Ethereum’s Gambit: A Proof by Contradiction

Karen Scarbrough
10 min readJan 4, 2021

TL/DR : Ethereum proposes to change the rules entirely. If the rules Ethereum plays by prove to be valid, major innovations are on the horizon. For early crypto start ups, the rules seem to be working…

“Reducto ad absurdum [proof by contradiction]….it is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

G.H. Hardy

Proof by Contradiction: An Example

In 300 BC, Euclid published his work Elements, giving us the postulates that are the foundation of geometry. Among them was his fifth postulate: parallel lines exist, or if two straight line segments are intersected by another line a, then the sum of the interior angles on the same side is less than two right angles, then the lines will extend far enough to intersect somewhere in space.

Euclid’s 5th Postulate — If a & b are less than 180 degree, then two lines will intersect.

Euclid set about to assert a baseline from which to compare the movement of rigid bodies with the above postulates.

In 1733, Girolamo Saccheri sought to prove Euclid’s fifth postulate by contradiction. In other words, Saccheri assumed a world existed in which the a and b angles in the above picture were less than 180 degrees, yet the lines did not intersect. If Saccheri could disprove this statement, then parallel lines would then be “proven” in a mathematical sense.

He failed, but he gifted the world with the basis for hyperbolic geometry. Think instead of a flat plane extending infinitely, a plane over a sphere or a circle — like as if it was a tennis ball. In this dimension, we could draw two parallel lines through which the intersection produce angles a and b there were less than 180 degrees.

Parallel lines existing in hyperbolic geometry — intersecting angles a and b total less than 180 degrees in contradiction to the Euclidean plane yet the lines existing in parallel.

So what? The creation of this new world, hyperbolic geometry, is giving us insight to understanding quantum space time and special relativity. Both of which continue our progress in physics and understanding of our universe.

Contradiction proofs assume new rules, and give the world new paradigms to consider. Newly assumed rules send shock waves through science, technology, markets and nations.

  • A group of people assumed a nation could be run as a democracy with new rules.
  • Another group of people assumed there would be a world wide internet with flow of information (and money if we’re honest, see error code 402).
  • Another group of people assumed financial decisions could be based on mathematics alone and prove profitable.

At the time, the above assumptions were absolutely radical. Those who pursued those ideals didn’t join the pursuit in order to break limitations but to rewrite the rules entirely. Proofs by contradiction work in a similar way not to prove existing assumptions but to see if they can be disproved in light of new rules.

Ethereum is a proof by contradiction.

Ethereum has not sought out to be a comparison with existing financial systems or technologies. It has a new set of rules entirely. Perhaps this is why adoption, beyond price speculation, has not even truly begun? Maybe it’s why enterprise proof of concepts or proof of value have fallen flat? In order to test out the hypothesis of Ethereum, or any public blockchain, we need to play by the new rules of the Ethereum paradigm, not the old ones.

Ethereum has not proven all of its rules. It is trying to create a world in which these rules can exist.

Here’s what Ethereum’s rules are:

1. Public blockchain (predominantly Ethereum) will function as an ultimate settlement layer for value.

Ethereum was meant to allow programmable money with a worldwide virtual machine for running programs (smart contracts). Public blockchain will be a settlement layer for value — one layer of many. Think the U.S. judicial system, every court case does not go to the supreme court, but the supreme court is there to interpret the laws, if needed. Other blockchains and systems will tie back to Ethereum to allow the ultimate transmissions of value across services without siloed friction.

See Loopring and how this non-custodial exchange has moved to a Layer 2 solution on top of the public Ethereum blockchain that provides users with minimal transaction cost, yet this still offers liquidity of operating within the entire Ethereum ecosystem should the user choose to move their funds back to the main Ethereum network.

While centralized institutions will continue to provide services around public blockchains, the spectrum between completely centralized stacks of value transmission and information verification to completely decentralized systems will change — narrowing and widening with appropriate use cases.

