Volume 22: Bitcoin

I've never understood people's need to create golden effigies of their cryptocurrencies.

Finally, A Practical Use for Mathematics

“Many individuals grew suddenly rich. A golden bait hung temptingly out before the people, and, one after the other, they rushed to the tulip marts, like flies around a honey-pot. Every one imagined that the passion for tulips would last forever,” – Charles Mackey, Popular Delusions and the Madness of Crowds, 1841.

“The market can stay irrational longer than you can stay solvent,” – John Maynard Keynes


It is either a revolutionary way to conduct all of life’s transactions, or a means to move dark money for illegal activities. It is based on a piece of mathematics that will either change the way we think about record keeping or a complex formula whose calculations waste more electricity than used by the nation of Nigeria. They are worth $20,000 each or nothing at all.

Whatever it is, Bitcoin has captured the world’s attention. A meteoric rise created millions - and millionaires - out of thin air. But the problems with a decentralized, unregulated currency have shown themselves to all but Bitcoin’s most aggressive backers. Without rules to be enforced, scams and frauds have added to the risk inherent in any new investment.

Any asset - stock, bond, currency or real property - is worth what somebody will pay for it. But having worth is not the same as having value. Just because somebody will pay for something doesn’t mean that they should. Here, we will describe Bitcoin is, and we’ll try to decide if there is a good reason for it to exist.

  • What is blockchain?

  • What is Bitcoin?

  • Does bitcoin have any value?


What is blockchain?

A ledger is a system for storing the records of who owns what. Your bankbook, showing all the deposits and withdrawals you’ve made, is a ledger of your account balance.(1)

The collection of deeds kept by your local government is a ledger of who owns what real estate. The Depository Trust Company facilitates trading of financial assets by helping to create a ledger of who they belong to. You might consider cash itself to be a ledger, representing ownership of a theoretical currency in the background.

There are a lot of problems with traditional methods of keeping ledgers. An entire industry, title insurance, exists to interpret the real property ledger; you will pay one of these companies a lot of money when you want to buy a home.(2) Ledgers for some assets are kept on paper, with all the risks thus entailed. Those kept on a computer are susceptible to attacks of the digital kind. Banks have massive security measures in place against those who would access their ledgers, but it is easy to imagine an attack that created fictitious transactions, moving your money to the account of the attacker.

We can classify the problems of a traditional ledger into several categories:

  • Centralization: If the ledger exists only in one place, it is impossible to differentiate real and fake transactions. Making a copy doesn’t help; if one copy was altered, how would you determine the true ledger from the altered version? Also, there is little recourse against the centralization agency unilaterally modifying the ledger.

  • Cost: As in the case of title insurance, traditional ledgers can greatly increase the cost of completing transactions. Your bank spends a fortune on data security; these costs are eventually passed along to customers.

  • Trust: Traditional ledgers generally require asynchronous execution. For example, my book editor required half of her payment upfront, with the remainder on delivery. This required that I trust her not to walk away with the deposit; she had to complete the work, trusting I would pay for the balance.(3)

Blockchain was created to address these issues. Created in 2008, blockchain is a piece of open source software based on a brilliant mathematical foundation. It allows for the creation of digital ledgers. In theory, blockchain ledgers are completely decentralized, allow for low-cost transactions, and lack any central governing bodies in which participants must place trust. If this sounds revolutionary, that’s because there is a real possibility that it might be.

Blockchain is not the first attempt at creating a digital ledger, but it is the first to solve the critical problem of double spending. Double spending is not an issue when using cash. If you have a $100 bill in your pocket, and spend it at the grocery store, you won’t have the bill anymore and cannot spend it again. If you take $100 out of your checking account, the bank reduces your balance by this amount; if it was your last $100, the bank knows not to let you have any more money. In a decentralized ledger, it is far more difficult to prevent people from using assets they don’t own. If I simultaneously put two transactions in the ledger, and the sum exceeds my balance, how do you know which transaction occurred first, and is therefore valid?

Blockchain solved this problem by introducing the concept of blocks. A block is a group of transactions that, with respect to the ledger, occur at the same time. All transactions in a block are checked against the ledger to be sure that the senders have the asset they are attempting to spend. If they do, the information for these transactions – sender, receiver, amount – becomes a valid block. Then, a bunch of computers run some really complex calculations on this block. The product of this work is to link the block to previous blocks via a code that is called a hash. Through the hash, each new block validates all previous blocks. In this way, the blocks form a chain.(4) As the chain is known to everybody in the blockchain network, there is no central authority and no need to trust other network members. The process of adding new blocks to the chain is called mining, for reason that will shortly become clear.

One obvious question arises: what if two different blockchain miners choose different blocks to add to the chain? This would create two different versions of the ledger. The blockchain protocol has an algorithm for determining which of two ledgers is the “best.” Generally, the best chain is the one that is the longest. When a miner sees a chain that is better than the one on which it is working, it begins work on the new chain, and the old one is discarded. This miner will also send the new chain on to other members of the mining network. While it is theoretically possible to change old blocks in the chain, it is highly impractical to do so. Because blocks are linked by the hash, a miner attempting to alter transactions in a block would need to mine every following block, in order to be long enough to be viewed by the network as the valid chain. Given the massive computing power required to mine blocks, this is a practical impossibility. The blockchain ledger is secure due to the amount of work required to change it.

What is Bitcoin?

Because the mathematics of blockchain is open source, with a little work, anybody can create their own decentralized ledger, processing any transactions their hearts might desire.(5) While its creators intentionally permitted anybody to use it, there was also a specific application for which it was created: the cryptocurrency Bitcoin.(6)

Bitcoin is an instance of a blockchain ledger. It began with a “genesis block” showing the initial state of the ledger. This block stated the initial owner of every bitcoin. The owner of a bitcoin can transfer it by appending a signature, based on a secret code to which only they have access. Despite the secret code being impossible to reproduce, it is easy to verify.(7) The amount of bitcoin in the transaction is checked against the ledger to ensure that the sender has a large enough balance to complete the transaction. Verified transactions are included in a block, which is then connected to the chain via mining, as we described above.

But, who does the mining? In order to add a block to the chain, Bitcoin requires around 200 quintillion calculati