How Much Math Is Knowable? Scott Aaronson

Theoretical computer science has over the years sought more and more refined answers to the question of which mathematical truths are knowable by finite beings like ourselves, bounded in time and space and subject to physical laws. I’ll tell a story that starts with Godel’s Incompleteness Theorem and Turing’s discovery of uncomputability. I’ll then introduce the spectacular Busy Beaver function, which grows faster than any computable function. Work by me and Yedidia, along with recent improvements by O’Rear, Riebel, and others, has shown that the value of BB(549) is independent of the axioms of set theory; on the other end, an international collaboration proved last year that BB(5) = 47,176,870. I’ll speculate on whether BB(6) will ever be known, by us or our AI successors. I’ll next discuss the P!=NP conjecture and what it does and doesn’t mean for the limits of machine intelligence. As my own specialty is quantum computing, I’ll summarize what we know about how scalable quantum computers, assuming we get them, will expand the boundary of what’s mathematically knowable. I’ll end by talking about hypothetical models even beyond quantum computers, which might expand the boundary of knowability still further, if one is able (for example) to jump into a black hole, create a closed timelike curve, or project oneself onto the holographic boundary of the universe.

Watch at: www.youtube.com

Egosyntonicity and emotion regulation: a probabilistic model of valence dynamics

Eleonora Vitanza , Chiara Mocenni and Pietro De Lellis

In this paper, we introduce a novel Markovian model that describes the impact of egosyntonicity on emotion dynamics. We focus on the dominant current emotion and describe the time evolution of its valence, modelled as a binary variable, where 0 and 1 correspond to negative and positive valences, respectively. In particular, the one-step transition probabilities will depend on the external events happening in daily life, the attention the individual devotes to such events, and the egosyntonicity, modelled as the agreement between the current valence and the internal mood of the individual. A steady-state analysis shows that, depending on the model parameters, four classes of individuals can be identified. Two classes are somewhat expected, corresponding to individuals spending more (less) time in egosyntonicity experiencing positive valences for longer (shorter) times. Surprisingly, two further classes emerge: the self-deluded individuals, where egosyntonicity is associated to a prevalence of negative valences, and the troubled happy individuals, where egodystonicity is associated to positive valences. These findings are aligned with the literature showing that, even if egosyntonicity typically has a positive impact in the short term, it may not always be beneficial in the long run.

Read the full article at: royalsocietypublishing.org

Quantifying Human-AI Synergy

Christoph Riedl, Ben Weidmann

We introduce a novel Bayesian Item Response Theory framework to quantify human–AI synergy, separating individual and collaborative ability while controlling for task difficulty in interactive settings. Unlike standard static benchmarks, our approach models human–AI performance as a joint process, capturing both user-specific factors and moment-to-moment fluctuations. We validate the framework by applying it to human–AI benchmark data (n=667) and find significant synergy. We demonstrate that collaboration ability is distinct from individual problem-solving ability. Users better able to infer and adapt to others’ perspectives achieve superior collaborative performance with AI–but not when working alone. Moreover, moment-to-moment fluctuations in perspective taking influence AI response quality, highlighting the role of dynamic user factors in collaboration. By introducing a principled framework to analyze data from human-AI collaboration, interactive benchmarks can better complement current single-task benchmarks and crowd-assessment methods. This work informs the design and training of language models that transcend static prompt benchmarks to achieve adaptive, socially aware collaboration with diverse and dynamic human partners.

https://osf.io/preprints/psyarxiv/vbkmt_v1 

Self-Reinforcing Cascades: A Spreading Model for Beliefs or Products of Varying Intensity or Quality

Laurent Hébert-Dufresne, Juniper Lovato, Giulio Burgio, James P. Gleeson, S. Redner, and P. L. Krapivsky

Phys. Rev. Lett. 135, 087401

Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions—the spread of ideas, beliefs, innovations—can lose or gain in momentum as they spread: ideas can get reinforced, beliefs strengthened, products refined. We study the impacts of such self-reinforcement mechanisms in cascade dynamics. We use different mathematical modeling techniques to capture the recursive, yet changing nature of the process. We find a critical regime with a range of power-law cascade size distributions with nonuniversal scaling exponents. This regime clashes with classic models, where criticality requires fine-tuning at a precise critical point. Self-reinforced cascades produce critical-like behavior over a wide range of parameters, which may help explain the ubiquity of power-law distributions in empirical social data.

Read the full article at: link.aps.org