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From Nash to Lyapunov Knowing where you want to go is not the same as getting there, and other mathematical topics presented in plain English.

If you thought game theory was cool, wait til you find out about Lyapunov. #TokenEngineering

medium.com/block-science/…

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A #TokenEngineering visionary and sage advisor of the @commonsstack. Thanks @trentmc0 for all the inspiration over the years!

x.com/commonsstack/s…

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This is one goal of the @commonsstack's #CyberPhysicalCommons - including Conviction Voting (a flavor of dynamic average consensus) & Bonding Curves (algorithmic markets) for information aggregation in various forms.

#EmergenceEngineering #TokenEngineering

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Multi-agent coordination and collective sense-making are already well established tech in swarm robotics & controls engineering.

With #TokenEngineering, we can leverage similar tools for the coordination of socio-economic systems towards mutual goals.

sciencemag.org/news/2020/12/w…

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Kicking off the Token Engineering Commons The TEC envisions a world with safe digital economies that protect and support public goods

The @tecmns is also innovating on technology in this area, iterating on open-source tools with the aim to create safe & ethical digital economies for the production & maintenance of public goods, in this instance geared towards #TokenEngineering.

medium.com/token-engineer…

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The first @cadcad_org MOOC from @cadCAD_Edu has arrived! πŸ”₯πŸ”₯πŸ”₯

Course materials are informative and step-by-step. This is by far the best way to skill-up on one of the most in-demand skills in the web3 space. #TokenEngineering

Congrats to all involved + course sponsors! πŸŽ‰

x.com/cadCAD_Edu/sta…

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I had a lot of fun talking about warm data, complexity, @cadcad_org & the @commonsstack with @Sys_innovation & @NoraBateson last week!πŸ™Œ

Looking forward to more chats about applying complex systems thinking in novel cryptoeconomies using a growing #TokenEngineering toolkit. πŸ› οΈπŸ”₯

x.com/Sys_innovation…

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Always fun riffing on the latest @commonsstack research with @thegrifft!

Stick around til the end for my favorite all time super useful google calendar hack, on top of all the #TokenEngineering stuffs. πŸ˜†

x.com/commonsstack/s…

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The need for #TokenEngineering is everywhere.

Without tools like @cadcad_org to model, simulate & test our infrastructure for stability, it is difficult to protect against the systemic risks piling up in #DeFi.

Ethical engineering design is a must.

x.com/AdamScochran/s…

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A must read piece on the importance of #TokenEngineering πŸ”₯πŸ”₯πŸ”₯

x.com/trentmc0/statu…

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Token Engineering Explained in 3 Levels of Difficulty Inspired by Bettina Warburg’s well-known blockchain explainer, here is how I would explain Token Engineering to three vastly different…

Having difficulty understanding #TokenEngineering sometimes? 🀯

@gablerjonathan from @block_science @tokengineering lays out the basics of the rigorous design of web3 tools to a preschooler, a high school student, and a PhD grad student. Don't miss it!

medium.com/@gablerjonatha…

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Great to see @TrojanDAO continue to lead the #TokenEngineering design space! πŸ™ This Differential Specification diagram for Moloch DAO is a key part of the @cadcad_org design process. πŸ”₯

x.com/TrojanDAO/stat…

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Prereq course for advanced #TokenEngineering - anyone interested? Chime in!