2. There exists direct to customer interoperable non-custodial financial services and liquidity.

FinTech is codifying the old financial system — very much needed, and the effort is unlocking banking services closer to the end user.

However, the difference with the Ethereum financial tools is that the decentralized financial tools do not need to hold my funds in a centralized system. I can use the same wallet to exchange tokens on one platform and then lend and borrow on other platforms — all without these entities holding my funds. Funds are held in wallets and smart contracts. Take for example the ability to take a loan out of Aave or Compound protocols using the same wallet — without the need for either to hold funds. And you can trade, withdraw, or repay 24 hours a day, 7 days a week, 365 days a year. Furthermore, even liquidity for exchanges is even held in publicly accessible smart contracts.

KYC (Know Your Customer) activities are not precluded here — those can be codified as well, your Ethereum address (or wallet) is you, after all.

3. Tokenized assets and securities across industries.

If assets and securities could be traded across a protocol or tying back to a single protocol, we would unlock enormous rigidity in our financial structure. If the sale of an asset or a divestiture of an organization could be verified by regulators and transmitted to new owners under even just the same ownership guidelines, much would be achieved. For example, say you wanted to sell you car. All you would have to exchange is Ethereum addresses. Not do you have Venmo? Do you have Zelle? Would you take a check? Do you have Bank of America? Barring regulatory restrictions, users could use any service or even code for themselves to send and receive tokens — it all works on the same underlying protocol.

You could even set up a smart contract that accepts a variety of tokens that your customer desires to pay in and converts them immediately to your desired token of choice, accounting for slippage in trading! And then that smart contract could transfer the ownership of the car when complete. Barring the government regulated physical paper transfer of the title, of course.

4. Tokenized national currencies supported by central banks, public banks, private banks, and private institutions.

Ethereum is not meant to solely function off the transfer of Ether and fluctuating tokens from projects. Projects such as MakerDAO and Circle have been providing a method of accessing USD equivalent tokens on the Ethereum chain since 2018. I can recall in 2018 there was less than $100M tokenized as USD on Ethereum via MakerDao, and now, there is over $1.3 billion. In total, all stable coin projects together have over $30B tokenized as stable coins tied to some form of national fiat currency.

Banks have the opportunity to participate in this new ecosystem as well. Just this year, the US has given the green light to banks to allow for crypto custody services. Although Grayscale’s fund has swung open a door to price exposure, along with others, wait until hedge funds and and banks understand what they can actually do with stable cryptocurrencies…

Even today, through the synthetic assets platform, Synthetix, with the collateralization of their stable token, users can gain exposure to the price of gold, oil, and other commodities on the public Ethereum blockchain. Besides regulation and coding up these projects in general, what else is stopping more synthetic assets, custom made derivatives, and options from proliferating?

5. Early adopter and community owned companies, organizations, or other entities.

In September, Uniswap, a decentralized exchange on Ethereum that is regularly seeing higher per day transaction fees than Bitcoin, deployed a token to its ~250,000 early users. Over the course of minutes, throughout the world, any one that had used Uniswap had instant stake in the company to the tune of around $1,200. Assuming sanity, for Silicon Valley, that user acquisition cost is not out of the realm of rationality at all. Uniswap rivals have followed suit, and new protocols have even enlisted the user lists from old protocols to disseminate their tokens.

While Uniswap boasts a robust list of conventional investors, the project is far on the spectrum of near complete decentralization ideals. As an exchange, they hold no funds of their customers, liquidity is sourced from the community and rewarded, and now, early community members can have a stake in the game as well. And if you missed out as an early user, you can indeed purchase the UNI tokens through the Uniswap exchange.

In a world of inflation, real estate swings and a mystery stock markets, wouldn’t it be nice to have a stake in the companies that you actually use just by way of using them? Not airline miles with blackout dates or credit card points but actual value that you can exchange anywhere. Even while ownership remains concentrated companies, which is not a bad thing, the dissemination of ownership opens up worlds of possibilities for new users and start ups alike to collaborate and build together. If complete ownership by the community is better without a central team or investors being involved, it just needs to be proven.

