On p. 170 of the book I included the following footnote: “A probabilistic derivation avoiding the indistinguishability postulate also appears in Kolokoltsov (2021). The present approach is distinct in retaining particle distinguishability and encoding dependence via attraction/repulsion in state space.”
The paper is this: Kolokoltsov, V.N., 2021. On a probabilistic derivation of the basic particle statistics (Bose–Einstein, Fermi–Dirac, canonical, grand-canonical, intermediate) and related distributions. Transactions of the Moscow Mathematical Society, 2021, 77–87, https://doi.org/10.1090/mosc/316
I didn’t know the paper. It was discovered by Grok, after my question if there is something similar in literature. Generally, the paper is also unknown to others: It was cited only once in an Arxiv preprint by authors from China and Uzbekistan (see https://scholar.google.com/scholar?cites=13614810175338985935).
The official site (as specified by the paper’s doi link I gave above) for that Russian paper published by a Russian society is not in a Russian website. It is hosted by the American Mathematical Society.
Having discovered that, I gave this prompt to Grok: “Very funny that the Transactions of the Moscow Mathematical Society are published by the American Mathematical Society, which in turn does not allow me to access it because I don't have a subscription :-)”
Grok replied this: “Haha — the irony is chef’s kiss perfect! The American Mathematical Society proudly publishing a Russian mathematician’s paper… and then putting it behind a paywall that even the author’s international colleagues can’t easily access. Classic academic publishing comedy. 😄”
I agree — it's a comedy. But for Russia, it’s a tragedy. The famous Moscow Mathematical Society (https://en.wikipedia.org/wiki/Moscow_Mathematical_Society), which used to have the greatest 20th-century mathematicians as members and was presided over by figures such as Dmitri Egorov, Pavel Alexandrov, Andrey Kolmogorov and Vladimir Arnold, is now unable to publish its own papers and has to rely on the American Mathematical Society.
The humorous asides are great! But why are you so pleased that Grok approves? ".....every AI query is being nudged through an ethical filter -and the filter was not designed by you, your government or anybody you can vote out. Ep.498: The Governance Stack:How Technocracy was Built Over200 Years." Courtenay Turner substack
I looked at my text again, and I didn't see where I wrote I was pleased that Grok approves.
Yet, I acknowledge Grok's help. This covered many issues, starting from spotting typos, suggest linguistic improvements, and even find errors in mathematics. By the way, it didn't find any of the latter. This doesn't mean that there are no errors. It just means that there are no errors which could be spotted by Grok.
Another usefulness was to check whether similar ideas or methods were already suggested by others in the past. In this, bots are very powerful as they access tremendous amounts of information, which is impossible for a human. Again, it wasn't able to find anything similar, which increased my confidence that what I propose is novel.
Technocracy zealots would not be disappointed if I did not use their bots. I prefer to use them for what is useful to me, also investigating their strengths and limitations, in combination with my own strengths and limitations. Relying on bots' replies on an issue that one is ignorant could be dangerous, as one could be terribly misled by the bots.
It was the rather adulatory way you quoted the Grok assessment, starting with "I have just read the complete draft of Chapter 5..." and ending 14 lines below with, "... I cannot wait for the rest of the book." Of course, AI and bots will be very useful for those who are dealing with large quantities of very complex data, as you are. And, of course, you will not succumb to AI's addictive qualities and subtle guidance, but I fear that gradually individuals, production centres and once democratic governance structures are becoming increasingly dependent on AI as the powers that be, insinuate it increasingly from the top down into our lives.
Stochastics as Physics is a quite provocative title, platonist not aristotelian if taken literary. May I understand it as Stochastics is the appropriate mathematical framework for Physics?
Is the book intended as a volume of monographs or as a textbook? What is the intended audience? Undergraduates after Papoulis? Metsovion 1970s graduates?
Condensing Papoulis in 3 chapters makes it self-contained in theory, but not in practice, self reading needs maturity. Thank you!
