Do you have any sources for that claim? Because I've heard the argument that it was actually the Enlightenment, and the removal of religion from government (e.g. separation of church and state, reason and science in place of dogmatism), that was the primary source of inspiration for the country's founding. A search for "Declaration of Independence" with "Enlightenment" provides many references for this.

But how do you know that induction is valid to use on natural numbers? It's because their definition/construction follows a set of rules that makes them inductive. Some languages like Coq make this explicit by providing an 'Inductive' keyword for defining inductive types.

Hello,

I've been wondering what the hardware requirements for running Optimism's infrastructure are relative to just running a Mainnet node. If Optimism can process more transactions than the main chain, does that mean state growth is also much higher? How is Optimism thinking about this problem as it moves to decentralize the sequencer in the future?

This is a fantastic question for pretty much every scaling solution out there — as the initial engineering work on rollups finish, many of the fundamental scaling problems re-emerge on L2. Right now, our system's hardware requirements are very similar to L1 mainnet, but the state is growing.

There are two solutions in the future: statelessness, and block-producer/verifier asymmetry. Statelessness (and related concepts like state expiry) has been under active research in Ethereum for years, and we've recently started our own contributions with a new stateless Ethereum client [1]

The other part of the solution is to leverage asymmetries between the hardware requirements of block producers and verifiers. TLDR: this lets you have high HW requirements for sequencers, but still secure the network with laptops. Vitalik recently wrote about this; you can read that here [2]

[1] https://twitter.com/ben_chain/status/1488275978983915523?s=2... [2] https://vitalik.ca/general/2021/12/06/endgame.html

I've found that aspartame gives me really bad insomnia. Almost every time this happens I'll go through what I ate that day and it's always something containing aspartame that was not in my normal diet. This is how I learned that those flavor packets that are mixed into water bottles and some zero-calorie flavorings used at coffee shops contain aspartame.

I've heard this strategy referred to as "follow the follower." Apparently it comes from sailing, where if you want to maintain a lead all you need to do is copy what the boat behind you is doing.

Interestingly, mutable data is also sufficient to achieve general recursion in a typed language:

  let fact' = ref (fun x -> x) in
  let fact = fun n -> if n = 0 then 1 else n * !fact' (n-1) in
  fact' := fact; fact 3