In search of Marconi in Writtle and Chelmsford

Here's my key Philosophy a freak like me just needs infinity This is Gary Gek of the Gary Gek dot-com website I'm just a normal guy, but I wanted to make this my very first YouTube video talking about the secret side of history And take your time Today I'm going to cover the absolute infinity its contradictions and Mathematics as explored by gay or Cantor who lived 1845 to 1918 well, okay a lot of this stuff may not be so secret But why should just a handful of scholars and graduate students have all the fun? So I'm gonna bring some of this stuff that only they normally have access to to normal guys and gals everywhere So today I want to talk specifically about the metaphysics of gay or Cantor He's one of the most important mathematicians who ever lived I'm gonna get into some of the mind-blowing Mathematics, but that stuff is talked about quite often What I'm gonna get into is also some of the deeper stuff that isn't really talked about very often Cantor was the father of our mathematical understanding of infinity But he is also the father of set theory which is what he used to understand Infinities set theory is foundational today not only in mathematics But it's also important in philosophy logic and even in computer science Although they usually leave out some of the metaphysics and the more mystical philosophy that Cantor Clearly held which partly led to many of his discoveries You know, I'm not gonna be leaving that out today because I feel it's important to honestly represent what Cantor believed It doesn't mean that I'm endorsing what he believed I'm just trying to represent it because I feel like as truthful and honest of a study is that really deserves the light of day To quote David Hilbert, no one shall expel us from the paradise that Cantor has created for us But like so many other geniuses in his life Cantor struggled to get a good job when his work was often bitterly attacked by his critics despite the fact that Cantor could Rigorously demonstrate his most important ideas. They were often far too radical for his time And so at first he had to bury a lot of his results in unassuming ways to get them published Among less radical topics and even later on when he had gained some fame later in life He would still have to strip out the philosophical and metaphysical statements in his publishings especially in the French and English translations the preface of the English translation called the Contributions to the founding of transfinite numbers, which will from here on out simply be called contributions for short refers to itself as quote logically purified Basically, this means that they forced him to strip away much of the philosophy and metaphysics that you might find in the original German Publishings and yet this very same introduction on Page VI says quote the philosophical revolution brought about by Cantor's work was even greater perhaps than the mathematical one with few exceptions mathematicians joyfully accepted the Foundations of Cantor's undying theory, but very many philosophers combatted it This seems to be because very few understood it Many factors including the Caustic attacks that Cantor endured from his philosophical and mathematical Enemies and the sudden tragic death of his son Contributed to the roughly four years that professor Cantor Collectively spent in mental asylums throughout his life plus many today believe that he suffered from manic depression But it is clear that Cantor felt alone in his interests and he was mostly ignored and isolated from the larger Community by all accounts He was a loving father and a husband but still Cantor's biography is generally not a very happy one two excellent books that I used extensively to pair for this YouTube video are Gay or cancer his mathematics and philosophy of the infinite by Joseph Warren Dobbin published in 1979 by Princeton University Press and an essay by Rudiger Thiele Cancer which appeared in a book called mathematics and the divine published in 2005 by Elsevier Both books are available at Gary Geck comm if you click on the books button at the top of my site menu I've also studied Contributions in detail it is now in the public domain and I'll provide a link to the free copy in the book section of Gary Geck comm I've also sought out as many primary works as possible And I urge everyone to always try to focus on the primary works Wikipedia is great, but it's only gonna get you so far Now there's other YouTube videos out there on cancer and infinity and I highly recommend I especially like the videos called the infinities between one and two by the seller academic So I'd like to give him a shout out. My video is going to focus on a lesser known story Which is not on YouTube at present and that's Cantor's metaphysics and how Cantor viewed his work as Revealing the secret knowledge of God. So this will be some pretty light hearted stuff To Cantor God existed mathematics was God's language in an extension of God's possibilities in power Cantor accepted the actual this is in real dramatic contrast to Potential infinite one of the underlying Theses of garygeck.com is that there's two main branches in Western philosophy But we're only really familiar with one of them we are familiar with the one that is very much opposed to metaphysics and respects physical science about philosophy the tradition of Plato Leibniz Cantor Kurt Gödel saw things very differently put much more emphasis on the Philosophy and metaphysics of mathematics as these individuals and