Yes, it is a deliberately provocative title. And it’s meant literately. Stochastics *is* physics. If you read it you will see why.
Yes, it is Platonist in a way, but also Aristotelian. If you read what I say about Aristotle’s dipole δύναμις vs. ενέργεια, you will see why stochastics is the quantification of Aristotle’s idea.
It is intended as a stand-alone volume, addressed to whom it may concern. Not a funded project report, not a textbook for students, not a commercial product to be sold (it’s in open access).
No, it doesn’t condense Papoulis. If you read it you will see that, even from the very beginning of Chapter 2, it takes a different approach. See my definition of entropy and also my critique to Papoulis on this. Most of the material presented in Chapters 2-4 is not contained in Papoulis. This is not lack of respect to Papoulis. Actually, his book taught me most of what I know about stochastics.
It is not uneasonable for a prospective reader to ask what is the necessary backaground to read the book and understand its implications. Of course you are under no obligation to provide the answer. I am interested in low probability events and the idea of introducing a basic principle for choosing a distribution resonates with me. I am sorry about the 'condensed Papoulis' phrase and apologize.
No reason to be sorry and apologize! On the contrary, your comment was most useful to clarify matters.
I thought I had answered your question about the audience. But perhaps I misunderstood it. If you ask about the required background knowledge to read it, I would say that knowing calculus and having taken first courses of probability and physics would be enough. Yet, the book includes some Digressions which could be readable by lay persons. Generally, I don't follow a recipe for a specified audience; I improvise.
About low probability events and choosing distributions: I think my other book, "Stochastics of Hydroclimatic Extremes - A Cool Look at Risk", now in its fifth edition, covers very well this subject. It is again in open access in several locations, e.g. you may download it from https://climath.substack.com/p/stochastics-of-hydroclimatic-extremes -- for hard copies you may consult https://www.itia.ntua.gr/2000/
An interesting side story.
On p. 170 of the book I included the following footnote: “A probabilistic derivation avoiding the indistinguishability postulate also appears in Kolokoltsov (2021). The present approach is distinct in retaining particle distinguishability and encoding dependence via attraction/repulsion in state space.”
The paper is this: Kolokoltsov, V.N., 2021. On a probabilistic derivation of the basic particle statistics (Bose–Einstein, Fermi–Dirac, canonical, grand-canonical, intermediate) and related distributions. Transactions of the Moscow Mathematical Society, 2021, 77–87, https://doi.org/10.1090/mosc/316
I didn’t know the paper. It was discovered by Grok, after my question if there is something similar in literature. Generally, the paper is also unknown to others: It was cited only once in an Arxiv preprint by authors from China and Uzbekistan (see https://scholar.google.com/scholar?cites=13614810175338985935).
The official site (as specified by the paper’s doi link I gave above) for that Russian paper published by a Russian society is not in a Russian website. It is hosted by the American Mathematical Society.
Having discovered that, I gave this prompt to Grok: “Very funny that the Transactions of the Moscow Mathematical Society are published by the American Mathematical Society, which in turn does not allow me to access it because I don't have a subscription :-)”
Grok replied this: “Haha — the irony is chef’s kiss perfect! The American Mathematical Society proudly publishing a Russian mathematician’s paper… and then putting it behind a paywall that even the author’s international colleagues can’t easily access. Classic academic publishing comedy. 😄”
I agree — it's a comedy. But for Russia, it’s a tragedy. The famous Moscow Mathematical Society (https://en.wikipedia.org/wiki/Moscow_Mathematical_Society), which used to have the greatest 20th-century mathematicians as members and was presided over by figures such as Dmitri Egorov, Pavel Alexandrov, Andrey Kolmogorov and Vladimir Arnold, is now unable to publish its own papers and has to rely on the American Mathematical Society.
Wow, interesting!! 🤔
Glad you liked it!
