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10 episodes with Archimedean
2 episodes with Archimedean
2 episodes with Archimedean
2 episodes with Archimedean
Tobi Lütke is the founder and CEO of Shopify, a $130 billion business that powers over 10% of all U.S. e-commerce. Starting as a snowboard shop in 2004, Shopify has become the leading commerce platform by consistently approaching problems differently. Tobi remains deeply technical, frequently coding alongside his team, and is known for his unique approach to leadership, product development, and company building. In our conversation, we discuss:• Why complexity kills entrepreneurship• How to develop and leverage your unique talent stack• How specifically Tobi approaches thinking from first principles• The importance of focusing on unquantifiable qualities like joy and delight• Why Tobi works backward from a 100-year vision• Why metrics should support decisions, not make them• The power of following your curiosity• What Tobi believes it takes to be a great product leader• Much more—Brought to you by:• Sinch—Build messaging, email, and calling into your product• Liveblocks—Ready-made collaborative features to drop into your product• Loom—The easiest screen recorder you'll ever use—Find the transcript at: https://www.lennysnewsletter.com/p/tobi-lutkes-leadership-playbook—Where to find Tobi Lütke:• X: https://x.com/tobi• LinkedIn: https://www.linkedin.com/in/tobiaslutke/• Website: https://tobi.lutke.com/—Where to find Lenny:• Newsletter: https://www.lennysnewsletter.com• X: https://twitter.com/lennysan• LinkedIn: https://www.linkedin.com/in/lennyrachitsky/—In this episode, we cover:(00:00) Welcome and introduction(04:17) The Tobi tornado(07:10) Maximizing human potential(11:05) Education and personal growth(16:47) Operating without KPIs(25:00) First-principles thinking(40:04) Remote work(45:59) Why Tobi never stopped coding(54:46) Embracing disagreement(01:01:27) The 100-year vision(01:09:29) Balancing tactics and positioning(01:17:15) Encouraging entrepreneurship(01:19:34) The power of good UX(01:28:42) The talent stack and unique opportunities(01:34:30) The role of passion in product development(01:36:39) Final thoughts and farewell—Referenced:• How Shopify builds a high-intensity culture | Farhan Thawar (VP and Head of Eng): https://www.lennysnewsletter.com/p/how-shopify-builds-a-high-intensity-culture-farhan-thawar• Breaking the rules of growth: Why Shopify bans KPIs, optimizes for churn, prioritizes intuition, and builds toward a 100-year vision | Archie Abrams (VP Product, Head of Growth at Shopify): https://www.lennysnewsletter.com/p/shopifys-growth-archie-abrams• The ultimate guide to performance marketing | Timothy Davis (Shopify): https://www.lennysnewsletter.com/p/performance-marketing-timothy-davis• Brandon Chu on building product at Shopify, how writing changed the trajectory of his career, the habits that make you a great PM, pros and cons of being a platform PM, how Shopify got through Covid: https://www.lennysnewsletter.com/p/brandon-chu-on-what-its-like-to-build• IRC: https://en.wikipedia.org/wiki/IRC• Goodhart's law: https://en.wikipedia.org/wiki/Goodhart%27s_law• Glen Coates on LinkedIn: https://www.linkedin.com/in/glcoates/• How Shopify builds product: https://www.lennysnewsletter.com/p/how-shopify-builds-product• The Last Dance on Netflix: https://www.netflix.com/title/80203144• Autoregressive Models for Natural Language Processing: https://medium.com/@zaiinn440/autoregressive-models-for-natural-language-processing-b95e5f933e1f• Archimedean property: https://en.wikipedia.org/wiki/Archimedean_property• Tabula rasa: https://en.wikipedia.org/wiki/Tabula_rasa• Daniel Weinand on LinkedIn: https://www.linkedin.com/in/danielweinand/• World of Warcraft: https://worldofwarcraft.blizzard.com• Harley Finkelstein on LinkedIn: https://www.linkedin.com/in/harleyf/• Monorepo: https://en.wikipedia.org/wiki/Monorepo• The Sarbanes Oxley Act: https://sarbanes-oxley-act.com/• Shopify builds Shopify Balance with Stripe to give small businesses an easier way to manage money: https://stripe.com/customers/shopify• Stanford marshmallow experiment: https://en.wikipedia.org/wiki/Stanford_marshmallow_experiment• Brian Armstrong on LinkedIn: https://www.linkedin.com/in/barmstrong/• We are the Web: https://link.wired.com/public/32945405—Recommended books:• Finite and Infinite Games: https://www.amazon.com/Finite-Infinite-Games-James-Carse/dp/1476731713• The Infinite Game: https://www.amazon.com/Infinite-Game-Simon-Sinek/dp/073521350X/—Production and marketing by https://penname.co/. For inquiries about sponsoring the podcast, email podcast@lennyrachitsky.com.—Lenny may be an investor in the companies discussed. Get full access to Lenny's Newsletter at www.lennysnewsletter.com/subscribe
In the first half of a 2-part series examining claims of lost ancient high technology, I look at specific examples of advanced technology in the past that seems to have been lost to time, with a focus on the legendary inventions of Archimedes. Switch to Mint Mobile and get a new 3-month unlimited wireless plan for just 15 bucks a month. Visit MINTMOBILE.com/BLINDNESS! This episode is sponsored by BetterHelp. Visit BetterHelp.com/historical today to get 10% off your first month. Direct all advertising inquiries to advertising@airwavemedia.com. Visit www.airwavemedia.com to find other high-quality podcasts! Find a transcript of this episode with source citations and related imagery at www.historicalblindness.com sometime before the release of the next episode. Pledge support on Patreon to get an ad-free feed with exclusive episodes! Check out my novel, Manuscript Found! And check out the show merch, which make perfect gifts! Further support the show by giving a one-time gift at paypal.me/NathanLeviLloyd or finding me on Venmo at @HistoricalBlindness.Some music on this episode was licensed under a Blue Dot Sessions blanket license at the time of this episodes publication. Tracks include "Tarte Tatin," "Game Lands," "Cicle Vascule," "Delicates," and "Cicle Gerano." Additional music, including "Wake Up" and "Remedy for Melancholy," is by Kai Engel, licensed under Creative Commons (CC BY 4.0). Learn more about your ad choices. Visit megaphone.fm/adchoices
JACK DEJOHNETTE – DEMON'S DANCE Englewood Cliffs, N.J., December 22, 1967Demon's dance, Floogeh, Message from TraneWoody Shaw (tp,flhrn) Jackie McLean (as) Lamont Johnson (p) Scotty Holt (b) Jack DeJohnette (d) JAMES BRANDON LEWIS – CODE BEING May 16 and 17 2021 – Hardstudios Winterthur, Switzerland.Resonance, Archimedean, Code BeingJames Brandon Lewis (st) Aruán Ortiz (p) Brad Jones (b) Chad Taylor (dr) RUSS FREEMAN TRIO Los Angeles, October 27, 1953Don't worry 'bout me, Bock's tops, Yesterday's gardenias, Backfield in motion, The eye opener Russ Freeman (p) Joe Mondragon (b) Shelly Manne (d) Continue reading Puro Jazz 14 febrero 2024 at PuroJazz.
JACK DEJOHNETTE – DEMON'S DANCE Englewood Cliffs, N.J., December 22, 1967Demon's dance, Floogeh, Message from TraneWoody Shaw (tp,flhrn) Jackie McLean (as) Lamont Johnson (p) Scotty Holt (b) Jack DeJohnette (d) JAMES BRANDON LEWIS – CODE BEING May 16 and 17 2021 – Hardstudios Winterthur, Switzerland.Resonance, Archimedean, Code BeingJames Brandon Lewis (st) Aruán Ortiz (p) Brad Jones (b) Chad Taylor (dr) RUSS FREEMAN TRIO Los Angeles, October 27, 1953Don't worry 'bout me, Bock's tops, Yesterday's gardenias, Backfield in motion, The eye opener Russ Freeman (p) Joe Mondragon (b) Shelly Manne (d) Continue reading Puro Jazz 14 febrero 2024 at PuroJazz.
