Steph Macurdy investigates:
Where is there structure in randomness?
Steph, 2026.05.13: Hi All, My current leading investigation is to understand how and why there is structure in randomness? My main tool for investigating this is the Secure Hash Algorithm with 256 bit digest. Here's an example output based on the words in this email so far:
Hash output: 92a9bf98ae4fcb4786f70fc236a09700e169f26768ae4f6516fd21eaf4983545
This hash output is, for all intents and purposes, random. You cannot go backwards from it (italicized hexidecimal string) and get the input (bold words/letters). The hash function is a fundamental ingredient in all blockchains and is the "puzzle" to be solved in reference to proof of work mining (for example, in Bitcoin). This doesn't imply "pure randomness" necessarily, because the hash is deterministically generated, so it is more precise to call it "pseudorandom." But for all practical purposes, in domains like information theory, computation, and cryptographic security, it is random and we would require more resources than what's feasibly allowed in the universe to solve it.
And yet, each hash in a blockchain is carrying data about the transactions, metadata about the protocol, and the exact rule for determining each hash in the global sequence.
By viewing a set of hashes with a constrained or conditional rule, we can exploit a level of structure in the very process of generating hashes. Why is there something to exploit? Does this arise from the observer specifically? Is it getting smuggled in through a rather mundane process that we can't detect or know about?
Even without knowing the answer to these questions, we can still use the results to do practical things in the world we care about. This is what creates an economic commitment that a blockchain can use coordinate honest participants and defend against adversaries, while remaining permissionless and establishing immutability. This is where property rights, monetary units, and double entry accounting begin in a blockchain. And because the data is arbitrary, we can also define rules which can systematically enforce contracts of duration, identity, or logic.
I find the question of randomness and structure relevant to my other questions: 1) where does order come from, 2) why does order emerge, and 3) how can we use these insight to further cultivate complexity.
Discussion
2026.05.21 Andrius: Steph, thank you for your presentation yesterday. It inspired a couple of thoughts for me. I think your observations on the development of consensus can have a lot to say about what it means for us to arrive at a shared reality. I am curious how structure, randomness, entropy, information, hashing relate to that. It's interesting how the threshold for consensus can change, as in generating block chains. Also, I think you express with your "wall of energy" what I have felt since childhood, that if I put in enough work, within the proper context and in the proper way, then I can always get the key.