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SEMF | Emergence and the Role of Observeres in Coarse-Graining | Sean Carroll, Stephen Wolfram @SEMF | Uploaded October 2021 | Updated October 2024, 6 hours ago.
Extract from "How Universal Is the Idea of Numbers?" kindly contributed by Stephen Wolfram in SEMF's 2021 Numerous Numerosity: semf.org.es/numerosity

Full talk: youtube.com/watch?v=Sn7qlyMWbOM

SEAN CARROLL
Caltech Profile: https://pma.caltech.edu/people/sean-m-carroll
Blog: preposterousuniverse.com
Twitter: twitter.com/seanmcarroll?ref_src=twsrc%5Egoogle%7Ctwcamp%5Eserp%7Ctwgr%5Eauthor
ResearchGate: researchgate.net/profile/Sean-Carroll-6
Wikipedia article: en.wikipedia.org/wiki/Sean_M._Carroll
LinkedIn: linkedin.com/in/seanmcarroll

STEPHEN WOLFRAM
Wolfram Research: wolfram.com
Personal website: stephenwolfram.com
Wikipedia article: en.wikipedia.org/wiki/Stephen_Wolfram
ResearchGate: researchgate.net/profile/Stephen-Wolfram
Facebook: facebook.com/profile.php?id=100057988604325
LinkedIn: linkedin.com/in/stephenwolfram
YouTube channel: youtube.com/channel/UCJekgf6k62CQHdENWf2NgAQ

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Emergence and the Role of Observeres in Coarse-Graining | Sean Carroll, Stephen Wolfram

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$Causal Specificity, Functional Maps, Bijective Functions | Ameer Sarwar | Numerosity Workshop 2021 Session kindly contributed by Ameer Sarwar in SEMFs 2021 Numerous Numerosity Workshop: https://semf.org.es/numerosity/ ABSTRACT Neuroscientists are interested in understanding neural populations. This often involves comparing the effect of an intervention on population P1 with a controlled population P2. Since it is the only difference between populations, the intervention is taken to have causal powers (Waters, 2007; Woodward, 2003). Yet, neuroscientists are not interested in merely comparing manipulations or (statistical) differences. They instead want to understand the mechanisms that explain those differences, i.e., the ways in which causes influence their effects. Broadly speaking, causal influence comes in two varieties. On the one hand, it can be ‘coarse-grained.’ For example, neurosurgeons may lesion a brain area in order to reduce neural hyperactivity, e.g., during epilepsy. Indeed, this was done to patient H.M. when his medial temporal lobes were bilaterally removed. On the other hand, causal influence can be ‘fine-tuned.’ Rather than lesioning hyperactive areas, the medical doctor may, for instance, prescribe medication that inhibit neural firing, e.g., GABAergic. Neural hyperactivity, then, can be reduced in both ways, yet it makes a great deal of difference whether this occurs in a coarse-grained or fine-tuned manner. Philosophers of science have proposed ‘causal specificity’ as a way of understanding relative causal control (Weber, 2017a). According to this view, the causal set with the highest number of functional mappings onto the effect is most fine-tuned. What does this mean? Let A:{x, y, z} denote the set of sub-causes that influence population P. Here, A is the cause and x, y, and z are sub-causes. Let P:{f, g, h} denote the set of sub-effects influenced by A. Here, P is the effect and f, g, and h are sub-effects. Let us place these variables within an example. The cause may be an anticonvulsant (A), which acts via psychoactive proteins (x, y, z) that bind to postsynaptic receptors (f, g, h), thereby reducing neural hyperactivity (P). So, according to causal specificity, the degree to which the sub-causes of A—the values of the domain—map onto those of P—the values of the co-domain—constitutes the degree of causal control A exercises over P (relative to P’s other causes). Indeed, the A-to-P mapping must be functional: (1) All values of the domain must map onto at least one value of the co-domain, and (2) each value of the domain must map to no more than one value of the co-domain. The proponents of this view advance a numerical interpretation of ‘functional mapping,’ according to which “the number of values that the variables on both sides of the relation can take is vastly higher … than that of any other causal variables that bear the [same] relation” (Weber, 2017b, p. 32). My presentation will be a systematic critique of this view. First, the framework fails to capture the phenomena of dual effects, wherein a sub-cause influences two sub-effects. Second, the framework fails to capture causal redundancy, wherein a sub-cause fails to map onto any sub-effect in P. Third, the framework is incoherent when the numerical interpretation is advanced alongside the assertion that bijective functions are most specific. Finally, I want to suggest that the framework includes incommensurability. Accordingly, it seems that the very problem that motivated the discussion, namely whether a schematic can be developed for capturing relative causal control, cannot be accommodated. As a result, causal specificity as a view of causal control is misguided. AMEER SARWAR University of Toronto University of Oxford ResearchGate: https://www.researchgate.net/profile/Ameer-Sarwar Google Scholar: https://scholar.google.ca/citations?user=3L3z7rsAAAAJ Academia.edu: https://utoronto.academia.edu/AmeerSarwar SEMF NETWORKS Website: https://semf.org.es Twitter: https://twitter.com/semf_nexus LinkedIn: https://www.linkedin.com/company/semf-nexus Instagram: https://www.instagram.com/semf.nexus Facebook: https://www.facebook.com/semf.nexus$

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Emergence and the Role of Observeres in Coarse-Graining | Sean Carroll, Stephen Wolfram @SEMF