Welcome to worship! We're so happy you could join us! Here are some helpful links: Please sign in using the online connection card: https://forms.gle/6TvMUp86B2GZm5qt8 Donate online here: https://faithonline.ccbchurch.com/goto/giving Ask for prayers here: https://tinyurl.com/sk9pgsx To be added to our email list, send your contact info to hello@faithunited.org. For more information about our church, visit www.faithunited.org. CCLI streaming license #150856 Onelicense streaming license #A-735492 Individual licenses on file as needed. #havefaith #faithchurchwa #issaquahfaith
In this podcast, we talk with John Flemming, who created the High Desert Spiral sculpture located at the intersection of Simpson and Mt Washington just at the entrance to Broken Top in Bend, Oregon. We hear about his inspiration and some of the trials and tribulations of building the tallest sculpture in Bend at 39 feet. “There is something universal about spirals,” says the artist. “In the high desert, we find geological examples of lava cooling into spirals.” He also referenced the way traffic spirals around the roundabout in the Archimedean spiral, which features 60 steel blades that move in the wind. Note the inside of the blades are painted a bright yellow-orange, capturing “the glow you might find inside a volcano or lava flow.” This podcast is supported in part by a grant from the Bend Cultural Tourism Fund. Dirty Freehub, is a nonprofit organization that publishes hand-curated (and great!) gravel cycling route guides. Our mission is to connect gravel cyclists to where they ride through stories about culture, history, people, places, and lands with the hope that they will become involved as advocates, volunteers, or donors with organizations that protect and preserve recreation spaces. Our Podcast Channel / The Connection Our Route Guides / Dirty Freehub Our Ask / Donate
Welcome to the Convivial Society, a newsletter about technology and culture. I tend to think of my writing as way of clarify my thinking, or, alternatively, of thinking out loud. Often I’m just asking myself, What is going on? That’s the case in this post. There was a techno-cultural pattern I wanted to capture in what follows, but I’m not sure that I’ve done it well enough. So, I’ll submit this for your consideration and critique. You can tell me, if you’re so inclined, whether there’s at least the grain of something helpful here or not. Also, you’ll note that my voice suggests a lingering cold that’s done a bit of a number on me over the past few days, but I hope this is offset by the fact that I’ve finally upgraded my mic and, hopefully, improved the sound quality. Cheers!If asked to define modernity or give its distinctive characteristics, what comes to mind? Maybe the first thing that comes to mind is that such a task is a fool’s errand, and you wouldn’t be wrong. There’s a mountain of books addressing the question, What is or was modernity? And another not insignificant hill of books arguing that, actually, there is or was no such thing, or at least not in the way it has been traditionally understood. Acknowledging as much, perhaps we’d still offer some suggestions. Maybe we’d mention a set of institutions or practices such as representative government or democratic liberalism, scientific inquiry or the authority of reason, the modern university or the free press. Perhaps a set of values comes to mind: individualism, free speech, rule of law, or religious freedom. Or perhaps some more abstract principles, such as instrumental rationality or belief in progress and the superiority of the present over the past. And surely some reference to secularization, markets, and technology would also be made, not to mention colonization and economic exploitation. I won’t attempt to adjudicate those claims or rank them. Also, you’ll have to forgive me if I failed to include you preferred account of modernity; they are many. But I will venture my own tentative and partial theory of the case with a view to possibly illuminating elements of the present state affairs. I’ve been particularly struck of late by the degree to which what I’ll call the myth of the machine became an essential element of the modern or, maybe better, the late modern world. Two clarifications before we proceed. First, I was initially calling this the “myth of neutrality” because I was trying to get at the importance of something like neutral or disinterested or value-free automaticity in various cultural settings. I wasn’t quite happy with neutrality as a way of capturing this pattern, though, and I’ve settled on the myth of the machine because it captures what may be the underlying template that manifests differently across various social spheres. And part of my argument will be that this template takes the automatic, ostensibly value-free operation of a machine as its model. Second, I use the term myth not to suggest something false or duplicitous, but rather to get at the normative and generative power of this template across the social order. That said, let’s move on, starting with some examples of how I see this myth manifesting itself. Objectivity, Impartiality, NeutralityThe myth of the machine underlies a set of three related and interlocking presumptions which characterized modernity: objectivity, impartiality, and neutrality. More specifically, the presumptions that we could have objectively secured knowledge, impartial political and legal institutions, and technologies that were essentially neutral tools but which were ordinarily beneficent. The last of these appears to stand somewhat apart from the first two in that it refers to material culture rather than to what might be taken as more abstract intellectual or moral stances. In truth, however, they are closely related. The more abstract intellectual and institutional pursuits were always sustained by a material infrastructure, and, more importantly, the machine supplied a master template for the organization of human affairs. There are any number of caveats to be made here. This post obviously paints with very broad strokes and deals in generalizations which may not prove useful or hold up under closer scrutiny. Also, I would stress that I take these three manifestations of the myth of the machine to be presumptions, by which I mean that this objectivity, impartiality, and neutrality were never genuinely achieved. The historical reality was always more complicated and, at points, tragic. I suppose the question is whether or not these ideals appeared plausible and desirable to a critical mass of the population, so that they could compel assent and supply some measure of societal cohesion. Additionally, it is obviously true that there were competing metaphors and models on offer, as well as critics of the machine, specifically the industrial machine. The emergence of large industrial technologies certainly strained the social capital of the myth. Furthermore, it is true that by the mid-20th century, a new kind of machine—the cybernetic machine, if you like, or system—comes into the picture. Part of my argument will be that digital technologies seemingly break the myth of the machine, yet not until fairly recently. But the cybernetic machine was still a machine, and it could continue to serve as an exemplar of the underlying pattern: automatic, value-free, self-regulating operation. Now, let me suggest a historical sequence that’s worth noting, although this may be an artifact of my own limited knowledge. The sequence, as I see it, begins in the 17th century with the quest for objectively secured knowledge animating modern philosophy as well as the developments we often gloss as the scientific revolution. Hannah Arendt characterized this quest as the search for an Archimedean point from which to understand the world, an abstract universal position rather than a situated human position. Later in the 18th century, we encounter the emergence of political liberalism, which is to say the pursuit of impartial political and legal institutions or, to put it otherwise, “a ‘machine’ for the adjudication of political differences and conflicts, independently of any faith, creed, or otherwise substantive account of the human good.” Finally, in the 19th century, the hopes associated with these pursuits became explicitly entangled with the development of technology, which was presumed to be a neutral tool easily directed toward the common good. I’m thinking, for example, of the late Leo Marx’s argument about the evolving relationship between progress and technology through the 19th century. “The simple republican formula for generating progress by directing improved technical means to societal ends,” Marx argued, “was imperceptibly transformed into a quite different technocratic commitment to improving ‘technology’ as the basis and the measure of — as all but constituting — the progress of society.”I wrote “explicitly entangled” above because, as I suggested at the outset, I think the entanglement was always implicit. This entanglement is evident in the power of the machine metaphor. The machine becomes the template for a mechanistic view of nature and the human being with attendant developments in a variety of spheres: deism in religion, for example, and the theory of the invisible hand in economics. In both cases, the master metaphor is that of self-regulating machinery. Furthermore, contrasted to the human, the machine appears dispassionate, rational, consistent, efficient, etc. The human was subject to the passions, base motives, errors of judgement, bias, superstition, provincialism, and the like. The more machine-like a person became, the more likely they were to secure objectivity and impartiality. The presumed neutrality of what we today call technology was a material model of these intellectual and moral aspirations. The trajectory of these assumptions leads to technocracy. The technocratic spirit triumphed through at least the mid-twentieth century, and it has remained a powerful force in western culture. I’m tempted to argue, however, that, in the United States at least, the Obama years may come to be seen as its last confident flourish. In any case, the machine supplied a powerful metaphor that worked its way throughout western culture. Another way to frame all of this, of course, is by reference to Jacques Ellul’s preoccupation with what he termed la technique, the imperative to optimize all areas of human experience for efficiency, which he saw as the defining characteristic of modern society. Technique manifests itself in a variety of ways, but one key symptom is the displacement of ends by a fixation on means, so much so that means themselves become ends. The smooth and efficient operation of the system becomes more important than reckoning with which substantive goods should be pursued. Why something ought to be done comes to matter less than that it can be done and faster. The focus drifts toward a consideration of methods, procedures, techniques, and tools and away from a discussion of the goals that ought to be pursued. The Myth of the Machine Breaks DownLet’s revisit the progression I described earlier to see how the myth of the machine begins to break down, and why this is may illuminate the strangeness of our moment. Just as the modern story began with the quest for objectively secured knowledge, this ideal may have been the first to lose its implicit plausibility. Since the late 19th century onward, philosophers, physicists, sociologists, anthropologists, psychologists, and historians have, among others, proposed a more complex picture that emphasized the subjective, limited, contingent, situated, and even irrational dimensions of how humans come to know the world. The ideal of objectively secured knowledge became increasingly questionable throughout the 20th century. Some of these trends get folded under the label “postmodernism,” but I found the term unhelpful at best a decade ago—now find it altogether useless. We can similarly trace a growing disillusionment with the ostensible impartiality of modern institutions. This takes at least two forms. On the one hand, we might consider the frustrating and demoralizing character of modern bureaucracies, which we can describe as rule-based machines designed to outsource judgement and enhance efficiency. On the other, we can note the heightened awareness of the actual failures of modern institutions to live up to the ideals of impartiality, which has been, in part, a function of the digital information ecosystem. But while faith in the possibility of objectively secured knowledge and impartial institutions faltered, the myth of the machine persisted in the presumption that technology itself was fundamentally neutral. Until very recently, that is. Or so it seems. And my thesis (always for disputation) is that the collapse of this last manifestation of the myth brings the whole house down. This in part because of how much work the presumption of technological neutrality was doing all along to hold American society together. (International readers: as always read with a view to your own setting. I suspect there are some areas of broad overlap and other instances when my analysis won’t travel well). Already by the late 19th century, progress had become synonymous with technological advancements, as Leo Marx argued. If social, political, or moral