Randolph Grace

I’m pleased to share that our article on the origins of arithmetic, just published in Psychological Review, has been selected as an @APA’s Editor’s Choice article (open-access link below). Here’s a thread about it (1/17) @mathematics @mathcogsociety psycnet.apa.org/psycarticles/2…

@Lasermazer @davidbessis If aliens had fundamentally different brains and intuitions than us, they would develop their own mathematics that would be nothing like ours. Their formalism would reflect their cognitive reality, whatever that might be

@davidbessis Isn’t mathematical truth somewhat independent of the details of how human brains most naturally think about and explore mathematical concepts? Wouldn’t alien mathematicians agree with us on mathematical truth even with very different brains and intuitions?

Math is the only physical activity where formal teaching has taken over practical coaching.⤵️

@Golovanov_ammoc For the same reason that no one bothers to read the instruction manual for a well-designed consumer electronic device

Mathematicians, in general, unlike-wise von Neumann & his contemporaries, do not WORRY about foundational questions, and many, perhaps most, of them aren’t even interested in such matters. It is surely natural to ask what is the cause of this complacency & whether it is justified

For admins, rankings are not valid measures of their Uni’s performance relative to others. Don't view overall or component scores as ‘key performance indicators’, but develop and validate own metrics of research and teaching quality. Interpret ranking data with caution! (8/x)

It suggests QS maintains a ‘pecking order’ that limits the changes in rankings. What are the implications? Students should do their own research on Unis they are interested in, and ought not to view changes in scores or rankings as necessarily reflecting changes in quality. (7/x)

University World Rankings are used by students and administrators to make important decisions. But what do they mean – can we interpret them as objective measures of quality? I was curious and downloaded the QS university ranking data for 2022-2026 #QSWUR @TopUnis #HigherEd (1/x)

The year-on-year changes are highly correlated! Scores for almost all Unis increased from 2023 to 2024 and then again from 2025 to 2026. Overall the % of shared variance is 83.3% - much more than would be expected be if these scores were independent. (4/x)

Congratulations to @RBodeker58583 who's just published an article in The Conversation on the implications for treatment of methamphetamine addiction of her PhD research with rats. Well done, Rebecca! theconversation.com/3-in-4-meth-us…

@edfrenkel Interesting episode! If our minds are connected, as mathematical objects in the collective unconscious suggests, then the 'unreasonable effectiveness' of math in the physical sciences points toward nondualism

🚨 New episode of AFTERMATH (my new series) is about Unification of Mathematics & Analytic Psychology. Following Carl Jung, I propose that all mathematical objects & ideas come from archetypes in our Collective Unconscious, so Math is a Portal into the Human Psyche. KEY POINTS: 1. All mathematical objects and ideas (such as perfect lines and planes) are rooted in the shared structural elements of our Collective Unconscious, which Carl Jung called archetypes. These mathematical archetypes produce identical images in our individual minds – explaining why everyone imagines the same idealized mathematical forms; even those forms that don't appear in the outer, physical reality. 2. Similarly to how individuals project their undesired or repressed character traits onto others (manifesting the Jungian archetype of the Shadow), entire societies projected the mathematical archetype of Flat Space onto the surface of the Earth, accepting as an axiom that it was flat. This unconscious belief exemplifies how unintegrated archetypal forces shape our perception of physical reality in the absence of conscious scrutiny. 3. Progress and evolution occur when people recognize and integrate mathematical archetypes, as exemplified by Pythagoreans' insight 2500 years ago that the surface of the Earth might be spherical. Moving from unconscious acceptance to evidence-based inquiry mirrors the process of owning and integrating personal shadow elements. 4. The Enduring Spell of Flat Space: Even though we now realize that Earth is round, most of us still reflexively perceive the Universe as a three-dimensional flat expanse. This unconscious attachment to the archetype of the 3D Flat Space hampers serious consideration of curved or higher-dimensional geometries. When we integrate the archetypes of the 3D Flat Space, the 3D Sphere, and so on, new dimensions of Reality may well open up to us. 5. Brilliant scientists, such as Einstein, Wigner, Weil, Poincaré, and Ramanujan have stressed the essential role of the unconscious (and dream-based) revelations in their work. Such flashes of insight align with Jung's view of archetypes spontaneously emerging from the Collective Unconscious, fueling humanity's creative and mathematical breakthroughs.

I remember watching Blue Velvet in a small arthouse cinema in Somerville MA during its initial release... a mind-blowing experience. When I walked out it felt like the movie hadn't stopped…. RIP Mr Lynch you will not be forgotten

There have been so many tributes to David Lynch, well out of proportion to his commercial success as a director. This is very heartening because it shows that people instinctively value an artist with an authentic vision. ...let me add mine (1/2)

@stephen_wolfram This is brilliant stuff, but 104 steps to prove a•b=b•a is like proof of 1+1=2 in PM. Key question is, what is the psychologically simplest formal basis for boolean algebra?

Formalized math: meet computational irreducibility. A simple (if surprising) theorem. An automated proof nobody seems able to understand. A tale of adventure in the wilds of metamathematical space... writings.stephenwolfram.com/2025/01/who-ca…

For example: Philosophy of mathematics. How are we going to maximize the potential benefits of AI when we're not willing to ask questions about the nature of computation? Philosophy is vitally relevant for science (2/2)

The problem with this decision is that the deepest questions, those most likely to lead to breakthroughs, are interdisciplinary. The humanities are relevant for science because all knowledge is connected. That's why we have universities (1/2)

Today, I announced that the Marsden Fund would no longer be used for the humanities and social sciences. It is returning to its original purpose to fund science. beehive.govt.nz/release/marsde…

@drspidernz @cbsturdy @AaronBlaisdell @MathSpatCog Worthy of a gold medal at the Arthropod Olympics! 😎🎉

@cbsturdy @AaronBlaisdell Nice! Go spider!! Yes, they DO bite (not sting). Hey @RandolphGrace @MathSpatCog - this is what I was talking about the other day. The spider won. 😊

I saw a bee fly into a spider web and video captured what happened next. Commentary by me and my daughter.