys it contains. A wallet then stores the transaction hashes for its keys.

So what is important is only the keys. Only keys need backup.

For anonymity a new key is used for every transaction output.

With HD Wallets (HD = hierarchical deterministic), keys are generated from a seed and thus only the seed needs backup. With it the wallet can construct the keys and then query the blockchain.

Using the same HD wallet, the seed (key, phrase) can be used to regain access to all coins. The HD wallet name should be backed up, too, or the key derivation path.

Non-custodial software wallets:

Bitcoin: Bitcoin, Electrum, Pywallet, ...

Lightning: eclair, breez, muun, ...

ERC-20: bitbox, coinomi, metamask, zengo, brd, edge, trust bitpay (open source, visa functionality, segwit, schnorr)

Mining

Choose one time line (block chain) for more separate times (nodes).

• Make adding a block hard enough by proof-of-work (POW) to last enough human-relevant time to accumulate transactions (10 min).
• Make it easy to check the POW result.
• A random POW algorithm (trial-error) makes two parallel similar nodes about twice as fast, because twice as many trials are done.
• If none of the nodes is faster than the rest together it is impossible to overtake the longest chain.
• A node adds a block to the longest chain (= chain with most work).
• Longest chain with POW is the main consensus rule to choose the common time (ChainActive).
• ActivateBestChain/FindMostWorkChain decides to switch ActiveChain.
• Transactions (and its fees) count only in a matured ChainActive.

POW loop:

• try a nonce until the block hash becomes smaller then a arith_uint256 bnTarget, constructed from nBits (difficulty).

  The arith_uint256 type is used to represent a block hash. SetCompact constructs a large arith_uint256 bnTarget number from a compact uint32_t nBits.

• GetNextWorkRequired calculates nBits, CheckProofOfWork checks.

• A node mines in response to generatetoaddress.

  CreateNewBlock() create a CBlockTemplate, on which one finds nNonce, then ProcessNewBlock()/ActivateBestChain()/ConnectTip()/ConnectBlock()

getblocktemplate is

• an RPC API function
• a protocol

getblocktemplate allows to do mining separately:

• the miner asks the server about some fixed data (nVersion, hashPrevBlock, nTime, nBits) that needs to go into the block via getblocktempate.
• The miner can change hashMerkleRoot, nTime, nNonce to produce a hash that meets nBits difficulty.
• The miner calls submitblock on the server.

For a pure mining implementation in an ASIC, libblkmaker can be used to call getblocktemplate to a server. Then the miner can be simple, concentrating only on changing values to meet the difficulty (mining).

A bitcoin full node (server) can have more miners. This is called a mining pool. The full node is the server. It redistributes the reward to the miners.

Consensus

Apart from fulfilling the difficulty on longest chain, there are other relevant rules that decide, whether transactions and blocks are accepted by the network (MAX_MONEY, MedianTimePast(), ...). The coin is the result of the network consensus rules. The consensus rules decide, which transactions and blocks are accepted. The consensus rules are like a parallel program producing one time: the blockchain.

The nodes could have completely different implementations, if the behavior is the same. Two different implementations would need long testing against each other to produce the same behavior. The nodes are controlled by different parties, but they still choose the same implementation to produce the same behavior. The implementation of peers is not visible, though. If advantages are detected, individual nodes slightly change implementation and behavior here and there. The network adapts slowly by introducing new rules and checks them starting from a specific height or MedianTimePast() time. The upgrades have are named after BIPs or get special names, like taproot.

Changes in the behavior need to be taken over by all nodes simultaneously, or they are backward incompatible.

hard fork

If more nodes do not agree on the new rules, the transactions and/or blocks are mutually not accepted any more, which is a hard fork of the network and the into separate branches.

soft fork

In a soft fork changes need to have backward compatible behavior, to allow communication until almost all nodes are upgraded.

Fork above refers to chain forks. The software that creates a chain can also be forked. The software fork can possibly create a completely new chain with its own genesis block.

RPC Command

After starting, bitcoind exposes its interface as RPC. The RPC names and parameters are also command line arguments of bitoin-cli.

To list commands:

bitcoin-cli help

The simplest way to send money:

bitcoin-cli sendtoaddress [address] [amount]

Further information:

• bitcoin-from-cli tutorial
• In the source code scan for RPCHelpMan.

Information, Time, Energy

Information is all. Variable, time, energy.

Summary

In the evolution blog I started from "there is no one time", rather every independent change is its own time. This already says that information is time. To say "time is all" or "information is all" are equivalent. Statements are always meant per variable.

The objective here and in the evolution blog is interpretation of physics without the details to produce mathematical consistency.

To say W = I ⁄ t is like saying that energy is time divided by time. W stands for work.

Variable/value:

Values of a physical variable are defined by time and define time for the variable. Every variable has its own information and its own time.

