This paper is a perspective on Occam's razor and its role in the philosophy and practice of science. The paper begins with a general introduction which includes historical details on the genesis and fortune of Occam's razor. This is followed by the exploration of three main discussion points: a modern 'backlash' against Occam's razor, supported by a critique of the classical view of Copernicus' model of celestial mechanics as simpler than Ptolemy's; the connection between Occam's razor and Bayesian statistics; and the role of simplicity as a principle in the sciences that study complex systems, with specific reference to systems biology.

Overall the paper is in my opinion well written and informative, providing an interesting point of view on the importance of Occam's razor in science at a level which is eminently accessible to the practitioner who may (unfortunately) lack a strong background in philosophy of science. I have some minor remarks/questions on each section, which I will list below together with few typos I'd like to highlight. Please note that below I will refer to page numbers including the cover page (that is, page numbers as given by my pdf reader), as opposed to the page numbers printed in the paper.

1 Main comments
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1. regarding the discussion of the arguments around the simplicity of Copernicus' model compared to Ptolemy's. This section makes for a compelling story, but it would be improved by including more evidence to back up the statement that "It was the heliocentric system’s elimination of arbitrary and physically infeasible features, […] rather any circle count, that convinced an the giants of modern science that Copernicus’s system was simpler, and thereby more likely to be right.". This is stated multiple times in different forms ("Neither Copernicus nor his followers such as Brahe, Kepler, Galileo or Newton based their support for the supposed simplicity of his heliocentric model on any kind of crude circle count"; "So the giants of modern science were not fooled by Copernicus’ claim that his model was simpler than Ptolemy’s because, as a physical model of the world […] it was indeed simpler"), and is clearly the central message here. However, the direct evidence given that this was the case is sparse: we have a quote from Tycho Brahe (heliocentricity "circumvents all that is superfluous and discordant in the system of Ptolemy"), which however is rather generic: it is not incompatible with the interpretation given by the author, but at least out of its context it may also be interpreted as a general endorsement of Copernicus' ideas. Moreover, even accepting this quote as sufficient evidence on Brahe's view, this section of the paper repeatedly mentions Copernicus' other "followers", or "giants" such as Newton, Galileo, Kepler: what is the evidence that they were convinced that the power of Copernicus' theory resided in getting rid of features that made no physical sense in Ptolemy's model?

Just to be clear, I appreciate the argument made and I found it interesting and informative - I am not arguing against the idea that "getting rid of features that make little physical sense" is an advantage in Copernicus' model over Ptolemy (even if the number of circles is more or less the same in both theories). What I am suggesting is that this section of the paper would be strengthened if more evidence was presented for the claim that this was actually the opinion held by Brahe, Newton, Kepler, Galileo, etc. This is especially important because "what makes physical sense" is likely to be largely a cultural construct, and therefore we have no assurance that those early modern thinkers would share our intuition. For instance, take the sentence "What is an Earth year doing in the geocentric orbit of, say, Jupiter or Mars?". This is a very convincing observation from our point of view. However, if one's worldview posits that Man is the center of creation, it may be completely unsurprising to find that the fine details of the mechanics of the spheres of Jupiter or Mars are tuned to the same constants that also determine the mechanics of the sphere of the Sun (which controls the duration of a year).

1. between pages 11-12: "Although Bayesian inference was developed more than two centuries ago, it wasn’t until 1989 that, in his textbook on probability, the statistician Harold Jefferys [sic] pointed out that Bayesian inference automatically incorporates Occam’s razor. Jefferys’ provided more detailed arguments in the following years in papers in with James Berger in the early 1990’s". There is some confusion here between Harold Jeffreys (gephysicist and statistician, 1891-1989) and William Jefferys (astrophysicist, born 1940) (note the different, but confusingly similar, spelling of the surnames). Both have written about Occam's razor and Bayesian statistics. However, the former is the most influential. Indeed, a quantitative form of Occam's razor via Bayesian statistics is already described in chapter 5 of the first edition of his 1939 textbook, ^{1}. This seminal contribution is also cited as foundational by widely-cited historical papers on the topic, such as ^{2,3}. So the explicit, quantitative connection between Bayesian statistics and Occam's razor should be backdated by half a century, and credit should be given to H Jeffreys.

2. Page 13, top, while discussing the 60-face dice example. The example makes sense in the context of what will be discussed later on that same page ("The Bayesian razor is then a measure of the degree of collapse of the space of the possible data onto the space of the data.", etc), but it does not seem very convincing when presented in isolation. More precisely, it is not clear to me why to a naive reader the dice with 60 faces should constitute a "more complex" hypothesis than the dice with 6 faces. They are both dices, and work in exact the same way (as opposed to, say, an hypothesis that involved flipping a coin to determine which of two dices to throw). I suggest that this section is reworked so that the explanation of the concept of "complexity as flexibility of the model" appears before the dice example.

3. Page 16, lines 14-15. "A typical result would be that Bayesian methods (incorporating Occam’s razor) predict that all the flux goes through pathway B". This needs some unpacking. Why exactly a typical Bayesian result would be like that? Perhaps the example can be made more concrete, or expanded.

4. On the theme of Occam's razor and its special/universal role in rational decision making, I would like to point out that in recent years people have investigated the inherent relevance of Occam's razor to human cognitive processes: see for instance ^{4–6}.

2 Typos etc
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• page 1, line 25: "principal targets", not "principle targets"
• page 1, line 52: perhaps it'd be better to write "Covid-19 vaccine hesitancy remains (as of 2021) …" (if the numbers are indeed from 2021) to better situate, directly in the text, the historical context in which vaccine hesitancy is discussed in relation to covid.
• page 5, line 59 (and elsewhere): I think there is some interference between the numbering of the footnotes and the numbering of the bibliographical references. Please check.

3 References
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1. Jeffreys, H. /Theory of probability/. (Clarendon Press, 1939).

2. MacKay, D. J. C. [Bayesian Interpolation]. /Neural Computation/ 4, 415–447 (1992).

3. Gull, S. F. Bayesian Inductive Inference and Maximum Entropy. in /Maximum-Entropy and Bayesian Methods in Science and Engineering: Foundations/ (eds. Erickson, G. J. & Smith, C. R.) 53–74 (Springer Netherlands, 1988). doi:[10.1007/978-94-009-3049-0_4].

4. Piasini, E., Liu, S., Chaudhari, P., Balasubramanian, V. & Gold, J. I. How Occam’s razor guides human decision-making. 2023.01.10.523479 at (2023).

5. Gershman, S. & Niv, Y. [Perceptual estimation obeys Occam’s razor]. /Frontiers in Psychology/ 4, (2013).

6. Genewein, T. & Braun, D. A. [Occam’s Razor in sensorimotor learning]. /Proceedings of the Royal Society B: Biological Sciences/ 281, 20132952 (2014).