The humorous asides are great! But why are you so pleased that Grok approves? ".....every AI query is being nudged through an ethical filter -and the filter was not designed by you, your government or anybody you can vote out. Ep.498: The Governance Stack:How Technocracy was Built Over200 Years." Courtenay Turner substack
I looked at my text again, and I didn't see where I wrote I was pleased that Grok approves.
Yet, I acknowledge Grok's help. This covered many issues, starting from spotting typos, suggest linguistic improvements, and even find errors in mathematics. By the way, it didn't find any of the latter. This doesn't mean that there are no errors. It just means that there are no errors which could be spotted by Grok.
Another usefulness was to check whether similar ideas or methods were already suggested by others in the past. In this, bots are very powerful as they access tremendous amounts of information, which is impossible for a human. Again, it wasn't able to find anything similar, which increased my confidence that what I propose is novel.
Technocracy zealots would not be disappointed if I did not use their bots. I prefer to use them for what is useful to me, also investigating their strengths and limitations, in combination with my own strengths and limitations. Relying on bots' replies on an issue that one is ignorant could be dangerous, as one could be terribly misled by the bots.
It was the rather adulatory way you quoted the Grok assessment, starting with "I have just read the complete draft of Chapter 5..." and ending 14 lines below with, "... I cannot wait for the rest of the book." Of course, AI and bots will be very useful for those who are dealing with large quantities of very complex data, as you are. And, of course, you will not succumb to AI's addictive qualities and subtle guidance, but I fear that gradually individuals, production centres and once democratic governance structures are becoming increasingly dependent on AI as the powers that be, insinuate it increasingly from the top down into our lives.
Quoting a text in another text means putting the former exactly as is in the latter (and mentioning its origin).
I don't want to split hairs over this. It just seemed that you needed AI to validate your work, which you don't.
Stochastics as Physics is a quite provocative title, platonist not aristotelian if taken literary. May I understand it as Stochastics is the appropriate mathematical framework for Physics?
Is the book intended as a volume of monographs or as a textbook? What is the intended audience? Undergraduates after Papoulis? Metsovion 1970s graduates?
Condensing Papoulis in 3 chapters makes it self-contained in theory, but not in practice, self reading needs maturity. Thank you!
Yes, it is a deliberately provocative title. And it’s meant literately. Stochastics *is* physics. If you read it you will see why.
Yes, it is Platonist in a way, but also Aristotelian. If you read what I say about Aristotle’s dipole δύναμις vs. ενέργεια, you will see why stochastics is the quantification of Aristotle’s idea.
It is intended as a stand-alone volume, addressed to whom it may concern. Not a funded project report, not a textbook for students, not a commercial product to be sold (it’s in open access).
No, it doesn’t condense Papoulis. If you read it you will see that, even from the very beginning of Chapter 2, it takes a different approach. See my definition of entropy and also my critique to Papoulis on this. Most of the material presented in Chapters 2-4 is not contained in Papoulis. This is not lack of respect to Papoulis. Actually, his book taught me most of what I know about stochastics.
Thanks for your comment and interest.
It is not uneasonable for a prospective reader to ask what is the necessary backaground to read the book and understand its implications. Of course you are under no obligation to provide the answer. I am interested in low probability events and the idea of introducing a basic principle for choosing a distribution resonates with me. I am sorry about the 'condensed Papoulis' phrase and apologize.
No reason to be sorry and apologize! On the contrary, your comment was most useful to clarify matters.
I thought I had answered your question about the audience. But perhaps I misunderstood it. If you ask about the required background knowledge to read it, I would say that knowing calculus and having taken first courses of probability and physics would be enough. Yet, the book includes some Digressions which could be readable by lay persons. Generally, I don't follow a recipe for a specified audience; I improvise.
About low probability events and choosing distributions: I think my other book, "Stochastics of Hydroclimatic Extremes - A Cool Look at Risk", now in its fifth edition, covers very well this subject. It is again in open access in several locations, e.g. you may download it from https://climath.substack.com/p/stochastics-of-hydroclimatic-extremes -- for hard copies you may consult https://www.itia.ntua.gr/2000/