Cycle:

The finite number of values of a variable cycle until the variable ceases to exist. A variable has a curvature when expressed with its observables. Values exist only while occurring.

Information = time:

The information of a variable is the number of values in a cycle. I = ∫Wdt = Wt. W is constant and representing I. I cycles over a space extent in a time period t. The variable as a value (quantum) has a space-time extent.

Momentum:	p = ∂I ⁄ ∂x = mẋ.

Component of a value of a variable. Component of a time step.

Energy:	W =  − H = ∂I ⁄ ∂t.

I is constant: dI ⁄ dt = ∂I ⁄ ∂x ẋ + ∂I ⁄ ∂t = 0. The great trick is to associate the observed changes (the values) to the location where they are observed (create a field). Then one can look at a part of the system (Lagrangian L) and see the rest as potential P(x), from which information flows in: L(x, ẋ) = K(ẋ) − P(x) is an information unit (time unit) with a space direction. J = ∫Ldt counts change and ends with 0 after full cycle.

Force:	F = ∂W ⁄ ∂x =  − ṗ

Component of energy. Component of momentum change.

Levels:

A level consists of parallel variables (encapsulations of interactions or particles). The variables of the lower level become values in this level. Every level has its independent variables with own times.

Resolution:

Every level has its own information resolution. On the lowest physical level the information unit is h.

Mathematical summary:

I = τ   0 = dI ⁄ dt = (∂I)/(∂x) (dx)/(dt) + (∂I)/(∂t) ⇒ W(x, p) =  − H(x, p) = (∂I)/(∂t)   W = (∂I)/(∂t) = (∂τ)/(∂t) = f   W = (∂τ)/(∂x) (∂x)/(∂t) ⇒ W(∂x)/(∂τ) = (∂x)/(∂t) ⇒ m is W   H = pẋ − L = K + P ⎡⎣Hamiltonian: (dL)/(dt) = (d)/(dt)⎛⎝ẋ(∂L)/(∂ẋ)⎞⎠ ⇒ 0 = (d)/(dt)⎛⎝ẋ(∂L)/(∂ẋ) − L⎞⎠⎤⎦   L = pẋ − H = K − P [Lagrangian: phase of component, while constant H is for full system)   δJ = ⌠⌡⎛⎝δx(∂L)/(∂x) + δẋ(∂L)/(∂ẋ)⎞⎠dt = ⌠⌡δx⎛⎝(∂L)/(∂x) − (d)/(dt) (∂L)/(∂ẋ)⎞⎠dt   (δJ)/(δx) = 0 ⇒ (∂L)/(∂x) = (d)/(dt) (∂L)/(∂ẋ) ⇒ F = ṗ   F = (∂L)/(∂x) = (∂W)/(∂x) =  − (∂H)/(∂x)   p = (∂τ)/(∂x) = (∂L)/(∂ẋ) = (∂W)/(∂ẋ) = mẋ   W = (∂τ)/(∂x) (∂x)/(∂t) = mẋ²   P = ⌠⌡(∂W)/(∂x)dx = ⌠⌡Fdx = ⌠⌡ṗdx = ⌠⌡m(dẋ)/(dt)dx = ⌠⌡mẋdẋ = mẋ² ⁄ 2 = K   W = P(x) + K(ẋ) = mẋ²

Information-Time-Energy

Information

When we think of information we think of a language that conveys information. But first there need to be the alternatives the words of a language select from.

Our language consists of words. The word selects one of the concepts in the mind of the person we talk to. The concepts in the mind refer to real things. Tree, stone, house, ...

Dynamic systems evolve by alternatives and selection (mutation and selection). Think of the biological evolution, mind, science, economy, ... There is a creative phase and a selective phase. In human contexts they can also be called "search and find" or "trial and error" or "learn and control". But we can also point the two words to the same thing. The selection itself brings the thing into existence in the first place. Physical processes can be seen as such.

Many physical systems have no memory, but they have information. And, although we have a memory of concepts, they only become conscious those times we think of them.

But the mathematical set has operations like union and intersection. They are more complicated and can be decomposed into individual selections. The  ∈  of a set selects one element from a set. This set with only  ∈  is more fundamental. It is the ubiquitous variable. How could it be otherwise. Something so fundamental must be ubiquitous.

The variable is the foundation of mathematics, and more general the foundation of all dynamic systems.

The variable consists of values. Other words for values are alternatives or states.

A variable consists of all the values

• that occur (exhaustiveness) and
• that exclude each other (exclusiveness)

Information is the number of values of a variable.

Time

The values of the variable occur and excludes each other. In casual English one would say "a value at a time". That is exactly what physical time is.

A time step is the selection or change of value of a variable. In between selections that variable has no time.

Every variable has its own time.

