A great book on this is My Stroke of Insight, written by a neuroscientist who had a massive left-hemisphere stroke. Her experience was horrific in many ways, absolutely beautiful in others.

She also has a TED talk: https://www.ted.com/talks/jill_bolte_taylor_s_powerful_strok...

> Are you referring to written notation? Calling that geometry is a bit of a stretch.

Can you write without shape?

> There's also nothing geometric about maths encoded in computer code

Look at a computer chip under a microscope: nothing but geometry.

> or many types of mathematical thoughts

In re: math itself, perhaps there is such a thing as a mathematics of the formless (I doubt it but cannot rule it out) but to communicate it you are again reduced to some symbolic form.

> so I think you are just incorrect.

I've been thinking about this for a long time, and I'm still not 101% convinced, but I think it's true: you can't have information without form.

Check out "The Markable Mark" and "My Stroke of Insight". The act of distinction is the foundation of the whole of symbolic thought, and it is intrinsically a geometric act.

http://www.markability.net

> ... what is to be found in these pages is a reworking of material from the book Laws of Form.

> Think of these pages, if you like, as a study in origination; where I am thinking of 'origin' not in the historical sense but as something more like the timeless grounding of one idea on or in another.

Distinction is a physiological thing the brain does. It can e.g. be "turned off" by physical damage to the brain:

https://www.ted.com/talks/jill_bolte_taylor_my_stroke_of_ins...

https://en.wikipedia.org/wiki/My_Stroke_of_Insight

> Dr. Jill Bolte Taylor ... tells of her experience in 1996 of having a stroke in her left hemisphere and how the human brain creates our perception of reality and includes tips about how Dr. Taylor rebuilt her own brain from the inside out.

So whether you come at it from the mystical realm of pure thought or the gooey realm of living brains all math is geometric. (As far as I can tell with my gooey brain.)

Cheers!

I read the first half of this book about eight years ago and haven't stopped noticing the same story in different places. It shows up in meditation frameworks (Chuladasa's attention/awareness) to Jungian psychology (anima/animus), in Jill Bolte Taylor's story "My Stroke of Insight", and many more. Here's a list of my favorites: https://www.notion.so/cameronboehmer/de3eb3e0a9524b6989962c4...