Lost in Math: How Beauty Leads Physics Astray /1

Chp 2, What a Wonderful World, in Sabine Hossenfelder's Lost in Math: How Beauty Leads Physics Astray. Basic Books, NY. 2018.

[Commenting on J Kepler changing his mind, and accepting that it appears to be the planets' orbits around the Sun is better described as ellipses, not circles...]

He received criticism in particular from Galileo Galilei (1564–1641), who believed that “only circular motion can naturally suit bodies which are integral parts of the universe as constituted in the best arrangement.”2 Another astronomer, David Fabricius (1564–1617), complained that “with your ellipse you abolish the circularity and uniformity of the motions, which appears to me the more absurd the more profoundly I think about it.” Fabricius, as many at the time, preferred to amend the planetary orbits by adding “epicycles,” which were smaller circular motions around the already circular orbits. “If you could only preserve the perfect circular orbit and justify your elliptic orbit by another little epicycle,” Fabricius wrote to Kepler, “it would be much better.”3

[Later in the chapter...]

[...] Werner Heisenberg, one of the founders of quantum mechanics, boldly believed that beauty has a grasp on truth: “If nature leads us to mathematical forms of great simplicity and beauty we cannot help thinking that they are ‘true,’ that they reveal a genuine feature of nature.”15 As his wife recalls:

One moonlit night, we walked over the Hainberg Mountain, and he was completely enthralled by the visions he had, trying to explain his newest discovery to me. He talked about the miracle of symmetry as the original archetype of creation, about harmony, about the beauty of simplicity, and its inner truth. 16

Beware the moonlight walks with theoretical physicists—sometimes enthusiasm gets the better of us.

Cognitive uncertainty explains various core empirical regularities, such as why people often appear very impatient, why per-period impatience is smaller over long than over short horizons, why choices frequently violate transitivity, etc

Cognitive Uncertainty in Intertemporal Choice. Benjamin Enke & Thomas Graeber. NBER Working Paper 29577, DOI 10.3386/w29577. December 2021. https://www.nber.org/papers/w29577

Abstract: This paper studies the relevance of cognitive uncertainty – subjective uncertainty over one's utility-maximizing action – for understanding and predicting intertemporal choice. The main idea is that when people are cognitively noisy, such as when a decision is complex, they implicitly treat different time delays to some degree alike. By experimentally measuring and manipulating cognitive uncertainty, we document three economic implications of this idea. First, cognitive uncertainty explains various core empirical regularities, such as why people often appear very impatient, why per-period impatience is smaller over long than over short horizons, why discounting is often hyperbolic even when the present is not involved, and why choices frequently violate transitivity. Second, impatience is context-dependent: discounting is substantially more hyperbolic when the decision environment is more complex. Third, cognitive uncertainty matters for choice architecture: people who are nervous about making mistakes are twice as likely to follow expert advice to be more patient.

9 Discussion

Contribution. Much of behavioral economics views intertemporal choice, and famous empirical regularities, as largely determined by non-standard discount functions (preferences). This paper argues for and empirically documents an important role of cognitive noise and complexity for intertemporal decision-making. An innovation of our study is that we directly measure and exogenously manipulate cognitive noise through self-reported cognitive uncertainty. Using this tool, we document that a large share of short-run impatience and hyperbolic discounting are driven by bounded rationality and cognitive noise, rather than impatient preferences. These insights matter not just from a scientific perspective but arguably have real economic implications. On the intensive margin of decision-making, hyperbolic discounting depends on complexity. On the extensive margin, cognitively uncertain people welcome the advice of experts even when those experts don’t know their preferences. While we emphasize throughout the paper that cognitive noise is complementary to (rather than replaces) taste-based present bias, we have shown that cognitive noise provides a better account of many of key economic phenomena that are often ascribed to present bias. In all, we interpret these results as providing some of the first direct empirical evidence that cognitive noise and cognitive uncertainty are relevant for a broad set of economic aspects of intertemporal choice.

Link to cognitive effects in intertemporal choice research. We conjecture that our account of cognitive uncertainty provides a rationale for extant empirical findings about “cognitive” effects in intertemporal choice research. The perhaps most widely-known result on cognition and intertemporal choice is that, if the time delay is relatively short, a lower availability of cognitive resources is associated with less patient decisions. At the same time, Ebert (2001) presents evidence that suggests that, over long horizons, a lower availability of resources makes people more patient. Our account of the link between inelasticity and cognitive uncertainty reconciles this somewhat puzzling combination of results. 