A time step is a value of the variable.

Components of values ( = coordinates = observables), that change at the same time, physically constitute only one value.

Energy of a Variable

The values of a variable can occur slowly or fast. But that can only be seen, if we have another variable to compare to. Our mind has an internal clock that gives a comparison.

When we run a film in slow or fast motion, we get an idea that the time during film shooting can be seen as either slow or fast, depending on our reference time.

In other words: energy is time compared to time. The first "time" we call information or proper time.

W = (ΔI)/(Δt) = (Δτ)/(Δt)

The comparison W = ΔI ⁄ Δt is with an unrelated other variable t. This happens only in the mind. It is not physical. The other t is an arbitrarily chosen unit of information and W is the number value of information (I = Et). One can also do it in reverse, then 1 ⁄ t (Hertz, Hz) is the unit of W and I is the number value.

Energy is the rate of selection, or information rate or frequency.

In nature many variables are isolated. With just one variable the only time its own, and W = ∂I ⁄ ∂I = 1. The concept of information demands values, changes, time on its own. I itself has a proper time.

Do we need to choose another variable to have time? No. Our variable changes its values and that is the proper time of the variable. If values do not change, then there is no time and so the variable does not get into existence.

The variable thus defines:

• information
• and time

Information implies time and time implies information. Time and information are equivalent, physically. With just one variable information and time are synonyms and energy is just 1 or has no meaning.

When comparing to another variable, information implies energy and energy implies information. The comparison is often just a thing of our mind. The physical motivation for energy comes, when the selections of one variable matters with respect to the selections of another variable. The other variable is called time to distinguish it from the first variable, but that time is still information.

A physical change is looked at by arbitrary coordinates of the mind. More dx₁, dx₂, ... can constitute one physical change dI.

The value dI of a physical variable is an interaction between observables. An interaction is one time step with possibly more participants/observables.

The x_i take part in an interaction:

W = (∂I)/(∂t) =  − H =  − (∂I)/(∂x_i) (dx_i)/(dt) =  − p_iẋ_i

Cycle

As long as a variable exists a variable cycles through its values with constant rate W.

How much external time a cycle takes, depends on

• the number of values (information)
• and the rate of selection (energy)

t = (I)/(W)

Selections order the values. If the last value is reached, the selection continues with the first. This brings the first value near the last. How can you do that with one variable alone? We need to distinguish between mind variables and physical variables. Mind variables vary separately only in the mind, while physically they are only a component of a change. One physical value has more observable components, which do not vary independently and are thus not physical variables.

In two dimension you can create a circle, in which the last value is close to the first one. And indeed, nature has examples of values with two observables, think of the electric and magnetic fields in electricity or the elevation and velocity of a pendulum.

What is meant by a variable here is defined by a change, i.e. by a time step. Within one Δt changes of at least two observables combine to one.

All the value combinations of two or more observables together form a physical and inherently cyclic variable.

Levels

The physical world is layered. A level is defined by its variables and interactions.

Every level has

• an information quantum, which implicitly defines
• a typical information rate (energy)

On the physically lowest level, it is the Planck constant h:

EΔt = ΔI = h

Δt and ΔI are both information of some distinct variables. On the lowest level we have Δt = ΔI = h and thus W = 1.

ΔI also defines an acceptable deviation for a level. This is a generalization of energy levels of an electron in atom orbitals, and would be called information levels here.

One level builds on top of the other. All the cumulative changes through the levels are limited by the rate on the lowest level. Higher level changes are slower, because they involve lower level changes over more layers.

If a higher level changes faster, then the levels below need to get slower, because h itself does not change.

In higher levels the quantum of information can be quite large. One can still choose a natural unit of information for a level, like h for the lowest level.

Speed vs rate of information

W = I ⁄ t compares time with time. There is no physical space involved. So information cannot be attributed a speed in physical space.

The physical space is contained in the definition of a specific I by their simultaneous changes with the components of I along them (momenta).

If I say a word, the travel time of the word to my interlocutor and its interpretation to a concept, is one value in our interaction, in our communication. The changes (observables) of the communication partners to form and interpret the message is shared between the partners. This idea applies also to lower level physical interactions.

On the lowest level the signal speed is that of the speed of light c. On higher levels it is a lot slower (but could be called the c of the level).

c compares to an external time t already. ct removes that external time. This gives the proper time unit dI a space extent.

A value does not move from place to place, but it has a space extent, a space quantum. The components of a value are quantized. In the lowest level this is ΔpΔx = h.

The next value can occupy a different space close by. With hν photons that space is λ = c ⁄ ν away (hν = hc ⁄ λ), t = 1 ⁄ ν later (Et = hνt = h).

Higher energies cycle locally, which binds some h in a mass m. m encapsulates all the lower levels. W² = p²c² + m²c⁴. If p = 0, all the energy is within m.