x.com/mZargham/statu…

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But what is a Fourier series?  From heat flow to drawing with circles | DE4
But what is a Fourier series? From heat flow to drawing with circles | DE4 Fourier series, from the heat equation epicycles. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/de4thanks 12 minutes of pure Fourier series animations: https://youtu.be/-qgreAUpPwM Some viewers made apps that create circle animations for your own drawing. Check them out! https://www.reddit.com/r/3Blue1Brown/comments/cvpdn7/make_your_own_fourier_circle_drawings/ https://isaacvr.github.io/coding/fourier_transform/ Thanks to Stuart@Biocinematics for the one-line sketch of Fourier via twitter. As it happens, he also has an educational YouTube channel: https://www.youtube.com/channel/UCKOiJd9YCbv7LeL2LFOGiLQ Small correction: at 9:33, all the exponents should have a pi^2 in them. If you're looking for more Fourier Series content online, including code to play with to create this kind of animation yourself, check out these posts: Mathologer https://youtu.be/qS4H6PEcCCA The Coding Train https://youtu.be/Mm2eYfj0SgA Jezmoon http://www.jezzamon.com/fourier/index.html For those of you into pure math looking to really dig into the analysis behind this topic, you might want to take a look at Stein Shakarchi's book "Fourier Analysis: An Introduction" Timestamps: 0:00 - Drawing with circles 2:10 - The heat equation 6:25 - Interpreting infinite function sums 9:52 - Trig in the complex plane 14:11 - Summing complex exponentials 22:11 - Example: The step function 23:54 - Conclusion Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ These animations are largely made using a custom open-source python library, manim. See the FAQ comments here: https://www.3blue1brown.com/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ You can find code for specific videos and projects here: https://github.com/3b1b/videos/ Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown

Visualizing Fourier Series brings a new appreciation to those calculus classes back in the day. Understanding the real world applications of these mathematical tools gives some perspective on the potential of #TokenEngineering in ecosystem design. πŸ”₯πŸš€

youtube.com/watch?v=r6sGWT…

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A regulatory and financial stability perspective on global stablecoins The European Central Bank (ECB) is the central bank of the European Union countries which have adopted the euro. Our main task is to maintain price stability in the euro area and so preserve the purchasing power of the single currency.

The European Central Bank makes a clear case for the need of cascade failure analysis, fault sensitivity testing, and other nascent #tokenengineering techniques in their analysis of stablecoin proliferation:

ecb.europa.eu//pub/financial…

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Rather than being reductionist & mechanistic, Systems Engineering offers a holistic approach to risk mitigation & the safe design of public infrastructure.

imo, #TokenEngineering fits in the realm of systems/electrical/robotics/controls engineering.

x.com/mZargham/statu…

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From Curved Bonding to Configuration Spaces N2 - Bonding curves are continuous liquidity mechanisms which are used in market design for cryptographically-supported token economies. Tokens are atomic units of state information which are cryptographically verifiable in peer-to-peer networks. Bonding curves are an example of an enforceable mechanism through which participating agents influence this state. By designing such mechanisms, an engineer may establish the topological structure of a token economy without presupposing the utilities or associated actions of the agents within that economy. This is accomplished by introducing configuration spaces, which are proper subsets of the global state space representing all achievable states under the designed mechanisms. Any global properties true for all points in the configuration space are true for all possible sequences of actions on the part of agents. This paper generalizes the notion of a bonding curve to formalize the relationship between cryptographically enforced mechanisms and their associated configuration spaces, using invariant properties of conservation functions. We then proceed to apply this framework to analyze the augmented bonding curve design, which is currently under development by a project in the non-profit funding sector.

8/ So what comes next? Bleeding edge academic research from @crypto3conomics defines BCs as configuration spaces & estimators, bridging #TokenEngineering to existing engineering disciplines with established tools. This is huge.πŸ’₯

epub.wu.ac.at/7433/1/zargham… epub.wu.ac.at/7381/1/zargham…

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11/ Using #TokenEngineering, fractally scalable community structures can be designed to federate up to bioregional, national, or global jurisdictions. Group preference estimation & signal processing can be improved thru tools used in multi-agent coordination, e.g. swarm robotics.