progress stalled, then at least the advance of technology could be counted on. The story historian David Nye tells in American Technological Sublime is also instructive here. Nye convincingly argued that technology became an essential element of America’s civil religion (that’s my characterization) functionally serving through its promise and ritual civic commemoration as a source of cultural vitality and cohesion. It’s hard to imagine this today, but Nye documents how through the 19th and early to mid-20th century, new technologies of significant scale and power were greeted with what can only be described as religious reverence and their appearance heralded in civic ceremonies. But over the last several years, the plausibility of this last and also archetypal manifestation of the myth of the machine has also waned. Not altogether, to be sure, but in important and influential segments of society and throughout a wide cross-section of society, too. One can perhaps see the shift most clearly in the public discourse about social media and smart phones, but this may be a symptom of a larger disillusionment with technology. And not only technological artifacts and systems, but also with the technocratic ethos and the public role of expertise. After the Myth of the MachineIf the myth of the machine in these three manifestations, was, in fact, a critical element of the culture of modernity, underpinning its aspirations, then when each in turn becomes increasingly implausible the modern world order comes apart. I’d say that this is more or less where we’re at. You could usefully analyze any number of cultural fault lines through this lens. The center, which may not in fact hold, is where you find those who still operate as if the presumptions of objectivity, impartiality, and neutrality still compelled broad cultural assent, and they are now assailed from both the left and the right by those who have grown suspicious or altogether scornful of such presumptions. Indeed, the left/right distinction may be less helpful than the distinction between those who uphold some combination of the values of objectivity, impartiality, and neutrality and those who no longer find them compelling or desirable.At present, contemporary technologies are playing a dual role in these developments. On the one hand, I would argue that the way the technologies classified, accurately or not, as A.I. are framed suggests an effort to save the appearances of modernity, which is to say to aim at the same ideals of objectivity, impartiality, and neutrality while acknowledging that human institutions failed to consistently achieve them. Strikingly, they also retrieve the most pernicious fixations of modern science, such as phrenology. The implicit idea is that rather than make human judgement, for example, more machine-like, we simply hand judgment over to the machines altogether. Maybe the algorithm can be thoroughly objective even though the human being cannot. Or we might characterize it as a different approach to the problem of situated knowledge. It seeks to solve the problem by scale rather than detachment, abstraction, or perspective. The accumulation of massive amounts of data about the world can yield new insights and correlations which, while not subject to human understanding, will nonetheless prove useful. Notice how in these cases, the neutrality of the technology involved is taken for granted. When it becomes clear, however, that the relevant technologies are not and cannot, in fact, be neutral in this way, then this last ditch effort to double down on the old modern ideals stalls out. It is also the case that digital media has played a key role in weakening the plausibility of claims to objectively secured knowledge and impartial institutions. The deluge of information through which we all slog everyday is not hospitable to the ideals of objectivity and impartiality, which to some degree were artifacts of print and mass media ecosystems. The present condition of information super-abundance and troves of easily searchable memory databases makes it trivially easy to either expose actual instances of bias, self-interest, inconsistency, and outright hypocrisy or to generate (unwittingly for yourself or intentionally for others) the appearance of such. In the age of the Database, no one controls the Narrative. And while narratives proliferate and consolidate along a predictable array of partisan and factional lines, the notion that the competing claims could be adjudicated objectively or impartially is defeated by exhaustion.The dark side of this thesis involves the realization that the ideals of objectivity, impartiality, and neutrality, animated by the myth of the machine, were strategies to diffuse violent and perpetual conflict over competing visions of the true, the good, and the just during the early modern period in Europe. I’ve been influenced in this line of thought by the late Stephen Toulmin’s Cosmopolis: The Hidden Agenda of Modernity. Toulmin argued that modernity experienced a false start in the fifteenth and sixteenth century, one characterized by a more playful, modest, and humane spirit, which was overwhelmed by the more domineering spirit of the seventeenth century and the emergence of the modern order in the work of Descartes, Newton, and company, a spirit that was, in fairness, animated by a desperate desire to quell the violence that engulfed post-Reformation Europe. As I summarized Toulmin’s argument in 2019, the quest for certainty “took objectivity, abstraction, and neutrality as methodological pre-conditions for both the progress of science and politics, that is for re-emergence of public knowledge. The right method, the proper degree of alienation from the particulars of our situation, translations of observable phenomena into the realm mathematical abstraction—these would lead us away from the uncertainty and often violent contentiousness that characterized the dissolution of the premodern world picture. The idea was to reconstitute the conditions for the emergence of public truth and, hence, public order.”In that same essay three years ago, I wrote, “The general progression has been to increasingly turn to technologies in order to better achieve the conditions under which we came to believe public knowledge could exist [i.e., objectivity, disinterestedness, impartiality, etc]. Our crisis stems from the growing realization that our technologies themselves are not neutral or objective arbiters of public knowledge and, what’s more, that they may now actually be used to undermine the possibility of public knowledge.” Is it fair to say that these lines have aged well? Of course, the reason I characterize this as the dark side of the argument is that it raises the following question: What happens when the systems and strategies deployed to channel often violent clashes within a population deeply, possibly intractably divided about substantive moral goods and now even about what Arendt characterized as the publicly accessible facts upon which competing opinions could be grounded—what happens when these systems and strategies fail? It is possible to argue that they failed long ago, but the failure was veiled by an unevenly distributed wave of material abundance. Citizens became consumers and, by and large, made peace with the exchange. After all, if the machinery of government could run of its own accord, what was their left to do but enjoy the fruits of prosperity. But what if abundance was an unsustainable solution, either because it taxed the earth at too high a rate or because it was purchased at the cost of other values such as rootedness, meaningful work and involvement in civic life, abiding friendships, personal autonomy, and participation in rich communities of mutual care and support? Perhaps in the framing of that question, I’ve tipped my hand about what might be the path forward. At the heart of technological modernity there was the desire—sometimes veiled, often explicit—to overcome the human condition. The myth of the machine concealed an anti-human logic: if the problem is the failure of the human to conform to the pattern of the machine, then bend the human to the shape of the machine or eliminate the human altogether. The slogan of the one of the high-modernist world’s fairs of the 1930s comes to mind: “Science Finds, Industry Applies, Man Conforms.” What is now being discovered in some quarters, however, is that the human is never quite eliminated, only diminished. Get full access to The Convivial Society at theconvivialsociety.substack.com/subscribe
Archimedean points, issues in learning Yerushalmi, Halakhah as it is vis a vis how it ought to be - I think this is an excellent way in if you haven't been following the shiur, or haven't heard a Rabbi Klapper gemara shiur before
Jazz Ahead 150: Playlist: 1. Subasya, SCOPE, A Week From Monday/2020, Rous Records, 2021..2. Simulated Umbresya, SCOPE, A Week From Monday/2020, Rous Records, 2021..3. -3, SCOPE, A Week From Monday/2020, Rous Records, 2021..4. Bodiado, Thiago França, Bodiado, Autoproduzione, 2021..5. O Futuro um dia volta, Thiago França, Bodiado, Autoproduzione, 2021..6. Serenata Pra Ninguém, Thiago França, Bodiado, Autoproduzione, 2021..7. Lua (feat. Nailah Hunter), Winter, Lua, Leaving Records 2021..8. Archimedean, James Brandon Lewis Quartet, Code Of Being, Intakt Records, 2021..9. Code Of Being, James Brandon Lewis Quartet, Code Of Being, Intakt Records, 2021..10. Every Atom Glows, James Brandon Lewis Quartet, Code Of Being, Intakt Records, 2021
Jazz Ahead 150: Playlist: 1. Subasya, SCOPE, A Week From Monday/2020, Rous Records, 2021..2. Simulated Umbresya, SCOPE, A Week From Monday/2020, Rous Records, 2021..3. -3, SCOPE, A Week From Monday/2020, Rous Records, 2021..4. Bodiado, Thiago França, Bodiado, Autoproduzione, 2021..5. O Futuro um dia volta, Thiago França, Bodiado, Autoproduzione, 2021..6. Serenata Pra Ninguém, Thiago França, Bodiado, Autoproduzione, 2021..7. Lua (feat. Nailah Hunter), Winter, Lua, Leaving Records 2021..8. Archimedean, James Brandon Lewis Quartet, Code Of Being, Intakt Records, 2021..9. Code Of Being, James Brandon Lewis Quartet, Code Of Being, Intakt Records, 2021..10. Every Atom Glows, James Brandon Lewis Quartet, Code Of Being, Intakt Records, 2021
You might have noticed that Bitcoin, Dogecoin and [insert what-have-you]coin have been all the rage in the news. The bad news is that they sometimes crash, and Robert and Rashmi teach us a valuable skill sure to work when this has happened to you. If you're looking for an internship, (as I, Hari, am), I suppose you could do worse than joining the Summer Trainee program at the Bomb Squad. Real world experience and excitement guaranteed. Continued employment and survival not guaranteed! Sign up now! We at DIT are a bunch of history buffs. We take a look back at the possibly-apocryphal tale of Archimedes in his bath, discovering the law of displacement, his none-too-impressed (and possibly American) wife, and the most important lesson of all - always make sure the bathrooms have doors! All this and much more our show that's unknown, unplanned and unscripted! Go on, leave us a review: https://www.podchaser.com/podcasts/unscripted-with-dit-1264555/reviews Music: Rockapalooza by Shane Ivers - https://www.silvermansound.com
16 more Stars, while revisiting all 4 of the first-floor levels, as well as dips into Lethal Lava Land and Shifting Sand Land, and some cap stages. Also: the Archimedean principle, pilot-induced oscillation, and accounting fraud. Article on Sierra Entertainment
Archimedean Dynasty takes place in a dystopian future where mankind has been forced to retreat deep underneath the Earth’s oceans. A literal crust of dead organic matter coats the surface of the oceans, trapping the scant remnants of humanity beneath. In this grim world, all that is left to mankind is a precarious existence within the fragile mining stations that pepper the ocean’s floor. Yet despite these harsh realities, money still rules supreme. And it is your job, as legendary mercenary Emerald “Dead Eye” Flint, to make as much of it as you can while navigating the political turmoil of the far (wetter) future.And what a job it is, piloting your single person submarine in flight-sim fashion, destroying enemy vessels, escorting vulnerable targets and defending important locations. But has the gameplay and story of this 1996 title truly stood the test of time? Is it still fun to pilot the ocean’s depths with basically zero draw distance? With the fourth entry in the franchise due to release soon, is the original title even worth playing?On this episode, we discuss:How should background lore be delivered to the player? Archimedean Dynasty has a huge manual with its world history that should be read before playing the game. Is this better or worse than having the information gradually dispersed in game?What are the consequences of having a story presented almost entirely in dialogue between characters? Should this game also have had descriptive text to better set the scene?How well is information presented to the pilot of the submarine? WIth very low visibility on the ocean floor, you need to rely on your sensors and radar to properly navigate your environs. We answer these questions and many more on the 32nd episode of the Retro Spectives Podcast!