The p = mẋ = h ⁄ λ attribution of smaller λ to higher momenta are due to the many parallel lower level particles averaging and producing a space precision that is not there in the single particle.

Particle

If a variable itself is closed and it takes part in a higher level interaction, then it forms a value component of the higher level variable. The value component's internal information has no information in the higher level variable, but it has internal information.

A physical variable that acts as a value in a level is sometimes called a particle. A particle is a synonym to a variable used to distinguish in specific contexts.

Particles are information quanta. Particles have or are a time extent and also have a physical space extent. So the particle is a space-time quantum.

A variable level builds on a particle level. In an interaction between people, the person is the particle. Looking at a person's thinking as a variable, concepts are the particles.

The interactions in higher levels take a longer time and involve more physical space. But the information needs to cycle during such long times, to conserve its information. There are cycling encapsulations all the way down to the lowest level, which cycles with h. Interaction in higher levels are via particles in lower levels.

A particle has its internal interactions, its internal time. Mass is another name for energy, meaning the inner cycling of a particle.

Static vs dynamic Information

Our mind/brain has its own time. We often neglects the physical time implied by a physical variable and use our brain time on the values instead, but that brain time is a different time than the time of the observed variable itself. Mind variables are also physical, because the mind is physical, but when mapping from reality, the time is replaced by that of the brain.

In mathematics the same logic can be followed by different brains, i.e. different times, different time durations. Mathematics considers variables without time, but to actually exist all these variables need to be thought, i.e. time needs to be added. Mathematics often abstracts away how the values came into existence, and that they came into existence at different times.

In a variable without time we only have the count of values (static variable). One can make the count of values using combinations of values of other static variables. We use the variable of 0, .., 9 (digit) to count or the a, .., z (alphabet) to address concepts. One could also use digits for addressing. Computers use the bit 0, 1, because that is the smallest variable one can still choose from. Since the bit is smaller than the digit, the word length is larger (100000000 vs 256).

The number of bits/digits/alphabets needed to produce the combinations I:

S = logI

S counts the unit variables to produce a value combination count. The unit variable itself counts as 1. This look is that on a level, where the variable is a value.

Between levels, when including a lower level, e.g. because the lower level matters, we transition from addition to multiplication. In the other direction, we transition from multiplication to addition, i.e. we use the logarithm.

In thermodynamic systems we have two levels. The upper level does not distinguish between all the 2^S combinations of values from the lower level.

Entropy is the upper level part in a two level system. Entropy is the count of independent variables, the molecules, whose values (timing) are compared independently (lower level energy).

The lower level part is the temperature T, which is the average energy of a molecule.

The interactions between upper level compartments would be to exchange molecules, i.e. entropy S.

Lower level temperature interaction (heat equation) is quite similar to the quantum mechanical Schrödinger equation. Both compare the time of one level with a two level process. Change and thus time happening in the upper level is due to different information rate in the lower level.

For comparison, the wave equation compares the two times of two levels (not one time) with the space components of two levels.

Temperature T is the average energy per molecule. Similarly pressure p is the average energy per volume (energy packet = particle) and V is a higher level variable that counts the lower level packets.

ST = pV

A higher level equilibrium means no time in the higher level, but it corresponds to a maximum number of lower level interactions. All the exchange of information (W) is in the lower level and at equal rate in both direction.

If more exchange were in the higher level, the lower level would have less.

The molecules have still further lower levels and they exchange information, too: via electromagnetic radiation. If the temperature increases the molecule velocity increases. Velocity alone has no energy, because it is a value, but in collisions a higher velocity means more steps to reach 0 or v. Molecule velocity change is in the thermal level. Because there is more change in the thermal level, the atom's orbital timing needs to decrease or increase, which produces discrete photon emissions or absorptions in the orbitals, but experience a random Doppler shift due to relative thermal motion, which leads to the Planck law.

Energy as Information Flow

W = ∂I ⁄ ∂t can compare the whole variable to some unrelated variable t, in which case I stays constant and the rate W = I ⁄ t stays also constant But we can also look at a part of the system, and see W = ∂I ⁄ ∂t as inflow or outflow of information (see Lagrangian below).

Adding or removing information to the system is a higher level time. If information is added to a variable, the variable becomes a different variable.

Information can exist only as cycling variables. So information is transported as information/energy packets (particles), for example as molecules of a certain chemical energy content. The molecular interactions use atoms as packets. The atomic nucleus uses nucleons as packets. Every layer has its own packets.

Every layer has its own energy, i.e. frequency of packet exchange. A variable serving as time to compare to is level-specific. Energy is expressed in a unit relevant for the level. Relevant, usable energy is level-specific.