Moreover, Cubitt et al. (2018) present intriguing evidence that people’s decisions are much less sensitive to variation in the time delay when intertemporal decisions involve cross-domain comparisons (car now vs. vacation later) than when they only concern within-domain comparisons (car now vs. nicer car later). While no preferences-based intertemporal model predicts such effects, we conjecture that they are driven by higher cognitive noisiness in cross-domain comparisons.

Limitations. Our paper does not purport to explain nearly all intertemporal choice anomalies. One regularity that our study does not address are well-known framing effects, such as the speed-up / delay asymmetry (Loewenstein and Prelec, 1992) or date / delay effects (Read et al., 2005). At the same time, we do conjecture a potential link between such framing effects and our work: if one choice option is presented to people as the default that they can “speed up” at a cost, it seems plausible that people use that option as a cognitive default. Based on this idea, we conjecture that speed-up / delay asymmetries are more pronounced when cognitive uncertainty is high. More generally, this conjecture highlights that further research is needed to understand potential cognitive default actions. In this paper, we estimate the default action to be “intermediate,” which is consistent with various documentations of central tendency effects in cognitive psychology. Yet, it is important to note that the specific intertemporal choice context we study is one with which people have little or no experience. Future research will explore how potential cognitive default actions depend on experience and contextual influences.

The rise and fall of rationality in language

The rise and fall of rationality in language. Marten Scheffer, Ingrid van de Leemput, Els Weinans, and  View ORCID ProfileJohan Bollen. Proceedings of the National Academy of Sciences, December 21, 2021 118 (51) e2107848118; https://doi.org/10.1073/pnas.2107848118

Significance: The post-truth era has taken many by surprise. Here, we use massive language analysis to demonstrate that the rise of fact-free argumentation may perhaps be understood as part of a deeper change. After the year 1850, the use of sentiment-laden words in Google Books declined systematically, while the use of words associated with fact-based argumentation rose steadily. This pattern reversed in the 1980s, and this change accelerated around 2007, when across languages, the frequency of fact-related words dropped while emotion-laden language surged, a trend paralleled by a shift from collectivistic to individualistic language.

Abstract: The surge of post-truth political argumentation suggests that we are living in a special historical period when it comes to the balance between emotion and reasoning. To explore if this is indeed the case, we analyze language in millions of books covering the period from 1850 to 2019 represented in Google nGram data. We show that the use of words associated with rationality, such as “determine” and “conclusion,” rose systematically after 1850, while words related to human experience such as “feel” and “believe” declined. This pattern reversed over the past decades, paralleled by a shift from a collectivistic to an individualistic focus as reflected, among other things, by the ratio of singular to plural pronouns such as “I”/”we” and “he”/”they.” Interpreting this synchronous sea change in book language remains challenging. However, as we show, the nature of this reversal occurs in fiction as well as nonfiction. Moreover, the pattern of change in the ratio between sentiment and rationality flag words since 1850 also occurs in New York Times articles, suggesting that it is not an artifact of the book corpora we analyzed. Finally, we show that word trends in books parallel trends in corresponding Google search terms, supporting the idea that changes in book language do in part reflect changes in interest. All in all, our results suggest that over the past decades, there has been a marked shift in public interest from the collective to the individual, and from rationality toward emotion.

Keywords: languagerationalitysentimentcollectivityindividuality

Comments by Alex Tabarrok The Rise and Decline of Thinking over Feeling - Marginal REVOLUTION: The authors blame the change in language towards feelings on the failure of "neo-liberalism" which seems dubious and without plausible mechanism. If anything, I would put the causality the other way. A more plausible explanation is more female writers and the closely related feminization of culture.

Potential Drivers

Inferring the drivers of this stark pattern necessarily remains speculative, as language is affected by many overlapping social and cultural changes. Nonetheless, it is tempting to reflect on a few potential mechanisms. One possibility when it comes to the trends from 1850 to 1980 is that the rapid developments in science and technology and their socioeconomic benefits drove a rise in status of the scientific approach, which gradually permeated culture, society, and its institutions ranging from the education to politics. As argued early on by Max Weber, this may have led to a process of “disenchantment” as the role of spiritualism dwindled in modernized, bureaucratic, and secularized societies (21, 22).

What precisely caused the observed stagnation in the long-term trend around 1980 remains perhaps even more difficult to pinpoint. The late 1980s witnessed the start of the internet and its growing role in society. Perhaps more importantly, there could be a connection to tensions arising from neoliberal policies which were defended on rational arguments, while the economic fruits were reaped by an increasingly small fraction of societies (23⇓–25).

