# I unified the Grassmann-Clifford-Hodge formulas

It might be difficult for you to grasp, but technically I am the person who discovered the significance of the Hodge complement and how it is used in geometric algebra.

Yea, the Hodge complement is an old idea, but nobody in the Hestenes-Doran-Dorst-etc lineage knew about the Hodge complement.

None of the Clifford algebra papers ever used the correct definitions for Hodge complement, except for a single paper by Hestenes once.

So when I figured out the geometric product form of the Hodge complement, I posted about it a million times on the internet, presented it at the 2019 Julia conference, wrote it into my paper in 2019, and have been teaching it since then.

Then you had people like @elengyel who published his new book, and before he published it, he double checked with me, because he learned my ideas about the Hodge complement from my videos.

Yet he NEVER acknowledged that he learned all that about the Hodge complement and how it is expressed using the geometric product from me and watching my videos, where I explained it very clearly for the first time for everyone to fully understand how it actually is defined in terms of geometric product and the Grassmann contraction variants.

Nobody else in history ever compared the Hestenes lineage of interior products and complements to the Grassmann-Hodge lineage of interior products and complements.

It was ME, i was the first person to make a big deal and point out the differences between the Hestenes-Doran-Dorst lineage and the Grassmann-Hodge lineage.

Now, some people throw around these ideas as if it has always been obvious what the significance of the Grassmann-Hodge variants are, compared to the incorrect ones adopted by the “community”

John Browne did explain some of that in his book, but never was able to combine it with the geometric product like I did. I was the person who pointed out in 2019 how it fits together with the geometric product.

Now, there are several Grassmann.jl imitation projects in Julia language, such as the one recently posted on here. They decided to adopt the same exact Hodge complement definitions that I have been teaching, along with imitating my API design and aspects of my type system, copying some functions and modifying them, and so on. Then they change the license and do not attribute their sources or where the definitions and inspiration came from. This is plagiarism.

I was the person who told the world how to think about the Hodge complement in a modern geometric algebra setting.

Nobody will ever acknowledge that, yet I was the person who figured that out. I was the only person for a long time trying to explain to as many people as possible what the Grassmann-Hodge variants are and how they can be understood using geometric products.

They all ridiculed me on the chat group while I tried to use mathematical proofs, showing that their definitions are incorrect and lead to mathematical inconsistencies.

First they ridicule me, then some people eventually take these ideas as self evident, and never acknowledge that I was the person who did the hard work of raising awareness about it. Nobody else in the Clifford algebra space was discussing it, they all ridiculed me for it because it contradicted their own definitions.

So yea, i’m not gonna get any credit or attribution for introducing people to the truth, when I was very clearly the first person in this modern time to point out how wrong everyone else is with their geometric algebra definitions. Yes, the Grassmann-Hodge stuff existed a century ago, but not using the geometric product formula I presented in 2019.

If you use the same definitions using the geometric product for Grassmann-Clifford-Hodge variant of geometric algebra, then technically you should have attributed that to me. Talking to @elengyel and other people imitating ideas I promoted to the world.

Show me where you got the geometric product forms of the Grassmann-Clifford-Hodge variants?

It can be traced back to my Grassmann.jl discussions and what I said online. I gave these formulas to the world, demonstrating how Grassmann-Hodge is supposed to combine with Clifford algebra.

So when I refer to Grassmann.jl as a Grassmann-Clifford-Hodge algebra, that is MY unification. I am the person who unified Grassmann-Hodge with the Clifford algebra properly and presented it in 2019.