If levels interact more levels need to be considered. If one level's frequency is called energy, then the next higher level's frequency is called power. For example, in electricity energy W = UQ is an energy of one level and power P = UI = fW is the energy of the next level.

The energy is important as a measure to express the relative rate of information exchange between systems. How fast an exchange is in comparison to the other, decides

• where the accumulation of information happens
• who survives how long

If we have only accumulation on one side, the joint system dies, when there is nothing to accumulate any more.

If there is a back and forth of accumulation, the joint system survives longer. One system is the potential energy for the other system and vice versa. The states of the joint system are the values of the system as a variable.

The exchange of information packets takes time, but that time is shared between the two systems. The time step thus makes both changes as one.

A variable is an information unit I. Comparing it to an external variable t cannot change the internal physics. Energy W = I ⁄ t is a property of the variable, not of the value, and especially not of the components of a value. To express energy as functions of values gives a wrong picture. It is an indirect mapping: value -> variable -> energy. The variable has one energy. All values just map to this energy, which is the same for all values.

Saying W = mẋ² ⁄ 2 + mgx describes the v, h observables sharing the same energy W, i.e. the energy of a variable and not of a value. Expressing W = mẋ² ⁄ 2 or W = mgx separately and as a function of values has no meaning.

The word energy is often used in the sense of information, as understood here. Here information implies time and thus also energy. That physically they are the same, is the major statement here.

Mathematics uses information in a static sense, although physically it exists only when processed by a brain. Also physics uses entropy S or mass m for static information, but according to the understanding here, this just neglects lower level dynamics (m) or this level's dynamics S. So, although not physical, to distinguish between energy and information makes sense as a tool to give a shorter description of a local context.

Interaction between Levels

"Information is time" means that information does not exist without processing. Higher level particles have more inner processing and are thus higher in low level energy. They are energy packets.

The high level interactions can be slow (low in level energy) compared to lower levels. A level has a more or less constant information rate. The parallel particles encapsulate more lower levels (animal, cell, molecule, atom, ...). Each level has information processing and thus stores energy.

Information flows between levels, too. For example, when two molecules react, they release energy to the thermodynamic level (Enthalpy ΔH). Lower level variables get destroyed to create higher level variables, i.e. higher level processing.

The Maxwell Demon (controller) works between levels. Many-level systems like living beings (microorganism, plants, animals, ...), but also companies or social structures in general use this principle of control.

The controller maps the higher level logic to a lower level, which processes faster. The lower level simulates the logic of the higher level. As the lower level is faster, it can pick high energy packets. Then the controller uses the inner energy of the high energy packet, to keep its own interactions (keep T) running or to reproduce (increase S) (change T or S in a generalized W = TS).

Higher energy packets demand for energy storage. Storage divided by consumption determines the rate of high level interaction. Higher level exchange rates are slower.

When the higher level changes its logic the controller must adapt (learn to control). Such changes are slower than the selection of the energy packets.

• The DNA in living organisms is a mapping of the ecosystem. It changes with the ecosystem or gets extinct.
• Emotions change with the availability of resources over generations.
• Rational thinking adapts within the lifetime.

That he total information flow distributes to complex levels on earth is due to slow cooling (annealing) over a long time. If W goes down, ST can keep a constant T by reducing S at a level, e.g. by making larger molecules. Systems that encapsulate, live longer in the presence of cooling. To live longer means a smaller rate, i.e. less W. The same happens in the learning brain, to the economy, and other dynamic systems.

Newton

Newton (rephrased): An object rests or moves in a straight line with constant speed, unless there is an interaction (force) with another object and that force changes both objects (actio=reactio).

A straight line would imply an infinity. There is no infinity in the physical world. Real systems always cycle until they cease to exist as system. Every curved line seems straight with enough zooming. That is why in physics one always uses manifolds instead of the flat ℝⁿ. Newton's straight line needs to be replaced by a geodesic, whose curvature is that of the components of the cycling variable.

Information implies time. Time is force. There is always a force.

Normally one looks at objects that are obviously interacting. They have a time. An isolated object does not exist. If you found one, it already interacted with you. If that interaction does not explain its behavior, you need to search for other objects it interacts with.

With the actio=reactio, it is implied that the two object's changes are observables of one change, and thus constitute one time step. The force is shared between the interacting objects.

Velocity cannot be seen or measured physically from inside its own inertial frame, so it has no information. And so it has no information from outside, neither. Velocity is a component of a value and not a physical variable. A value does have no information. Only a variable has information, and thus exists. Not even a change of velocity, as seen from the flat space of our mind, does exist, because it is a value and not a variable. And indeed within a geodesic the acceleration cannot be measured.

