Thread by @sfiscience

"Explosive Proofs of Mathematical Truths"

In just a moment, we'll start live coverage of @SimonDeDeo's SFI Seminar-by-Zoom on a data science study of the epistemic structure of actual proofs.

(Seminar not streamed, but recording will be shared soon.)

santafe.edu/events/explosi…

Theodor Adorno proposed that political preferences are consequences of the kind of explanations people prefer — individual or systemic.

#SocialScience research by Jinwoo Kim asked: is there a correlation between the social and physical narratives preferred by authoritarians?

"We can think better about cultural evolution. We need to go beyond the infection metaphor and include more cognitive #science."

- @SimonDeDeo interrogating #memetics and the validity of #mimetic behavioral science interventions

Errors in any one step of a mathematical proof rapidly erode the probability that the entire proof is correct:

"Somewhere between 100 and 1000 steps is where you should stop believing in proofs altogether."

- @SimonDeDeo in today's virtual seminar:
santafe.edu/events/explosi…
#math

#Math proofs are not actually linear sequences of successive premises, but #networks of claims with different degrees of inter-relatedness.

This enables the emergence of certainty even when skeptical of any particular step's validity.

#Euclid & #Gödel's proofs c/o @SimonDeDeo:

Mathematicians describe proofs with linear narratives, but the data shows that proofs are in fact constructed as #networks—and the assembly of proofs appears to obey a power law of ~2. Not all claims are created equal.

@SimonDeDeo re: #Euclid #Appolonius #Spinoza

Proofs made of deductive pathways are directed acyclic graphs, but by allowing abductive pathways ("What could be true to make what I know more true?" or how #SherlockHolmes actually reasons: backwards), certainty in overall truth can emerge even with errors in individual axioms.