Oh joy! I bought this book over three decades ago and read it briefly when I purchased the thing. There are reasons that I was attracted to the book. As well, anyone who took some semblance of a western civilization course would have run into Descartes. Then, of course, mathematicians know of the man.
And, in terms of residue and remainings, philosophers have the guy entirely wrong. That has been my opinion for decades. But, was I right? Well, all of this time, there was nothing to make me think otherwise.
That is, until I reread the book during the past few weeks. And, that reading was at a desk marking the book as a student might while venturing off to the reference material, especially in regard to the history of mathematics. And so, now being through the book and wishing to build a case for both Descartes and Vico (PJ Davis and his co-author use this guy as a foil very well) there will be a series of posts.
- Descartes' Dream - PJ Davis, R Hersh, 1986 -- Page forward, please, and look at the Contents. My interest is the loss of meaning that we see now with GenAI on the landscape muddying the waters as well as consuming unreasonable amounts of resources, such as energy.
I must add two more links before going further as this will be split into many posts with sidetracks.
- Goodreads - I like this site but do not want an account nor do I use Apple (did in the beginning - but I am a developer believing in open methods) or Amazon (never spent time on the site; probably am the oldest person alive who never bought Amazon, do not intend to). So, this post is a 10 for the book (100?) out of 5 ;>).
- Cambridge - This is obligatory as most of the brainy who came here as colonists were of that ilk and not of Oxford. That's an issue that we can look at in detail given the subject of these posts. So, their post is about the dreams of Descartes that people want to hear about.
Okay, the motivation.
- Truth engineering - This link is to my collection of posts and articles that deal with subject of interest to discussions on intelligence, AI, machine learning and such from several levels due to my roles. I am a mathematical economist who worked in the role of engineering support. And, in particular, it was a long time effort at supporting advanced computational systems which included numeric modes (say, like Nvidia is pushing), knowledge based engineering (which would tame machine learning - and did back in the day), and general expert systems where I was immersed in Lisp via the machines and systems built upon them plus doing all of this in the context of real work (taming numerics, geometrically) that had measurable and highly effective rewards.
- Immanuel Kant (1704- 1804) - Now, of course, Kant came later but did overlap the life of Vico. We will look at that. For a few years now, I have been arguing that Kant was overlooked. His Prolegomena and Logic (some posts will do a review of this work with respect to its significance) are very much apropos to what we need to think about. Hint: Kant was superb in representing an insight that bridged the dynamics with which PJ&R deal; as such, and given his time, his conclusions can be taken as universal; that is, of course, with parallels being discussed with respect to time (+/- one generation) and space (oh yes, the world as we can now see it given the lenses possible with computational assists - some have been explored); we will entertain others and weigh in on non-euclidean nonsense.
- Dreams - This phenomenon has significances that are known widely yet are scoffed at by the mindset described in this book with respect to its long evolution. Okay?
There are other motivations that will be marked as such as the discussion unfolds. Simultaneously with these posts, there will be summaries on Linkedin and Quora. More detail will be provided as we get the first of these links in place
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PJ&R (henceforth, the reference to the book) start off with the dreams in order to grab attention. It got mine, but I was disappointed as I can lay out tales much deeper than they allow. Having said that, I know the PJ is a first-rate mathematician (Harvard guy - his Math Genealogy profile). He proved that time and again in this work. One of his popular ones from earlier times dealt with explaining the mathematical experience.
And, in this book, PJ&R do a very good job of grounding examples (see end of this post - vagus) upon experience which includes thinking as well as the practical aspects brought by the likes of Brouwer with intuitionistic, constructistic ways.
But, let's look at the two key guys starting with a disclosure: I will for the most part provide the birth and death year for people referenced. See Kant above. Also, given my situation as of the U.S. and researcher for the Thomas Gardner Society, Inc. which deals with the colony of Massachusetts and its role in the birth and growth of the U.S., I will related things across the waters to activities here (U.S.).
Example, of late, we are dealing with Bosworth and its relationship to our studies. That is when the Tudor reign started which ended with Elizabeth (Origins and motivations) who was several generations after Bosworth. However, the colonies, 100 years after Henry VIII, created an offshoot of the Ancient & Honorble Artillery Company of Massachusetts. Henry's group and this New England group still exist and are affiliated. There are many more parallels to explore (heard of CS Peirce or JW Gibbs of thermodynamics fame; there are many more).
