The math didn't add up!

Introduction:

• Ethereum is changing from a layer one focused community; where transactions, settlement, recording, consensus and security all occur on one blockchain, to one where these functions are divided up between two blockchains, the second blockchain being now referred to as Layer Two.
  This is important because dividing up the core functions of one blockchain creates security issues, potential attack vectors or vulnerabilities. Exciting stuff for sure, but the focus of this post is the math stuff. This elegant solution solves the math problems Ethereum faced and still faces.

The Problem

Ethereum is faster than the very first cryptocurrency blockchain: Bitcoin.
Ethereum is faster than the second cryptocurrency blockchain; Litecoin. Ethereum is slower than practically every other blockchain that was developed after it was....

Speed, is it everything?

Ethereum is very good at many things, and it processes transactions 100 times faster than a human can or could. But compared to newer blockchains, the new ones are 100-1000 times faster, some can be 1,000,000 times faster.
And speed has become a problem.

Define Speed?

• As in transactions per second?
• As in blocks verification?
• As in block size?
• As in settlement time?
• A veritable smorgesbord of delicious word games to play and numbers to crunch.
• Are we getting excited yet?

The Math stuff

• Ethereum was invented to deploy Smart Contracts, and these Smart Contracts give Ethereum functionality and or Utility Bitcoin doesn't have.
• These are not value judgements, just facts, statements, not bad, not good, not better, it is just a comment on what is...

Any who...

• Ethereum became the land of DeFi or decentralized finance. Something the creator Vitallic Butterin has gone on record admitting he didn't anticipate. - Which is cool, because he made something to open up possibilities and this wonderful possibility called decentralized finance developed.
• Decentralized finance is quite possibly one of the most important contributions to the future of finance and economic equality of our lifetimes.
• So nothing but respect for the man who made this possible.

Bitcoin gave us Rules without Rulers.
Ethereum gave us Smart Contracts and Non-fungible Tokens (NFTs) and these two things have given us : *Transactions without Middlemen and
Credit without credit scores .

Why is this important and when do we get to the math?

• Decentralized finance increased in size 1000 times in one year.
• 1000 times the amount of money invested
• 1000 as many transactions
• Solutions like changing from Proof of Work consensus to Proof of Stake consensus, specifically the flavor of Proof of Stake deployed gave increases in Speed defined as transactions per second of 4x, 8x, 16x and 64x.
• As impressive as these increases were, they were no match for increases in transactional volume of 10x, 100x and 1000x.

Arithmetic , Geometric and Exponential progressions

This is the math beauty of the situation.
Arithmetic progressions 2x, 4x, 6x, 8x, 10x, 12x
Geometric progressions 2x, 4x, 8x, 16x, 32x, 64x, 128x
Exponential progressions 10x, 100x, 1000x, 10,000x

Maths don't lie

Proof of Stake offered arithmetic progressions of scaling/increases in transaction capacity, even attacking it in three areas:
#TPS transactions per second
#Block-size
#Settlement-speed I think this is correct...

Proof of Stake plus sharding, partial blockchain downloads for nodes and other things offered geometric progressions

• 2x
• 4x
• 8x
• 16x
• 32x
• 64x
• 128x in peoples wildest dreams LOL

But the problems with DeFi was exponential growth

• 10x
• 100x
• 1000x
• 10,000x

Enter Second layer solutions

• Okay Defi increased transactional volume 1000x in one year
• How about we add a blockchain with 10,000x transaction speed of Ethereum
• Or two blockchains with 10,000x the speed of Ethereum
• Or ten blockchains with 10,000x of the speed of Ethereum

Ah ha ! The solution fits the problem

• Don't give me arithmetic progression solutions to exponential progression problems and tell me every thing will be okay.
• And Vitallic Buterin didn't do that...
• He quietly started a working group on Polygon
• He quietly started a working group on Roll-ups
• He planted the seeds and once again let them grow into something greater then the seed.
• That my friends is the beauty of the math solution. Maths don't lie.
• That is the beauty of the current solution Layer one and Layer Two, transactions on Layer two, settlement and security on Layer one, consensus and recording on both or one depending on the mechanism.