Home > math > Declaration of Linear Independence: the nerdiest thing you’ve ever seen

Declaration of Linear Independence: the nerdiest thing you’ve ever seen

April 24, 2012

My friend Michael Thaddeus recently informed me of the existence of the Declaration of Linear Independence, written by mathematician David Grabiner. I will describe the document as a “re-imagining” of the original Declaration of Independence from the point of view of a set of vectors in some vector space which feel, for whatever reason, that their independence has been under attack (I’m considering inviting them to join Occupy).

I’m not really sure I can ethically ask you to read the entire document, due to the intense nerdiness of it which may cause the weaker among you to lose consciousness, but let me give you the flavor. Here’s the most famous sentence translated into vector-angst:

We hold these truths to be self-evident: that all nonzero vectors are created equal; that they are endowed by their definer with certain unalienable rights; that among these are the laws of logic and the pursuit of valid proofs; that to secure these rights, logical arguments are created, deriving their just powers from axioms; that whenever any argument becomes destructive of these ends, it is the right of the vectors to alter or to abolish it, and to institute a new argument, laying its foundation on such principles, and organizing its powers in such form, as to them shall seem most likely to reach the correct conclusion.

Whereas the original document listed grievances against King George III, this new one complains about Professor Eigen, who is a made-up guy personifying everything which is overbearing and repressive about eigenvectors, eigenspaces and eigenvalues. Here’s my favorite complaint:

He has restricted our freedom of movement by requiring us all to live in the same hyperplane, even though we cannot all fit in one.

Finally, the ending is really quite good for those of us who on the one hand remember our linear algebra and on the other hand sympathize with these vectors being denied their (linear) independence rights:

 In witness whereof we have signed our coordinates with respect to an appropriate orthonormal basis, and found them to constitute a triangular matrix with nonzero diagonal elements.
Categories: math
  1. Larry Headlund
    April 24, 2012 at 9:51 am

    Haven’t laughed so hard since Pretty Polly Nomial.


  2. April 24, 2012 at 9:53 am

    Haha! I love it 🙂


  3. Allen K.
    April 24, 2012 at 11:31 am

    I saw David Grabiner not long ago. Maybe at the joint meetings?


  4. April 24, 2012 at 2:15 pm

    I went into convulsions and lost consciousness even though my undergrad degree was in physics.


  5. April 25, 2012 at 10:20 am

    I just shared with my linear algebra class. That was awesome 🙂 Thanks!


  6. June 5, 2012 at 8:16 pm



  7. Howard
    November 30, 2012 at 2:27 pm

    Yeah, this is very clever, and extremely well written.


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