In the following, assuming ∂τ ⁄ ∂x dx ⁄ dt constant, demands that ∂τ ⁄ ∂x and dx ⁄ dt change in opposite directions (the minus sign). Mathematically speaking that is partial integration with vanishing integral, which is done below with the Lagrangian. Here we demand constant energy, while in the Lagrangian method constant energy follows from stationary action/information. But energy stands for information, too (W = I ⁄ t).

0  = (dW)/(dt) = (d)/(dt)⎛⎝(∂τ)/(∂x) (dx)/(dt)⎞⎠ =       =  − (d)/(dt)⎛⎝(∂τ)/(∂x)⎞⎠ (dx)/(dt) + (∂τ)/(∂x) (d²x)/(dt²) =       =  − (∂W)/(∂x) (dx)/(dt) + m(dx)/(dt) (d²x)/(dt²)     [(∂)/(∂t) (∂τ)/(∂x) = (∂(∂τ)/(∂t))/(∂x) = (∂W)/(∂x)]

Divide by dx ⁄ dt to get Newton's force law:

⎡⎣F≔(∂W)/(∂x)⎤⎦ = ma

The part in brackets is a definition of force.

To get to Newton's formula an unexplained step was used:

p = (∂τ)/(∂x) = m(∂x)/(∂t)

This is thus a consequence of Newton's force law. p = mẋ is by observation. Then it is assigned to (∂τ)/(∂x) by definition. If we do that definition, than W = mẋ² further down. The physics behind that is that ẋ and x are independent components of a time step: Δτ = mẋΔx.

That a value has components solves the vis-viva debate that was going on between Newton (mẋ), Leibniz (mẋ² ⁄ 2) and others. ∂τ ⁄ ∂x is a component of a change, i.e. of a time or information step. Time is an interaction with more partners. This leads to the concept of energy:

Also mass turns out to be a kind of energy:

W = (∂τ)/(∂t) =  − H =  − (∂τ)/(∂x) (∂x)/(∂t)   (∂x)/(∂t) = H(∂x)/(∂τ) = m(∂x)/(∂τ)

Comparisons to t are not physical, but a necessity of the mind. By comparing more observable changes to one external time t, one can relate changes and create a topology and a metric on it for a specific system.

W = (∂τ)/(∂x) (∂x)/(∂t) = m(∂x)/(∂t) (∂x)/(∂t) = mẋ²

W is the full energy. m summarizes lower level energies. With c as maximum v, there are no lower level changes possible any more, and thus mass is exactly the movement itself: m = W ⁄ c².

Mind vs Reality

Our mind is a physical system itself, and has its own time. Actually there are independent parallel processes in the mind, which have separate times. But they are compared, which creates one time and the feeling of conciousness.

A variable is defined by its values. The number of values is the information I of the variable. dI is the system change and thus the system time.

"Space" means generally the value-components of an interaction (a value), not necessarily physical space.

Values do only exist in conjunction with the variable, which exists, because it has information and time. The space values exist only when actually happening. This also applies to physical space. Our memory of physical space, for example when moving the hand through the air, is not the physical space itself.

A change can have more components within the same time. The components are mind variables, also called observables or coordinates. The mind can change them independently, i.e. give them their own time, but the physical system may not.

Comparing independent variables, results in these quantities:

• energy W = ∂I ⁄ ∂t compares times of two variables
• momentum p = ∂I ⁄ ∂x compares time with a component

Independent variables have separate times. Independent variables can exist in parallel, at the same higher level time, or sequentially.

Entropy S = logI counts parallel variables of same kind, whose actions sum up physically. S = logI is also the word length, of a language to address values of a larger variable.

A variable exists as long as its values cycle. Since the values are cyclic, there need to be at least two components to connect the last value with the first. p, x are such two conjugate components. They are called phase space to express in which phase the cycle of the variable is in. A dI time step corresponds to a ∂I ⁄ ∂x dx = pdx in the phase space.

x is a mind variable, where we can spend a lot of time looping to arbitrary precision, but the physical dI is limited by the Planck constant h. h is the smallest, lowest level, unit of counting, i.e. the smallest time unit of nature. Nature is layered, though, and every level further up has a larger time unit.

I = ψ. In the Schrödinger and the Dirac equation, it is compared to another external time t: (∂ψ)/(∂t) Time is information.

The physical world is imprecise and finite. How to describe finite systems with our infinite variables of the mind? This is done by convolution ∫ψ*ψdxdt =  < ψ|ψ > .

Any x, t our mind has finite precision. To any x, t of our mind the physical world, still and also, has imprecision. ψ summarizes both imprecisions. ψ counts how many alternative by chance states there are for a given x, t.

That a complex probability amplitude is used for ψ, allows to map whatever physical variables to two cycling meta-variables. Multiplying (convolving) with the conjugate  < ψ|ψ >  finally projects the cycle onto the direction of the observer.