- René Descartes (1596-1650) - We all know of him through his work. As a young man, I liked it when I ran into his "Methods" thinking. But, I had a geometric bent anyway and ended up dealing with modeling (on the digital twin side of things) with regard to the guts of the matter (not being an engineer; but this was more fun than the dismal stuff of economics; besides most engineers would not venture into the realms that I saw; which, btw way as a message to to GenAI/LLM folks, is very much pertinent to pulling you guys out of the holes that you dug for yourselves and us). Cartesian space? Yeap, listen up, non-euclidean might be fun; but, bringing in Plato and Vico, we will address that with a modern take, okay?).
- Giambattista Vico (1668-1744) - He had several influences but had a focus on humans and their lot and ways. As such, PJ&R were right in using him as the foil to discuss ins and outs of the Descartesian issues. We look forward to bringing in Baruch Spinoza (1632-1677) who was slightly older than Vico.
PJ&R gave their work a subtitle: The World According to Mathematics. An image of both gentleman is provided in the Preface. Then, the first section, chapters deal with the dreams, their aftermath, and then some comments on the historical contexts that bring Descartes' ideas into scope. As one reads this material, references to computing would be before 1986 which actually is a good thing.
Of late, many of the older people have been reminiscing about their experiences. As with any human activity, there was lots of activity with unlimited dreams and unbounded motivations. Yet, those years had glorious results some of which deals with the underpinnings of modern computing. Let's point to a couple of examples from Sperry Univac who was #2 to IBM, but there were more companies (say, those of Cray who did one of the first supercomputers): Adventures in Truth Engineering; Women behind Eniac. There are more examples, but these two set the tone that our use of recent events (as historical analogs) is based upon real experiences (and would be loved by Kant).
The second section of PJ&R's book? The Social Tyranny of Numbers. Wow, that is so apropos to the current situation. Remember, 1986 was when I was hotly involved with lots of knowledge systems in many different domains. Eventually, that focus reduced to digital product development (of major physical systems which had requirements of precision and meeting stringent constraints).
My first reaction on seeing GenAI/LLM two-plus years ago was that we could use knowledge modeling to remove some of the issues. However, the other side of the coin was that the "omni" drive of training which came from the motivations that were not mature created a mess. And, crap built into a system cannot be removed (think GIGO, modernized). Quality is built into a product through a quality focus throughout the processes involved. Six sigma is an example but has problems, too.
PJ&R's book addresses these. We will bring out their arguments and tune them to the current situation. This post is an introduction and overview. Some post will be more top-down for obvious reasons. We will have posts that are technically tuned. How deep we go depends upon several things? But, "deep" is relative. Flip it and one has a broadened shallow piece of work.
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But, here is an imperative (thank Kant). After twenty years of assessing truth and its issues from many angles which are touched upon in this blog and others, we concluded that, with respect to cognition which is what I had as a focus, a very proper frame would be at the level of theorectical chemistry. And, along that line, people offer the best of frameworks for study. And, then we can get into the knowledge universe of medicine and much more. Albeit, right now, ponder your vagus system which is depicted with this graphic.
For all of us, this system drives our life. Yet, we went eons without the types of insight into the dynamics. So, one set of positions were set by those associated with Descartes versus those of the Vico persuasion. And, mathematics? Does not like psychology? Well, this system tells us a lot, including possible motivations across eons, again, ending up with the likes of Jung and more. Gosh, we have to end this but will have common themes such as this one.
Last word? "Grounding?? So popular to certain philsophers and electricians? We will demonstrate that this provides a grounding which robotics can only dream of. And, cognitive processes residing solely upon heated circuits throwing out buckets of bits? Come on.
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Afterword. Did diving deeply into the work change my mind? Nope. Harvard is amiss, several ways. The mathematics of destruction was honed in that environment. But then, lots of cultures were at fault.
This book getting more attenion might be the salvation of Harvard (one of my interests). Perhaps, we are talking more of a "redemption" which is long overdue.
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Follow our series as we expand concurrently along the themes of meaning in the senses of man/machine and of being: Taming GenAI/LLM.
Remarks: Modified: 04/25/2025
04/25/2025 -- Added link for PJD's profile at Math Genealogy.
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