members of this tradition made their groundbreaking discoveries now I'm generalizing here because as you get into the higher reaches of scholarship and graduate studies These topics do come But to the average person in the normal guys and girls the stuff is kind of not really very well known Which is what this video is for Now my video series will expose many of the secrets of mathematics To professors and grad students, here's one example In the difference between I mentioned the potential in the actual Infinity now it was believed by Cauchy that he had finally put calculus on a firm ground Without any recourse to the metaphysics that had been at least Smelled prior to Cauchy's Formalization. In fact, we use Cauchy's famous equation today when we learn calculus 99% of the time And we all know about the the Delta Y over the Delta X equals the function of X plus epsilon minus F of X over epsilon but as Abraham Robinson pointed out in his 1969 article on the metaphysics of the calculus in a book also available on Gary Geck comm What Cauchy did here was just simply put off further the problem and no one seems to have noticed this to quote Abraham Robinson when talking about the perceived weaknesses of Method used before Cauchy that is Leibniz's method quote the weaknesses had been associated Throughout with the introduction of entities which were commonly regarded of denizens of the world of actual infinity It now appeared that Cauchy was able to remove them from that domain into base analysis on the potential compared to Cantor and Corrucio he did this by choosing as basic the notion of a variable which intuitively suggests potentiality rather than actuality And so it happened that a grateful public was willing to overlook the fact that from a strictly logical point of view The new method shared some of the weaknesses of its predecessors and indeed introduced new weaknesses of its own unquote that's from page 161 on the philosophy of mathematics that I will link to on my site in other words the sober-minded mathematical public have been forced to stare at actual infinity for over a hundred years and absolutely despised Philosophically in the form of an infinitesimal but the works of Abraham Robinson and others in the 1960s proved the Leibniz's method was actually perfectly sound and rigorous and that the attempts of Cauchy and others to Simply sweep infinity under the carpet and replace it with the variables was more smoke and mirrors than anything actually rigorous But yet we still use Cauchy's method today in calculus textbooks not Leibniz's So I guess Robinson's words have fallen on deaf ears, but I digress I'd like to make a quick note about Abraham Robinson He really is such an interesting guy that he deserves his own video and perhaps you'll see one on garygeck.com Soon enough. I would like to recommend a biography, however also by Joseph Warren Dauben called Abraham Robinson the creation of non-standard analysis a Personal and mathematical odyssey you can get this book at garygeck.com This book makes an interesting parallel between Robinson and Cantor on pages 354 to 355 it makes the astute point that Robinson helped define and legitimize the infinitely small Just as Cantor did the same with the infinitely large in the form of the transfinite That Cantor rejected the infinitely small Infinitesimal is especially ironic because Robin seems to have had serious doubts about the actual infinite so you have Robinson basically proving the existence of the infinitesimal while disbelieving the actual infinite and you have Cantor proving the actual infinite but rejecting the infinitesimal Robinson relied highly on Cantor's work and he considered himself as operating in the set theoretic tradition of Cantor And I'd like to build upon this By noting that both Cantor and Robinson were both basically Platonists well, at least they could be said to know their way around the works of Plato and even the Neoplatonists in fact Robinson had a dual doctorate in mathematics and in Philosophy so like Cantor he was highly educated in philosophical matters Both men can be described as generally well-rounded with interests in music theater, etc Both had happy marriages and loving wives on page 98 of Dobbin's biography on Robinson He writes when talking about the discussion that Robinson had one night with Chaiman and his wife Miriam Abramsky While the three were staying together through the horrible and deadly London Blitz quote Abramsky was impressed by Robinson's wide range of interests which included not only philosophy But a very broad spectrum of German culture Abby's substantial knowledge of Goethe was he thought remarkable Robinson was just as happy discussing Maimonides Which Abramsky admitted again surprised me because Maimonides I thought was quite remote from modern aspects of mathematics Bombs were falling outside, but inside there was much song hilarity unquote Robinson was the head of mathematical departments in universities such as UCLA Yale the University of Jerusalem and other world-renowned institutions Robinson was an advocate of non-standard analysis being the new way that mathematics and even mathematical physics would be done Following in a more Leibniz Ian tradition. It was far more intuitive he argued and To this day, I know many engineers who agree and use it in their projects simply to save time Many mathematical discoveries have been made using it But afterwards those discoveries have always been translated back into standard analysis I'm sure Robinson is rolling in his grave