The evolution in time t of I = ψ is the energy W (Schrödinger equation):

iħ(∂ψ)/(∂t) = Eψ

i because of the differentiation and ħ = (h)/(2π) due to hν = ħω.

Since I = ψ implies time, the left side is time by time. The right side is what components constitutes one time step.

In the Dirac equation the ψ has four components corresponding to the same time.

The cycling produces spin. For a photon it is the cycling between electric field E and magnetic field B and it can be mapped to x_i, t ( = x_μ) via the Maxwell equations. The E, B-cycling correspondence to one x_μ-rotation makes the photon a spin 1 particle.

If more variables are involved one cycling corresponds to more or less physical space rotations. For the Dirac ψ, one space rotation is only half of the cycle: Fermions have spin 1 ⁄ 2.

Lagrangian and Hamiltonian

The information I of a variable is its number of values. The values constitute time steps. The components of all the values form a curved space that allows the variable to cycle. Comparison to an external time, W = ∂I ⁄ ∂t, does not change I. W is a constant of motion.

Energy by itself is kinetic (K), because it is about time steps, i.e. about changes, but one can usually not consider all parts. Therefore one summarizes the remaining parts in potential energy (P) and associates it with the location of the observed part.

The Lagrangian L looks at a possibly small part of the system and measures the information flow per time from the potential part to the kinetic (.i.e. observed) part.

L(x, ẋ) = K − P = pẋ − H(x, p(ẋ))

pẋ − H(x, p(ẋ)) is a Legendre transformation.

pẋ = mẋ² is the full energy. Splitting off the non-observable part of the system half-half, makes K(ẋ) = mẋ² ⁄ 2.

L constitutes a time step in the interaction between the two systems, while H represents the information itself. H =  − W = I ⁄ t.

H(x, ẋ) = K + P

pẋ in L = pẋ − H varies over time. So L(x, ẋ) oscillates around 0. L expresses the phase of the observed components. The sum over a cycle becomes minimal, because the information exchange cancels over one cycle.

Calculus of variations produces a condition that needs to be satisfied to have stationary information, i.e. constant information.

W =  − H stays constant. ∫Wdt would count system time to infinity. L(x) = mẋ² + W = mẋ − H oscillates and returns to the same value in a cycle. J = ∫Ldt returns to the same value after one or many cycles. This is bounded and can be minimized.

With a stationary J = ∫Ldt one gets the Euler-Lagrange equation or the Hamilton Equation (further down). This corresponds to demanding that H =  − W is constant, as was done above (Newton).

In general, equations of motion (eom) produce the proper time and information I of the system (on-shell). Else we would count more than what actually constitutes one time step (off-shell).

δJ  = ⌠⌡⎛⎝δx(∂L)/(∂x) + δẋ(∂L)/(∂ẋ)⎞⎠dt     partial integration of second part      = ⌠⌡δx⎛⎝(∂L)/(∂x) − (d)/(dt) (∂L)/(∂ẋ)⎞⎠dt     (δJ)/(δx) = (∂L)/(∂x) − (d)/(dt) (∂L)/(∂ẋ) = 0

Stationary condition δJ ⁄ δx = 0:

(∂L)/(∂x) − (d)/(dt) (∂L)/(∂ẋ) = 0

By replacing ∂_ẋL = p and F = ∂_xL, this is Newtons F = ṗ = ma. Note, F = ∂L ⁄ ∂x and p = ∂L ⁄ ∂ẋ = ∂τ ⁄ ∂x are by definition.

• We need to add a physical p and F separately to find L (Newton approach): e.g. p = mẋ or F = GmM ⁄ r²
• Or we need to add a physical L to get p and F (Lagrange approach): e.g. L = mẋ² ⁄ 2 − GmM ⁄ r = mṙ² ⁄ 2 + mr²φ̇² ⁄ 2 − GmM ⁄ r.

One cannot derive Newton's laws from the minimization of the action J. One cannot derive physics. One needs to observe.

L(x, ẋ) is transformed to H(p, x) via a Legendre transformation. H(p, x) considers the system as a whole, rather than the inflow or outflow of information from a component, as with L.

(dL)/(dt) = (d)/(dt)⎛⎝ẋ(∂L)/(∂ẋ)⎞⎠ + (∂L)/(∂t)   0 = (d)/(dt)⎛⎝ẋ(∂L)/(∂ẋ) − L⎞⎠ + (∂L)/(∂t)   H(x, p) = pẋ − L(x, ẋ(p, x))

∂I ⁄ ∂t =  − H is the Hamilton-Jacobi equation. Information I is Hamilton's principal function.

Interactions have a constant rate unless the exchanged energy packets become of higher value. The cycling values of a variable from this level form the energy packet of the next higher level.

