Gaussian Timepieces

Visual expression of time and ownership on chain

Summary / tl;dr

Example timepieces. New owners who do not have many on-chain NFTs will have sparser timepieces, simpler, quieter — like those along the top row. Those with more on-chain NFTs will populate their timepiece with more elements, illustrated along the bottom row. Gaussian timepieces have a main hand (circle) orbiting the bezel according to a fixed time. But around the piece are complications, including: a representation of timing variability (crescent on inside bezel), the on-chain NFTs of an owner (markers on bezel), a dynamic “dial” of moving elements, and a marker of the real, actual time of day (UTC time 12-hour clock, triangle on outside of bezel). The block numbers relevant to the timer are shown beneath the timer’s block count (e.g., beneath “+2”), and the asterisks “*” show the current price of gas in increments of 25 (capped at 300 gwei). Colors and dial update with each cycle of block time. Details presented in post below.

Contents

  1. Introduction
  2. Time, NFTs and Blockchain
  3. “Bitcoin is Time”
  4. Ethereum as a Clock
  5. Gaussian Timepieces
  6. Features, Distribution, Terms
  7. Conclusion
  8. Endnotes and Sundries

1. Introduction

Tick, tock. Etherscan.

2. Time, NFTs and Blockchain

Shvembldr’s “Alien Clock” on Art Blocks.
Gigi’s blog post. Date “666,053” is time based on Bitcoin’s block height, from early 2021.

3. “Bitcoin Is Time”

4. Ethereum as a Clock

Average block time across 10 blocks is about 133.37 / 10 ~ 13 seconds.
The average block time across 100 blocks is about 1334s, or 13.3 seconds per block.
The spread (standard deviation; SD) drops relative to the average (M) as time increases.

5. Gaussian Timepieces

  1. It should express the long-term tendencies of the timing regime, even if imprecise. This marks the stochastic but long-range stable characteristics of the blockchain.
  2. The timepiece should also have indices regarding the relative precision based on unit of time (a few blocks vs. a dozen or more blocks). This is more variable, less stable, yet more pertinent to reading off the timer for a specific period of block time.
  3. The timepiece should contain signatures of uncertainty that cue its holder into a sense of transition from one moment to another inevitable moment despite the randomness that can intervene between them.

5.1 Projections

5.2 Elements

2-block timer (sped up for smaller GIF); owner with many on-chain NFTs (many checks on bezel, see below)

6. Features, Distribution, Terms

6.1 Contract features

6.2 Attributes

  • Block counts: 2, 4, 8, 16, and 32 (equally common)
  • Colors: Dark mode and light mode (equally common)
  • Shapes: Circles (common), blocks (rarer)

6.3 Distribution

6.4 Terms, Conditions, Rights

7. Conclusion

8. Endnotes and Sundries

  1. While reorgs may in a sense “reverse time,” they are also constrained by the arrow of time. Reorgs only work if they establish a “heavier” set of block solutions — in other words, maintaining the direction of time, even if the past can be to some extent rearranged. In Ethereum (and proof of work generally), this is done by achieving greater cumulative computation than the blocks that are being replaced. Curiously enough, perserving our analogy with human time, the brain sometimes hovers in this realm of temporal uncertainty.
  2. Ethereum’s block times have sometimes fluctuated due to various features of the protocol, in particular difficulty adjustments and related issues. I ignore some of these details in this project. For example, under proof of stake, Ethereum 2.0 will likely have more consistent 12-second block times.
  3. James Prestwich (@_prestwich) has a very nice little blog post from several years ago hinting at these themes. James writes we are now “setting up social processes and technological systems, building these distributed technologies, and tipping them into eternal clockwork motion. We will rarely get a chance to right our mistakes once they’ve left our hands, and we may not always be around to tend our creations. When someone finds our work lying on the ground in the forest, its gears spinning and its hands turning, what will they conclude about us?” James describes innerworkings of such systems, with watches as an example, and I skirt over possible further relationships here for simplicity. For example, in a watch, the balance wheel serves as the key mechanical piece that maintains time, and will deviate only slightly even after years when well designed. In Gaussian timepieces, the corresponding computational element is the keyframes duration set on the SVG animation — simply as a linear function of block count, tB. In Ethereum itself, the analogous maintenance is sustained by a more complex function, illustrated below from a detailed summary of difficulty adjustment on Ethereum.
From Thomas Jay Rush’s nice summary here.

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Dynamic distributed data displays. Intermittent. Friendly.

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