When Reid Hoffman creates a handle for some new network or system, his usual choice is “Quixotic.” At an early age, his love of tabletop games inspired him to think of life as a heroic journey, where people come together in order to accomplish lofty things. This framing also prompted him to consider the rules and systems that guide society—and how you might improve them by identifying key points of leverage. At first, he thought he’d become an academic and work with ideas as one of those Archimedean levers. But he ended up focusing on technology instead, helping to build PayPal, LinkedIn, and now many other ventures as an investor at Greylock Partners. But he still thinks ideas are important and tries to employ a “full toolset” when trying to shift systems. Reid joined Tyler to talk about all these leverage points and more, including the Silicon Valley cultural meme he most disagrees with, how Wittgenstein influenced the design of LinkedIn, mystical atheism, what it was like being on Firing Line, why he’s never said anything outrageous, how he and Peter Thiel interpret The Tempest differently, the most misunderstood thing about friendship, how to improve talent certification, what’s needed from science fiction, and his three new ideas for board games. In DC on Feb 17? Register for our next live show with John McWhorter here. Follow us on Twitter and IG: @cowenconvos Email: cowenconvos@mercatus.gmu.edu Follow Reid on Twitter Follow Tyler on Twitter Facebook Newsletter
Pascal Kaufmann (@PascalKaufmann) is a neuroscientist-turned-entrepreneur, who founded Starmind - one of Europe’s leading artificial intelligence technology companies - and Mindfire - a foundation created to incentivize collaboration in AI research. Inc magazine mentioned Pascal in the same sentence with no other than Elon Musk and Stephen Hawking. In this episode we’ll talk about how Pascal became fascinated with artificial intelligence research, some of the experiments he worked on, what advice he has for aspiring entrepreneurs, and unique insights into Starmind. Please follow me on Instagram (https://www.instagram.com/remokyburz/), Twitter (https://twitter.com/TheRemoKyburz), and my Website (http://www.leaptakers.com/), where I post new episodes, share cool stuff & interesting articles I found, blog occasionally, and provide glimpses into my life! Show notes: 02:38 -- How Pascal got interested in the topic of artificial intelligence 05:00 -- Scientific experiments connecting brains to machines 06:30 -- Why Pascal decided to found an AI company - Starmind 08:20 -- The general state of AI & where we are at 10:15 -- Resources to get started with a career in AI 12:30 -- Tips for aspiring entrepreneurs / mistakes to avoid 14:20 -- Insights into Starmind 15:40 -- Favorite books & movies 17:30 -- Pascal’s personal advisory board / mentors 19:10 -- Hobbies & habits to take your mind-off your startup 20:00 -- Advice to fellow entrepreneurs & future leaptakers 22:50 -- Closing thoughts - Switzerland as a hotspot for AI companies Resources mentioned: * The story of Prometheus (https://en.wikipedia.org/wiki/Prometheus) * Archimedean spiral (https://en.wikipedia.org/wiki/Archimedean_spiral) * Starmind (https://www.starmind.ai/) * Mindfire (https://mindfire.global/) * Captain future (https://www.imdb.com/title/tt0122336/) * Friedrich Nietzsche (https://www.amazon.de/gp/product/0140441182/ref=as_li_qf_asin_il_tl?ie=UTF8&tag=remokyburz-21&creative=6742&linkCode=as2&creativeASIN=0140441182&linkId=dad75174fa804d5486ec32de5fb53cb2) If you're enjoying the podcast, the best way to support the show is by leaving a review on iTunes (https://podcasts.apple.com/ch/podcast/the-leap-takers-podcast/id1468975811?l=en) or your favorite podcast app. Special Guest: Pascal Kaufmann.
Max Turnquist advises against wearing shorts while dumpster diving for used lab equipment. Almost every day, Max visits a university parking garage, where there are several small mountains of discarded equipment, some of it quite rare. Content Note: LanguageIt’s where he found his ion pump, and a lot of his rack-mounted monitoring gear and power supplies. He’s building a small nuclear fusion reactor from scratch in his bedroom, and he’s doing it on the cheap. Viable fusion power has long been a dream of scientists. Once a fusion reaction starts, its only waste products are helium, water, and relatively small amounts of neutron radiation. The fuel for these reactors is often Deuterium (aka. “heavy hydrogen), a common isotope of hydrogen found naturally in seawater. Compared to nuclear fission (the nuclear tech we currently use), fusion seems almost too good to be true—nearly free energy with few downsides. But there are a number of obstacles in the way. Getting atoms close enough to fuse takes massive amounts of force and heat. In the fusion reactors made by nature (stars), fusion happens because of the ridiculous amounts of gravity that create the high heat needed for this reaction. But here on earth, where sun-like gravity isn’t an option, scientists like Max have to rely on trickier methods. Max thinks that physicists are intuitive scientists. They observe something many times and gain an inherent knowledge of the universe. He says that the biggest laws that govern the physics are often quite simple, elegant. Max found himself drawn to one of the archimedean solids, and followed his hunch. His proof of concept reactor has a metal cage in the shape of a truncated icosahedron, a couple inches wide. In this shape, Max suspends particles in a cage of other particles. This shouldn’t be possible, based on Earnshaw’s Theorem, which in layman's terms, means that it’s really hard to keep the particle in the middle from squirting out the sides. But Max’s shape, along with a constantly changing voltage, suspends things in a Goldilocks-type way. He calls this “stably unstable”. His first proof of concept worked. Now he’s on his second. He says he’s almost ready to do a major fusion test, where he’ll drag his 300 pound reactor out to rural Maine, bury it in the ground and stand a safe distance away (to avoid the neutron radiation). And if it works, he’ll be on to solving the next problem, which is how to actually harvest the power it generates. Max doesn’t think the solution is a single step away. There are still many hurdles to overcome before fusion replaces the dirty and inefficient power we use today. And maybe those hurdles are too many, maybe it’s a fool’s errand. But he’s hopeful that fusion can save at least part of the world. A couple more links for you: Socrates, Plato’s cave and the “known unknowns”Fluctuations in the Reindeer Population on St. Matthew’s IslandCarl Jung’s Red BookProducer: Jeff EmtmanEditor: Jeff EmtmanMusic: The Black Spot, Serocell, Lucky DragonsCorrection: In the episode, we misstate the natural abundance of Deuterium. The correct abundance is .015%. We regret the error.
Join mathematician Chawne Kimber for a journey into Archimedean groups, lattice-ordered groups, and quilting.
Arthur Pedersen (Max Planck Institute/MCMP) gives a talk at the MCMP Colloquium (5 November, 2015) titled "Admissibility Decisions, Permissible Previsions". Abstract: In this talk I shall consider the problem of designing a theory of judgment and decision making that adequately addresses outstanding challenges to the normative adequacy of strict “Bayesian” theories inspired by the pioneering developments of Ramsey, de Finetti, and Savage. The questions I shall ask are basic ones: how are personal opinions expressed in situations of uncertainty, especially those where information is conflicting or scarce; what bearing do they have upon decisions taken to promote personal objectives; and what norms—in particular, what decision-making criteria—set appropriate standards against which to evaluate interrelated states of attitudinal judgments such as these? I shall propose a theory of judgement and decision making that advances constitutional reform along two dimensions: (a) it repeals gratuitous requirements the strict Bayesian canon imposes on states of attitudinal judgment (e.g., complete comparability of personal opinions), and (b) it enacts mandatory requirements the strict Bayesian canon fails to impose on such states (e.g., admissibility—rejection of weakly dominated courses of action). Unlike alternative proposals, the theory I advance (i) specifies the function of an agent’s judgments in inquiry and decision making, (ii) does not capitulate to the mathematical convenience of weakened Archimedean restrictions (or other regularity conditions, e.g., measurability, topological, or subsidiary cardinality restrictions), and (iii) subsumes existing proposals (admitting numerical representations in terms of formal power series fields in a single infinitesimal).