In many languages the trends in sentiment- and intuition-related words accelerate around 2007 (SI Appendix, section 9). One possible explanation could be that the standards for inclusion in Google Books shifted from “being in a library Google had an agreement with” to “from a publisher that directly deposited with Google” after 2004 to 2007, thus affecting the corpus composition. The 2007 shift also coincides with the global financial crisis which may have had an impact. However, earlier economic crises such as the Great Depression (1929 to 1939) did not leave discernable marks on our indicators of book language. Perhaps significantly, 2007 was also roughly the start of a near-universal global surge of social media. This may be illustrated by plotting the dynamics of the word “Facebook” as a marker alongside the frequency of a set of intuition and rationality flag words in different languages (SI Appendix, section 9).

Various lines of evidence underpin the plausibility of an impact of social media on emotions, interests, and worldviews. For instance, there may be negative effects of the use of social media on subjective well-being (26). This can in part be related to distortions such as the perception that your friends are more successful, have more friends, and are happier (27, 28) and more beautiful (29) than you are. At the same time, a perception that problems abound may have been fed by activist groups seeking to muster support (30) and lifestyle movements seeking to inspire alternative choices (31). For instance, social media catalyzed the Arab Spring, among other things, by depicting atrocities of the regime (32), jihadist videos motivate terrorists by showing gruesome acts committed by US soldiers (33), and veganism is promoted by social media campaigns highlighting appalling animal welfare issues (31). Many of the problems highlighted on social media will be real, and they may have been hidden from the public eye in the past. However, independently of whether problems are exaggerated or merely revealed online, the popular effect of such awareness campaigns may be the perception of an unfair world entangled in a multiplicity of crises. Further down the gradient from revelation to exaggeration we find misinformation. The spread of misinformation (34) and conspiracy theories (35) may be amplified by social media, as the online diffusion of false news is significantly broader, faster, and deeper than that of true news and efforts to debunk (36). Conspiracy theories originate particularly in times of uncertainty and crisis (35, 37) and generally depict established institutions as hiding the truth and sustaining an unfair situation (38). As a result, they may find fertile grounds on social media platforms promulgating a sense of unfairness, subsequently feeding antisystem sentiments. Neither conspiracy theories nor the exaggerated visibility of the successful nor the overexposure of societal problems are new phenomena. However, social media may have boosted societal arousal and sentiment, potentially stimulating an antisystem backlash, including its perceived emphasis on rationality and institutions.

Importantly, the trend reversal we find has its origins decades before the rise of social media, suggesting that while social media may have been an amplifier other factors must have driven the stagnation of the long-term rise of rationality around 1975 to 1980 and triggered its reversal. Perhaps a feeling that the world is run in an unfair way started to emerge in the late 1970s when results of neoliberal policies became clear (23⇓–25) and became amplified with the rise of the internet and especially social media. A central role of discontent would be consistent with the rise in language characteristic of so-called cognitive distortions (39) known in psychology as overly negative attitudes toward oneself, the world, and the future (40⇓⇓–43). If disillusion with “the system” is indeed the core driver, a loss of interest in the rationality that helped build and defend the system could perhaps be collateral damage.

Outlook

It seems unlikely that we will ever be able to accurately quantify the role of different mechanisms driving language change. However, the universal and robust shift that we observe does suggest a historical rearrangement of the balance between collectivism and individualism and—inextricably linked—between the rational and the emotional or framed otherwise. As the market for books, the content of the New York Times, and Google search queries must somehow reflect interest of the public, it seems plausible that the change we find is indeed linked to a change in interest, but does this indeed correspond to a profound change in attitudes and thinking? Clearly, the surge of post-truth discourse does suggest such a shift (44⇓⇓⇓–48), and our results are consistent with the interpretation that the post-truth phenomenon is linked to a historical seesaw in the balance between our two fundamental modes of thinking. If true, it may well be impossible to reverse the sea change we signal. Instead, societies may need to find a new balance, explicitly recognizing the importance of intuition and emotion, while at the same time making best use of the much needed power of rationality and science to deal with topics in their full complexity. Striking this balance right is urgent as rational, fact-based approaches may well be essential for maintaining functional democracies and addressing global challenges such as global warming, poverty, and the loss of nature.

Fig. 3. Ratio of intuition to rationality related words in the New York Times (A) and various book corpora represented in the Google n-gram database (B–E). The graphs depict the ratio of the mean relative frequencies of the sets of rationality-related and intuition-related flag words presented in Fig. 1, right-hand columns.