6. Cryptographic proofs facilitating B2B — procurement, quality, trading, etc.

I have a distinct memory in starting my career as a buyer for an oil services company in which I declined an invitation to lunch with a vice president because I had too many purchase orders to send out. To my naive fresh out of college mindset, it was clear that I had work to do, not networking — a product of an engineering degree, I suppose. I’ve learned, but the ERP systems have remained fairly stagnant.

Why did I have so much work to do for purchase orders that were generated out of a combination of an automated system and plant requests? While “digitized,” I was printing PO’s and sending them over a convoluted network of “procure to pay” systems that each company hailed as its total solution while the actual buyers and people using the system where jumping in an out, copy, pasting, emailing pdf’s, entering order information manually, confirming orders through email.

If all participants of a supply chain were to get together for an epic kaizen, we could remove thousands of non-value add work tasks by agreeing on a common process. Fortunately, that will never happen — and I say fortunately because we would need to continuously improve any ways.

But what if we could agreement on a common protocol? A common framework for how to prove data and reconcile? Not one that we all had to follow every single element, but one that could evolve. Take the United States drivers license — regardless of your state, you need a drivers license to drive, but each state has a slightly different looking license. For example, some states use a vertical drivers license to visibly show when a person is under 21.

Ethereum provides the gateway of an interoperable “driver’s license” system for supply chain exchange of information through zero knowledge proofs. Zero knowledge proofs provide a way of proving information without exposing data — a typical example is the ability to prove that you are over 21 without revealing your birthday. These proofs could be designed to “prove” relevant supply chain required between two parties without either party having to reveal private information. (If you think the privacy aspect is exciting, wait until you see zero knowledge’s ability to scale systems.)

So image a smart contract on the public Ethereum blockchain that two enterprises have agreed to for purchase orders verifying zero knowledge proofs with information that is stored off chain in ERP systems. No information revealed on chain, no buyers digging through legacy systems and emails — each company able to retain the ERP system they want to work with without having to compromise in B2B interoperability. Imagine several levels of this system for speed.

The above is the premise for Baseline, an open source project founded by Consensys, Ernst & Young, and Microsoft. None of these companies “own” the project, it is completely open source. This is the Linux of what could be for B2B operations.

If we have an opportunity in which we can verify information and transact value on the same protocol as enterprises, can you image how much efficiencies could be gained or corporate procurement fraud could be curbed? How many hours could be saved on expense reports? New vendor creation? Spot sourcing?

In the series, Halt & Catch Fire, in building out a vision for a new computer in the very early internet days, eccentric salesman Joe MacMillan says, “Computers aren’t the thing. They’re the thing that gets us to the thing [the internet].”

Here again, for public blockchains…

Digitized ERP systems, private blockchains consortiums, aren’t the thing. They’re the thing that gets us to the thing [public blockchain].


In 2018, plasma was all the rage to scale Ethereum, now there is a focus on zero knowledge proofs. A simple example that Ethereum is agile enough to shift and has already shifted in many ways.

You may be asking, of all the public blockchains to build on, why Ethereum? There are better transaction speeds, better privacy elsewhere. Many of these projects tie back to Ethereum already in some form or fashion. The massive Ethereum community of 30x the developers of any other public blockchain is a familiar argument. The fact that Ethereum is already launched and over hurdles of regulation is also a huge plus. Still, from a technology perspective, we could go back and forth all day. The good news is if a better public blockchain arises, all it really has to do is…prove it.

While the “rules” will change and be rewritten with new innovations in cryptography, regulations and new business models, in a nod to Churchill, history will likely be kind to Ethereum because the community is going to build it.



Karen Scarbrough

“If anything’s gonna happen, it’s gonna happen out there…” Captn’ Ron