Paolo Busotti (San Marino in Storia della Scienza) gives a talk at the MCMP Colloquium (7 May, 2015) titled "Giuseppe Veronese: The Fascination of Infinity". Abstract: Giuseppe Veronese (1854-1917) is one of the most interesting mathematicians lived between the end of the 19th century and the beginning of the 20th. He gave important contributions to geometry, in particular he developed the non-Archimedean geometries and David Hilbert (1862-1943) mentioned some of Veronese’s results in his Grundlagen der Geometrie. In connection to his geometrical researches, Veronese developed a theory of infinite numbers. In his huge (more than 600 pages) essay Fondamenti di geometria, 1891 (Foundations of geometry), Veronese premised an introduction which is a very treatise (about 200 pages) in which he developed a theory of the continuum and of the infinite numbers which was completely different from Cantor’s (1845-1918) and which, in the mind of his author, had to represent an alternative to Cantorian set theory. The great difference, in comparison to Cantor, was that Veronese admitted the existence of infinitesimal actual numbers, while Cantor always denied this possibility. Basing on his actual infinite and infinitesimal numbers Veronese constructed the continuum in a manner which is different from Cantor’s and Dedekind’s (1831-1916). Other mathematicians, as Paul Dubois-Reymond (1831-1889) and Otto Stolz (1842-1905) faced the problem of the infinite actual magnitudes in an original way, but they did not develop an entire theory, while Veronese did. From a mathematical point of view Veronese’s theory is problematic, because there are some serious inaccuracies and it is not developed in every detail. Nevertheless, the situation is very interesting from an epistemological and logical standpoint because many of the ideas carried out by Veronese were resumed by Abraham Robinson (1918-1995) in his famous book Non standard Analysis (1966), where a coherent theory of non-archimedean numbers is explained. Many of Robinson’s idea had already been expounded by Veronese, though in nuce. In my talk, I am going to explain Veronese’s theory of infinite numbers in comparison to Cantor’s as well as Veronese’s conception of the continuum.
Stewart Shapiro (Ohio) gives a talk at the MCMP Colloquium (18 December, 2014) titled "An Aristotelian continuum". Abstract: Geoffrey Hellman and I are working on a point-free account of the continuum. The current version is “gunky” in that it does not recognize points, as part of regions, but it does make essential use of actual infinity. The purpose of this paper is to produce a more Aristotelian theory, eschewing both the actual existence of points and infinite sets, pluralities, or properties. There are three parts to the talk. The first is to show how to modify the original gunky theory to avoid the use of (actual) infinity. It is interesting that there are a number of theorems in the original theory (such as the existence of bisections and differences, and the Archimedean property) that have to be added, as axioms. The second part of the talk is to take the “potential” nature of the usual operations seriously, by using a modal language. The idea is that each “world” is finite; the usual operations are understood as possibilities. This part builds on some recent work on set theory by Øystein Linnebo. The third part is an attempt to recapture points, but taking the notion of a potentially infinite sequence seriously.
Jan Plamper begins in his book, The Stalin Cult: A Study in the Alchemy of Power (Yale University Press, 2012), with two illuminating anecdotes that demonstrate the power and scope of Stalin’s personality cult. The first comes from Sergei Kavtaradze, an Old Bolshevik and longtime friend of Stalin. Upon his release from the gulag in 1940, Stalin and Beria accompanied Kavtaradze to his old apartment, which was then occupied by an old woman. When he woman saw Stalin at her door she staggered back and fainted. When Beria asked why she was scared by the “father of all peoples,” the woman replied, “I thought that a portrait of Stalin was moving towards me.” The second tale comes from Artyom Sergeev, Stalin’s adopted son. Sergeev recalled one night when Stalin learned that his biological son, Vasily, used his famous name to escape punishment from one of drunken binges. In response to Stalin’s rage, Vasily said, “But I’m a Stalin too.” “No you’re not,” Stalin rebuffed. “You’re not Stalin and I’m not Stalin. Stalin is Soviet power. Stalin is what he is in the newspapers and the portraits, not you, not even me!” The production of the Stalin personality cult that disembodied the man and turned him into a symbol of Soviet power is at the heart of Plamper’s text. The cult made Stalin more than a leader–it transformed him into the Archimedean point of historical time and space. For Stalin represented the communist future as well as the vantage point in the socialist present. At the heart of this cult was Stalin’s image, which was reproduced in a variety of media, including portraiture and film. But the crafting, production, and canonization of Stalin’s image was no simple endeavor. It involved technologies that gave Stalin’s cult a particularly modern flavor. As Plamper shows, the production and dissemination of Stalin’s cult, which began in earnest with his 50th birthday in 1929, involved an entire institutional apparatus including mass media, artistic unions, art criticism, artistic competitions, individual filters, particularly Stalin’s secretaries Lev Mekhils and Aleksandr Poskryobyshev, and art patrons like Defense Minister Kliment Voroshilov, on top of which stood Stalin at the apex. Indeed, Stalin’s personal role in crafting his cult has undergone much debate. Plamper finds that it is best to view Stalin’s relationship to his cult as a form of “immodest modesty.” Stalin wanted his own cult and meticulously controlled it, at the same time he purposefully disavowed it. And through this alchemy of institutional and individual power did Stalin’s personality cult penetrate the psyche of the Soviet citizenry. This interview with Jan Plamper is part of joint project with Russian History Blog. Please visit Russian History Blog beginning March 28 to join a discussion among several scholars on the significance of The Stalin Cult: A Study in the Alchemy of Power. Learn more about your ad choices. Visit megaphone.fm/adchoices
Jan Plamper begins in his book, The Stalin Cult: A Study in the Alchemy of Power (Yale University Press, 2012), with two illuminating anecdotes that demonstrate the power and scope of Stalin’s personality cult. The first comes from Sergei Kavtaradze, an Old Bolshevik and longtime friend of Stalin. Upon his release from the gulag in 1940, Stalin and Beria accompanied Kavtaradze to his old apartment, which was then occupied by an old woman. When he woman saw Stalin at her door she staggered back and fainted. When Beria asked why she was scared by the “father of all peoples,” the woman replied, “I thought that a portrait of Stalin was moving towards me.” The second tale comes from Artyom Sergeev, Stalin’s adopted son. Sergeev recalled one night when Stalin learned that his biological son, Vasily, used his famous name to escape punishment from one of drunken binges. In response to Stalin’s rage, Vasily said, “But I’m a Stalin too.” “No you’re not,” Stalin rebuffed. “You’re not Stalin and I’m not Stalin. Stalin is Soviet power. Stalin is what he is in the newspapers and the portraits, not you, not even me!” The production of the Stalin personality cult that disembodied the man and turned him into a symbol of Soviet power is at the heart of Plamper’s text. The cult made Stalin more than a leader–it transformed him into the Archimedean point of historical time and space. For Stalin represented the communist future as well as the vantage point in the socialist present. At the heart of this cult was Stalin’s image, which was reproduced in a variety of media, including portraiture and film. But the crafting, production, and canonization of Stalin’s image was no simple endeavor. It involved technologies that gave Stalin’s cult a particularly modern flavor. As Plamper shows, the production and dissemination of Stalin’s cult, which began in earnest with his 50th birthday in 1929, involved an entire institutional apparatus including mass media, artistic unions, art criticism, artistic competitions, individual filters, particularly Stalin’s secretaries Lev Mekhils and Aleksandr Poskryobyshev, and art patrons like Defense Minister Kliment Voroshilov, on top of which stood Stalin at the apex. Indeed, Stalin’s personal role in crafting his cult has undergone much debate. Plamper finds that it is best to view Stalin’s relationship to his cult as a form of “immodest modesty.” Stalin wanted his own cult and meticulously controlled it, at the same time he purposefully disavowed it. And through this alchemy of institutional and individual power did Stalin’s personality cult penetrate the psyche of the Soviet citizenry. This interview with Jan Plamper is part of joint project with Russian History Blog. Please visit Russian History Blog beginning March 28 to join a discussion among several scholars on the significance of The Stalin Cult: A Study in the Alchemy of Power. Learn more about your ad choices. Visit megaphone.fm/adchoices
Fakultät für Geowissenschaften - Digitale Hochschulschriften der LMU
Porosity and permeability are both parameters which may have a considerable impact on the characteristics of a volcanic eruption. Various processes, from magmatic flow during ascent to the point of magmatic fragmentation during an explosive eruption are influenced, and sometimes even controlled by the amount of volatiles trapped in a magma’s pore space and by the efficiency of their escape. Detailed investigations of the porosity of pyroclastic rocks and its relation to the gas permeability are therefore crucial for the understanding of such processes and may provide an important database for physical models. The combination of experimental work and field investigation represents in this context an effective approach to obtain a statistically relevant amount of data on the one hand, and, on the other hand, experimentally quantify the correlation between different parameters. For this study, density data of pyroclastic deposits from eight circum-pacific volcanoes were recalculated to porosity values using the determined matrix density of the corresponding rocks. The pyroclasts density was determined directly in the field with a method based on the Archimedean principle; the matrix density was determined in the laboratory using a He-Pycnometer. The comparison of the resulting porosity distribution histograms allows (a) the investigation of local features related to depositional mechanisms, if the distribution of single measurement points is evaluated, and (b) statements about large scale coherencies regarding the eruptive style and the explosivity of a volcano, if the compiled datasets of the volcanoes are compared. The shape and the variance of the distribution curves, as well as the positions of the porosity peak or mean porosity values are parameters that can be used for further interpretation. The differences in the porosity distribution patterns allowed the classification of the investigated