I = ∫dI = ∫Wdt is the full count of values, i.e. the full information of the system. W =  − H = ∂I ⁄ ∂t compares the system time steps dI to some other system's time t.

The Euler-Lagrange equation become the Hamilton equations.

(∂H)/(∂x) =  − (dp)/(dt)   (∂H)/(∂p) = (dx)/(dt)

F =  − ∂_xH is the reason for ∫Fds = W.

Without the external dt in the Hamilton equations, we have:

(∂I)/(∂x) = Δp   (∂I)/(∂p) = Δx

Or, integrating either of the two:

ΔI = ΔpΔx

Each dI change is represented by a phase space volume element ΔpΔx.

The information resolution of the physical world has a lower limit h.

ΔI = ΔpΔx ≥ h

Quantum mechanics realized that the ΔpΔx step is the time step: ∂ψ ⁄ ∂t = ∂²ψ ⁄ (∂p∂x). On the left side we have ∂t where on the right side we have ∂p∂x. The ψ is our information I.

The Schrödinger equation, and thus ΔI = ΔpΔx, is just an example. The Dirac equation has more observables falling into the same system time step.

The constant I is the information of the observed system. I represents a variable, which cycles, forming the geodesic of the curved component space of the system.

In the higher level I may be just one value, one time step, which by itself has no information and cannot be described.

Taking away values from the trajectory, e.g. reducing the radius in the hydrogen atom's electron orbital, creates a separate variable (a photon), i.e. a separate information packet to keep the total information constant.

Values do not Commute

dI is a time step and H compares it to some external time step dt. H(x, q) is the same for every time step, i.e. every component combination or point in the phase space. H corresponds to the h in the lowest level.

Hdt = dI = (∂I)/(∂p)dp + (∂I)/(∂x)dx = xdp − pdx ≥ h   ΔxΔp ≥ ħ ⁄ 2

So the values of a variable do not commute, because they are one time, one causal chain, serial.

The values of different variables do commute, because they are independent, parallel, without correlation. If one would sum over some external time stretch T and divide by T, one would get 0: 1 ⁄ T∫(dτ ⁄ dt)dt → 0. dτ would count any possible combined change of independent variables. dt would be of arbitrary size and would make T = ∫dt arbitrarily large, since there is no cycling.

Topology

A variable implies time, which implies processing. Two variables have two time, i.e. parallel processing. A variable by itself is sequential, i.e. causal, meaning the values of a variable form a sequence.

Serialization of variables, makes the variable to a value of a higher level variable.

Higher level variables are a mix of serial and parallel processing of lower level variables of varying size. The more or less independent times of the variables, i.e. the information encapsulations, account for all the topologies of our universe.

All the topology is constructed by parallel vs serial in levels starting from the elementary h.

Since information is time already, the universe evolves via information alone.

The timing of a higher level variable is the result of the topology of variables it builds upon. On the lowest level the rate is constant and given by h. All serial interactions summed over the layers cannot exceed h.

Fast higher level interactions slow down the lower level interactions. For example,

• in high gravity lower level clocks tick slower or
• if S changes fast in a thermodynamic ST we cannot reach equilibrium, which keeps T based exchange slow
• if humans interact a lot the thinking in the mind becomes slower due to the distraction

W is has an intrinsic uncertainty that defines a level.

With fixed W, large variables (with many values) cycle slowly. A higher level variable can become faster by making the lower variables of smaller size (W² = p²c² + m²c⁴) or parallel.

Within a level the interactions (W) are highest if lower variables are of same W, i.e. synchronized.

If interacting parallel variables do not cycle with same W, there is a distribution of information until in equilibrium. The distribution of information is also called entropy maximization.

More parallel variables increase the information throughput. Energy in higher levels thus compares the degree of parallelization. This is a generalization of the thermodynamic W = ST.

The inertia (mass) of a larger system is due to the time needed to change or synchronize lower variables. It takes information flow and that takes time.

Quantum Units

For W = I ⁄ t, all the variables that can work as external t are information, too. The lowest quantum h is therefore also a time quantum.

Δt_min = h

c = dx ⁄ dt with constant c and minimum time h, makes the minimum space quantum to

x_min = ch

Energy compares two times and its minimum is thus W = h ⁄ h = 1 in the lowest level. mc² = hν = 1 produces m = 1 ⁄ c². Setting the maximum coordinate speed to c = 1 makes the minimum mass m = 1.

E_min = 1   m_min = 1

Number values:

import scipy.constants as sc
c = sc.c # 299792458.0
h = sc.h # 6.62607015e-34
t = h
x = ch = sc.c*sc.h # 1.9864458571489286e-25

It makes sense to set h = 1 and c = 1:

Then the minimal values are

c = 1   h = 1   t = 1   x = ch = 1   W = m = 1

One can continue like that for other quantities, like electrodynamic E and B.