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Divergence and curl:  The language of Maxwell's equations, fluid flow, and more
Divergence and curl: The language of Maxwell's equations, fluid flow, and more Visualizing two core operations in calculus. (Small error correction below) Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/divcurl-thanks My work on this topic at Khan Academy: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives Timestamps 0:00 - Vector fields 2:15 - What is divergence 4:31 - What is curl 5:47 - Maxwell's equations 7:36 - Dynamic systems 10:37 - Explaining the notation 13:28 - No more sponsor messages Correction at 4:55, the narration should say "counterclockwise rotation gives positive curl, clockwise rotation gives negative curl". The diagram is correct, though. For more fun fluid-flow illustrations, which heavily influenced how I animated this video, I think you'll really enjoy this site: https://anvaka.github.io/fieldplay/ Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown

Calculus studies rates of change over time. In crypto design today, temporal dynamics are far too often oversimplified, or left out altogether. #TokenEngineering promises to fix that.

Great visualizations of fields as fluids, pred/prey models & more:

youtube.com/watch?v=rB83Dp…

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The nature of the solution must be an emergent, adaptive system of collective estimation, sense making, and action towards local solutions that abide by global constraints.

An ecosystem of peer-governed, community-oriented #CyberPhysicalCommons, enabled by #TokenEngineering.

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Economic Games as Estimators N2 - Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents? objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game?s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.

The @commonsstack aims to use #TokenEngineering to improve estimation & signal processing in community-based commons ecosystems, using tools like the Kalman Filter (& more).

Working off of research by @mZargham @paruch1 @jshorish @crypto3conomics:

epub.wu.ac.at/7433/1/zargham…

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This #TokenEngineering system design pattern will allow us to align our "moral" and "economic" landscapes (aka topologies or manifolds) so that we can align incentives between what is valued by our financial system and what is truly important to us. πŸ₯³

x.com/jeffemmett/sta…

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Congrats to everyone involved, incredible work to get to this point!

Stoked to see bleeding edge #tokenengineering concepts applied to fund important academic research! πŸ€“πŸ”₯

x.com/paulkhls/statu…

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The early beginnings of #tokenengineering as an academic discipline.

x.com/mZargham/statu…

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The World Has Gone Mad and the System Is Broken I say these things because: Money is free for those who are creditworthy because the investors who are giving it to them are willing to get back less than they give. More specifically investors lending to those who are creditworthy will accept very low or negative interest rates and won’t require ha

Couldn't agree with you more @RayDalio! Let's explore alternative, well designed microeconomic systems with robust #TokenEngineering fundamentals using web3 tech & the @commonsstack

#SystemsChange #ComplexityTheory #EcologicalEconomics

linkedin.com/pulse/world-ha…

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A Token Engineering Process The rapid development of the blockchain ecosystem has given rise to a new engineering discipline in the form of token engineering. What makes this discipline particularly complex is that we are dea…

Essential reading for anyone designing & building web3 architectures!

@stephen_yo lays out the process of #tokenengineering & the tools for complex system mapping (adapted from @meedabyte) for modelling & simulating cryptoeconomic systems in @cadcad_org.

syoung.org/2019/10/18/a-t…

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The @commonsstack will make cross-project collaborations much easier w/ interoperable mechanism design.

There is no *one* solution to governance, funding, etc - why not choose from a library of available mechanisms to combine as appropriate for your context? #TokenEngineering

x.com/mZargham/statu…

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Commons Stack You can view and join @commonsstack right away.

Exciting announcements!
πŸ‘‰@block_science's cadCAD is now OS
πŸ‘‰@commonsstack is LIVE, open for membership & contributions
πŸ‘‰a call for the formation of a #TokenEngineering Commons to fund & establish TE tools & standards

Join in the conversation:

x.com/commonsstack/s… t.me/commonsstack

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Blockchains are the equiv of low level embedded micro controllers in #tokenengineering, opening up a WHOLE NEW WORLD of economic design for us to explore.

Lots of work req'd to progress the stack all the way from micro controllers to dynamic stabilization, but we're en route!

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The killer use case of blockchain is, without a doubt, scaling the commons.

With well designed mechanisms using #tokenengineering we can move beyond 1D, profit maximizing economies.

It's time to prioritize people & the planet.

πŸ‘€ @commonsstack

x.com/mbauwens/statu…

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