volcanoes into three groups, corresponding to their eruptive characteristics: (1) dome-building volcanoes with predominantly block-and-ash-flow activity and occasional Vulcanian explosions (Merapi, Unzen, Colima), (2) cryptodome-forming volcanoes with a subsequent lateral-blast eruption (Bezymianny, Mount St. Helens), and (3) Subplinian to Plinian explosive eruptions (Krakatau, Kelut, Augustine). Furthermore, possible coherencies between the mean porosity values of selected eruptions and their explosivity, expressed in two different explosivity indexes, were evaluated. The ‘Volcanic Explosivity Index’ (VEI), introduced by Newhall & Self (1982), is mainly based on the volume of the erupted tephra, and shows a rough positive correlation to the mean porosity of eruptive products. A qualitative enhancement of this correlation, especially considering low-porosity, low-explosive deposits, was achieved by using the measured porosity values to determine the index of the ‘Eruption Magnitude’, introduced by Pyle 1995. Volcanoes with not only pure explosive (Vulcanian and/or Plinian) activity were found to deviate systematically from this correlation. Besides their relevance for the understanding and modeling of eruption physics, the interpretation of porosity data may help to discriminate eruption characteristics and explosivities also at historic and pre-historic eruption deposits. The main focus of this work was the experimental investigation of the gas permeability of volcanic rocks. In order to simulate degassing processes under strongly transient conditions, the experiments were performed on a shock-tube like apparatus. The permeability of a natural porous material depends on a complex mixture of physical and textural parameters. Evidently, the volume fraction of the materials pore space, i.e. its porosity, is one of the prominent factors controlling permeable gas flow. But, as a high scatter of measured permeability values for a given porosity indicates, it seems that parameters like vesicle sizes, vesicle size distribution, vesicle shape, the degree of interconnectivity et cetera may likewise influence filtration properties. Therefore it is almost impossible to predict the permeability development of natural material with theoretical cause-and-effect relations, and experimental work in this field is essential. By performing more than 360 gas filtration experiments on 112 different samples from 13 volcanoes, a comprehensive permeability and porosity database was created with this study, giving rise to profound empirical as well as quantitative investigations. The dependency of porosity and permeability of volcanic rocks was found to follow two different, but overlapping trends, according to the geometries of the gas-flow providing pore-space: at low porosities (i.e. long-term degassed dome rocks), gas escape occurs predominantly through microcracks or elongated micropores and therefore could be described by simplified forms of capillary (Kozeny-Carman relations) and fracture flow models. At higher porosities, the influence of vesicles becomes progressively stronger as they form an increasingly connected network. Therefore, a model based on the percolation theory of fully penetrable spheres was used, as a first approximation, to describe the permeability-porosity trend. To investigate possible influences of high temperatures on the degassing properties of volcanic rocks, a measuring method that allowed permeability experiments at temperatures up to 750 °C was developed and tested. A sealing coat of compacted NaCl, which was, if required, further compressed during the high-T experiment, was found to be the most promising approach to avoid gas leaking due to different thermal expansivities of the materials involved. The results of three dome rock samples showed distinct lower gas filtration rates at high temperatures. As this may, for the largest part, be attributed to changed gas properties at high temperature, the obtained permeability values must be corrected for the enhanced gas viscosity. The corrected permeability values of the samples were higher than those obtained at room temperature, possibly caused by thermal expansion of the pores. Since, however, compressional forces of the salt coating upon the sample cylinder may lower the permeability particularly of highly fractured rocks to a not quantifyable degree, these results must be interpreted accordingly and seen under certain restrictions. Comparison of the permeability values before and after the heating process revealed that no permanent structural changes in the pore network occurred. This was confirmed by a 5h-experiment on a trachytic sample, with permeability tests in an interval of 60 minutes. The influence of permeability on magmatic fragmentation is of special interest for the modelling of eruptive processes. In particular the ‘fragmentation threshold’, i.e. the physical conditions, at which magma is no longer able to reduce gas overpressure by filtration and fragments, represents an important boundary condition for explosive eruption models. Former studies defined this threshold to depend on either the porosity of the magma, or a combination of porosity and overpressure. The experimental results of this work, however, reveal that, in addition to porosity and applied overpressure, the permeability strongly influences the fragmentation threshold. By quantifying this influence in a simple, analytical equation, these results will provide a valuable tool for physical models of eruption mechanics.
Fakultät für Geowissenschaften - Digitale Hochschulschriften der LMU
Abstract The shear viscosity, density, thermal expansivity and specific heat capacity are important factors controlling the morphology, rheology, and texture of volcanic flows and deposits. These physical properties of silicate melts largely depend on chemical composition, water content, crystal content, bubble content and stress applied to the melt. Recently, it has been recognized that the applied stress plays an important role in the so called “glass transition” area of silicate melts. This kinetic boundary between brittle and ductile behavior affects the eruptive style. Thorough knowledge of the physical processes that occur at this brittle/ductile transition can affect the decision making of governments during volcanic crises and help to reduce and/or avoid loss of life and assets. Scientific knowledge from this research can be directly applied to the geomaterial industry. In addition, natural magmatic rocks are the major raw material in the production of microfibres and continuous fibres. Compared to normal glass fibres, rock fibres have a remarkable high temperature endurance, acid and alkali resistance and anti-heat impact. Rock products can be used as substitutes for metal and timber. They are likely to become more widely used in the near future. Further use for natural magmatic rocks include crushed stone, concrete aggregate, railroad ballast, production of high quality textile fibres, floor tiles, acid-resistant equipment for heavy industrial use, rockwool, basalt pipers, basalt reinforcement bars, basalt fibre roofing felt (ruberoid), basalt laminate (used as a protective coating), heat-insulating basalt fibre materials and glass wool (fibre glass). Since Bottinga and Weill (1970) first suggested that the density of melts in two or three component systems could be used to determine partial molar volumes of oxide components in silicate liquids, several models based upon this approach have been proposed in the Earth sciences literature. Considering that knowledge the densities of 8 Zn-bearing silicate melts have been determined, in equilibrium with air, in the temperature range of 1363 to 1850 K. The compositional joins investigated [sodium disilicate (NS2)- ZnO; anorthite-diopside 1 atm eutectic (AnDi)-ZnO; and diopside-petedunnite] were chosen based on the pre-existing experimental density data set, on their petrological relevance, and in order to provide a test for significant compositionally induced variations in the structural role of ZnO. The ZnO concentrations investigated range up to 25 mol% for sodium disilicate, 20 mol% for the anorthite-diopside 1 atm eutectic, and 25 mol% for petedunnite. Molar volumes and expansivities have been derived for all melts. The molar volumes of the liquids decrease with increasing ZnO content. The partial molar volume of ZnO derived from the volumetric measurements for each binary system is the same within error. A multicomponent fit to the volumetric data for all compositions yields a value of 13.59(0.55) cm3/mol at 1500 K. I find, no volumetric evidence for compositionally induced coordination number variations for ZnO in alkali-bearing vs. alkali-free silicate melts nor for Al-free vs. Al-bearing silicate melts. The partial molar volume of ZnO determined here may be incorporated into existing multicomponent models for the prediction of silicate melt volume. High temperature density determinations on ZnO-bearing silicate melts indicate that a single value for the partial molar volume of ZnO is sufficient to describe the volumetric properties of this component in silicate melts. The presence of alkalies and Al does not appear to influence the partial molar volume of ZnO within the temperature range investigated here. There is no volumetric evidence across this temperature range presented for composition to influence the coordination polyhedron of ZnO in silicate melts. The next physical property to be studied was thermal expansivity. Ten compositions from within the anorthite-wollastonite-gehlenite (An-Wo-Geh) compatibility triangle were investigated. Due to the lack of information about the thermal expansivities at supercooled liquid temperatures this study focused on the measurement of thermal expansivity using a combination of calorimetric and dilatometric methods. The volumes at room temperature were derived from densities measured using the Archimedean buoyancy method. For each sample density was measured at 298 K using glass that had a cooling-heating history of 10-10 K min-1. The thermal expansion coefficient of the glass from 298 K to the glass transition interval was measured by a dilatometer and the heat capacity was measured using a differential scanning calorimeter from 298 to 1135 K. The thermal expansion coefficient and the heat flow were determined at a heating rate of 10 K min-1 on glasses that were previously cooled at 10 K min-1. Supercooled liquid density, molar volume and molar thermal expansivities were indirectly determined by combining differential scanning calorimetric and dilatometric measurements assuming that the kinetics of enthalpy and shear relaxation are equivalent. The data obtained on the supercooled liquids were compared to high-temperature predictions from the models of Lange and Carmichael (1987), Courtial and Dingwell (1995) and Lange (1997). The best linear fit combines the supercooled liquid data presented in this study and the high temperature data calculated using the Courtial and Dingwell (1995) model. This dilatometric/calorimetric method of determining supercooled liquid molar thermal expansivity greatly increases the temperature range accessible for thermal expansion. It represents a substantial increase in precision and understanding of the thermodynamics of calcium aluminosilicate melts. This enhanced precision demonstrates clearly the temperature independence of the melt expansions in the An-Wo-Geh system. This contrasts strongly with observations for neighboring system such as Anorthite-Diopside and raises the question of the compositional/structural origins of the temperature dependence of thermal expansivity in multicomponent silicate melts. In addition, the partial molar volumes and the thermal expansivities of 10 samples from within the An-Wo-Geh compatibility triangle have been determined. They have been incorporated into existing multicomponent models in order to predict silicate melt volume. The resulting supercooled liquid volumes near glass transition temperatures (1135 - 1200 K) and at superliquidus temperature were combined to yield temperature independent thermal expansivities over the entire temperature range. In light of results presented in this study, together with the published data, it seems that binary and ternary systems have temperature independent thermal expansivities from the supercooled liquid to the superliquidus temperature at 1 atmosphere. By combining the high temperature densitometry data (i.e., above liquidus) from the literature with volume and expansivity data obtained at Tsc, a wide temperature range is covered. There is no volumetric evidence across this temperature range for temperature independent thermal expansivities in the An-Wo-Geh compatibility triangle. Furthemore, the thermal expansivities of three multicomponent glasses and liquids have been obtained over a large temperature interval (298 - 1803 K) which involved combining the results of low and high temperature measurements. The sample compositions investigated were derived from three natural lavas; Vesuvius 1631 eruption, Etna 1992 eruption and an Oligocene-Miocene lava flow from Slapany in the Bohemian massif. The original rocks are tephri-phonolite, trachybasalt and basanite, respectively. This is the first time this calorimetric/dilatometric method has ever been applied to natural magmatic melts. The low temperature volumes were derived from measurements of the glass density of each sample after cooling at 5 K.min-1 at 298 K, followed by measurements of the glass thermal expansion coefficient from 298 K to the samples´ respective glass transition interval. Supercooled liquid volumes and molar thermal expansivities were determined by combining scanning calorimetric and dilatometric measurements, assuming that the kinetics of enthalpy and shear relaxation are equivalent (Webb, 1992). High temperature densities were measured using Pt double bob Archimedean densitometry. In addition, the oxidation state of iron was analyzed using a wet chemistry method. Small amounts of samples were taken from the liquids using a “dip” technique at regular temperature steps during high temperature densitometry. The measured high temperature densities have been compared with predicted densities across the same temperature interval calculated using the multicomponent density models of Lange and Carmichael (1987) and Lange (1997). The resulting data for liquid volumes near glass transition temperatures (993 - 1010 K) and at super-liquidus temperatures (1512 - 1803 K) are combined to yield temperature dependant thermal expansivities over the entire supercooled and stable liquid range. These results confirm the observation of Knoche et al. (1992a); Knoche et al. (1992b); Toplis and Richet (2000); Liu and Lange (2001); Gottsmann and Dingwell (2002) of the temperature dependence of thermal expansivity. The molar volumes indicate, in general, a significant negative temperature dependence of the expansivity. The thermal molar expansivity of the glasses increase from SiO2-poor (basalt-basanite composition) to relatively SiO2-rich melts (tephri-phonolite composition). The thermal molar expansivity at supercooled liquid temperatures increases in the same manner as the glasses. In contrast, the thermal molar expansivity of the superliquidus liquid decrease from SiO2-poor to relatively SiO2-rich melts. Non-linear dependency of molar volume has been observed for all studied samples above the glass transition area. Molar volume from just above the glass transition area to about 1873 K can be predicted by a non-linear logarithmic curve. This study examined the expansivities and molar volumes of relatively basic compositions. Extending such a study to more SiO2-rich, but still geologically relevant, compositions remains a challenge, because the high viscosities of such melts preclude the use of immersion techniques. This problem can be solved using a high temperature densitometry where the volume is measured on levitated sample. I would like to urge studies of this sort in the future. Results from such studies should provide important information regarding a number of geological processes, which occur in such extremely high viscous liquids. A new viscosity measurement for melts spanning a wide range of anhydrous compositions including: rhyolite, trachyte, moldavite, andesite, latite, pantellerite, basalt and basanite are discussed in the last chapters. Micropenetration and concentric cylinder viscometry measurements cover a viscosity range of 10-1 to 1012 Pas and a temperature range from 973 to 1923 K. These new measurements, combined with other published data, provide a high-quality database comprising ~800 experimental data on 44 well -characterized melt compositions. This database is used to recalibrate the model proposed by Giordano and Dingwell [Giordano, D., Dingwell, D. B., 2003a. Non-Arrhenian multicomponent melt viscosity: a model. Earth Planet. Sci. Lett. 208, 337–349] for predicting the viscosity of natural silicate melts. The recalibration shows that: a) the viscosity (η)–temperature relationship of natural silicate liquids is very well represented by the VFT equation [log η=A+B/ (T−C)] over the full range of viscosity considered here, b) the use of a constant high-T limiting value of melt viscosity (e.g., A) is fully consistent with the experimental data. There are 3 different compositional suites (peralkaline, metaluminous and peraluminous) that exhibit different patterns in viscosity, the viscosity of metaluminous liquids is well described by a simple mathematical expression involving the compositional parameter (SM) but the compositional dependence of viscosity for peralkaline and peraluminous melts is not fully controlled by SM. For these extreme compositions we refitted the model using a temperature-dependent parameter based on the excess of alkalies relative to alumina (e.g., AE/SM). The recalibrated model reproduces the entire database to within 5% relative error. On the basis of this extended database the T-variation of the viscous response of strong and fragile liquids within a wide range of compositions shows three clearly contrasting compositional suites (peralkaline, metaluminous and peraluminous). As a result, I present an extended model to calculate the viscosity of silicate melts over a wide range of temperatures and compositions. This model constitutes a significant improvement with respect to the Giordano and Dingwell (2003a) study in that: 1) The number of experimental determinations over which the model is calibrated is larger. 2) The range of investigated compositions is larger. 3) The investigated temperature range is larger. 4) The assumption is made that at infinite temperature, the viscosity of silicate melts converges to a common, but unknown value of the pre-exponential factor (A=−4.07, Equation (7.1)). In particular the compositional range involves a large number of viscosity determinations for peralkaline and peraluminous compositions in a temperature interval between 949 and 2653 K. Furthermore, it is shown that the assumption of a common value of the pre-exponential parameter A produces an equally good representation of the experimental data as that produced by each melt having its own specific A-value. This optimization also induces a strong coupling between data sets that stabilizes the range of solutions and allows the different rheological behaviour of extreme compositions (peralkaline and peraluminous vs. metaluminous) to be discriminated. It was demonstrated that, although the parameter SM (Giordano and Dingwell, 2003a) can be used to model compositional controls on the viscosities of metaluminous liquids, it does not capture the viscosity of peralkaline and peraluminous liquids. The differences in the rheological behaviour of these extreme compositions reflect important differences in the structural configuration of metaluminous, peralkaline and peraluminous melts. Subsequently, a second regression of the experimental data was performed involving a second compositional parameter (AE) that accounts for the excess of alkali oxides over the alumina. Incorporating this temperature-dependent compositional parameter (i.e., AE) into the SM-based model (Equation 7.7) appears to account for the anomalous rheological behaviour of peralkaline and peraluminous liquids. The resulting model reproduces the entire experimental database to within an average RMSE of 0.45 log units. The model presented here is recommended for the estimation of the viscosity of anhydrous multicomponent silicate melts of volcanic interest.
Despite the abundant evidence for the enrichment of phosphorus during the petrogenesis of natural ferro-basalts, the effect of phosphorus on the physical properties of these melts is poorly understood. The effects of phosphorus on the viscosity, density and redox ratio of a ferro-basaltic melt have been determined experimentally. The viscosity measurements were obtained using the concentric cylinder method on a ferro-basaltic melt above its liquidus, at 1 atm, in equilibrium with air and with CO2. The density measurements were performed using the double Pt-bob Archimedean method at superliquidus conditions under 1 atm of air. The redox ratio was obtained by wet chemical analysis of samples collected during physical property measurements. Phosphorus pentoxide reduces ferric iron in ferro-basaltic melt. The reduction due to P2O5 is much larger than that for most other oxide components in basaltic melts. A coefficient for the reduction of ferric iron has been generated for inclusion in calculation schemes. The effect of P2O5 on the viscosity is shown to be complex. The initial reduction of ferric iron with the addition of P2O5 results in a relatively small change in viscosity, while further addition of P2O5 results in a strong increase. The addition of phosphorus to a ferro-basaltic melt also reduces the density. A partial molar volume of 64.5±0.7 cm3/mol for P2O5 in this melt has been obtained at 1300° C, yielding a volume of 12.9 cm3/mol per oxygen, consistent with a tetrahedral coordination for this high field strength cation. The effects of P2O5 on redox state, density and viscosity provide constraints on the structural role of phosphorus in these melts. The results suggest a complex interaction of phosphorus with the aluminosilicate network, and tetrahedral ferric iron. In light of the significant effects of phosphorus on the physical and chemical properties of ferro-basaltic liquids, and the extreme enrichments possible in these liquids in nature, the role of phosphorus in these melts should, in future, be considered more carefully.
The densities of thirteen silicate liquids along the Na2SiO3-TiO2 and CaSiO3-TiO2 joins and six other titanium-bearing silicate liquids of the general formula TiSiO5 (where X = Li, Na, K, Rb, Cs, Ca, Sr, Ba) have been measured in equilibrium with air using the double Pt bob Archimedean method. The Na2SiO3-TiO2 join was investigated from 10–50 mole% TiO2 in the temperature range 1000–1150°C whereas the CaSiO3-TiO2 join was investigated from 10–80 mole% TiO2 in the temperature range of 1400–1625°C. Density increases with TiO2 content along both joins. Partial molar volumes of the binary endmembers, Na2SiO3 and CaSiO3, and of TiO2 have been computed. The partial molar volume of Na2SiO3 agrees well with that determined by Bockris et al. (1955). The partial molar volume of CaSiO3 is in disagreement with that of Tomlinson et al. (1958). The partial molar volume of TiO2 derived from a linear fit to the Na2SiO3-TiO2 join is 27.6(3) cm3/mole at 1150°C. The partial molar volume of TiO2 derived from linear extrapolation of the CaSiO3-TiO2 data to TiO2 at 1600°C is 24.3(4) cm3/mole. Comparison of the partial molar volume data from these binary joins with TiO2 liquid density data (Dingwell, 1991) requires the existence of a large positive excess volume in the Na2SiO3-TiO2 system at 1150°C.
The temperature-dependent thermal expansivities of glasses and liquids in the ternary albite-anorthite-diopside have been determined using a combination of calorimetry, dilatometry and Pt and Ir double bob Archimedean densitometry. Supercooled liquid volumes and molar thermal expansivities were determined across the glass transition using a combination of scanning calorimetry and dilatometry, based upon the equivalence of relaxation of volume and enthalpy in the vicinity of the glass transition. Superliquidus volumes were determined using double Pt bob Archimedean densitometry at temperatures up to 1,650°C and double Ir bob densitometry at 1,800°C. Experimental access to liquid volumes near the glass transition temperatures (680–920°C) and at superliquidus temperatures (1,400–1,800°C) for these compositions results in the observation of a nonlinear temperature dependence of molar volume, i.e., temperature-dependent thermal expansivities. The diopside composition wxhibits the largest temperature dependence of thermal expansivity, decreasing by 50% between 800 and 1,500°C. Linear extrapolation of the high-temperature volume data of diopside to 810°C would result in a 3% overestimation of the molar voltime. The temperature dependence of the molar volume of anorthite is approximately linear. The thermal expansivities of the liquids in the albite-anorthite-diopside system appear to converge at high temperature. This study uses a combination of methods that allows interpolation rather than extrapolation of the extant melt-volume data into the petrologically meaningful (subliquidus) temperature range.
The density of Ga2O3 liquid in equilibrium with air has been measured at 18000 to 19000C using an Ir double-bob Archimedean method. The data yield the following description of the density of Ga2O3 liquid: ρ= 4.8374(84)–0.00065(12)(T −18500C). This density-temperature relationship is compared with the partial molar volume of Ga2O3 in glasses in the systems CaO–Ga2O3–SiO2 and Na2O–Ga2O3–SiO2, corrected to the glass transition temperature using thermal expansivities. The comparison illustrates that a positive excess volume term is required in these systems at low temperature. This observation is similar to those deduced from studies of the partial molar volumes of Fe2O3 and Al2O3 in silicate melts.
A method for the determination of relaxed silicate liquid molar volume and expansivity at temperatures just above the glass transition is discussed. The method involves the comparison of heat capacity and molar expansivity in the glass transition region. Glassy and liquid heat-capacity data are obtained using differential scanning calorimetry, and glassy thermal expansion data are obtained using scanning dilatometry. The molar expansivity of the liquid is calculated by a fictive temperature normalization of the relaxation behavior of both the heat capacity and the molar expansivity in the glass transition region, with the normalized heat capacity curve being used to extend the dilatometric data into the liquid temperature range. This comparison is based upon the assumed equivalence of the parameters describing the relaxation of volume and enthalpy. The molar expansivity of relaxed sodium trisilicate (Na2Si3O7) has been determined in this manner at temperatures above the glass transition temperature. This low-temperature determination of liquid molar expansivity has been tested against high-temperature liquid expansivity data obtained from high temperature Pt double bob Archimedean buoyancy measurements. The low-temperature molar expansivity (26.43±0.83xl0~4 cm3 mole"lβC_1 at 540°C) determined in this manner agrees within error with the high-temperature molar expansivity (23.29±1.39xl0~4 cm3 mole^ºC1 at 1400°C). This dilatometric/calorimetric method of liquid molar expansivity determination greatly increases the temperature range accessible for thermal expansion measurements. A weighted linear fit to the combined low and high temperature volume data gives a molar expansivity of 23.0010.25x10^ cm3 mole^ºC"1. The volume-temperature relationship thus derived reproduces the measured volumes from both dilatometry and densitometry with a RMSD value of 0.033 cm3 mole"1 or 0.14%. This represents a substantial increase in precision, which is especially important for liquids whose high liquidus temperatures restrict the temperature range accessible to liquid volume determinations.
The temperature-dependent thermal expansivities of melts along the join anorthite-diopside have been determined on glassy and liquid samples using a combination of calorimetry, dilatometry, and Pt double bob Archimedean densitometry. Supercooled liquid volumes and molar thermal expansivities were determined using scanning calorimetric and dilatometric measurements of properties in the glass region and their behavior at the glass transition. The extraction of low-temperature liquid molar expansivities from dilatometry /calorimetry is based on an assumed equivalence of the relaxation of volume and enthalpy at the glass transition using a method developed and tested by Webb et al. (1992). This method corrects for transient effects at the glass transition which can lead to serious overestimates of liquid thermal expansivity from “peak” values. Superliquidus volumes were determined using double Pt bob Archimedean densitometry at temperatures up to 1650°C. The resulting data for liquid volumes near glass transition temperatures (810–920°C) and at superliquidus temperatures (1400–1650°C) are combined to yield thermal expansivities over the entire supercooled and stable liquid range. The molar expansivities are, in general, temperature dependent. The temperature-dependence of thermal expansivity increases from anorthite to diopside composition. The thermal expansivity of anorthite is essentially temperature independent, whereas that of diopside decreases by 50% between 800 and 1500°C, with the consequence that the thermal expansivities of the liquids in the anorthite-diopside system converge at high temperature.
The rheology of vesiculating rhyolitic systems exerts a strong control on the transport of silicic magmas in the subvolcanic to volcanic environments. We present here an investigation of vesiculating and vesiculated rhyolites using dilatometric methods. This study examines the effect of vesicle content on the viscosity of a natural supercooled rhyolitic liquid with 0–70% vesicles. The experimental samples of rhyolitic glass are derived from fusion of a natural obsidian from Little Glass Butte, Oregon. Crystal-free rhyolite glasses of varying porosity were prepared by fusing obsidian powder in a Pt crucible. Differing porosities were obtained by varying the temperature (1300—1650°C) and duration (0.5–6 h) of the fusions. Cylindrical samples of the resulting vesiculated rhyolites were cored from the crucible using diamond tools and their ends were ground flat and parallel for dilatometry. The porosity of each sample was determined from Archimedean buoyancy density determinations and comparison with bubble-free rhyolite (2.331 g/cm3, porosity = 1 - p/po). The density of foamed samples was determined using their mass, volume and regular geometry. Viscosities were determined in the parallel plate mode at stresses of 5 × 103 to 105 Pa. The viscosimeter was calibrated using NBS 711 glass. The bubble contents were microscopically investigated using a video-reflected light system and image analysis software. Distribution functions of the size, orientation, aspect ratio and surface porosity were obtained. The viscosity of rhyolite decreases with increasing bubble content. A general relationship of the form: η(|) = η(0)/(1 + C|), describes the effect of porosity, | (in volume fraction) on the viscosity, η, where C is a dimensionless constant (= 22.4 ± 2.9) and log10η(0) = 10.94 ± 0.04 Pa s at 850°C.
The density of TiO2 liquid in equilibrium with air has been measured at 1875° to 1925°C using an Ir double bob Archimedean method. The melt density data have been combined with data extrapolated from the CaSiO3─TiO2 join at 1600°C. A combined fit to these density data yields the following description of the density of liquid TiO2: ρ= 3.7611 - 0.00028T(°C), in the temperature range of 1600° to 1925°C. This expansivity value is consistent with those obtained on TiO2-rich melts using a Pt-based system at lower temperature and with multicomponent oxide data. The similarity between the volume of liquid TiO2 and that of crystalline rutile implies a dominantly octahedral coordination of Ti in the liquid state.
The densities of 12 melts in the Na2O-FeO-Fe2O3-SiO2 system have been determined in equilibrium with air, in the temperature range of 1000–1500°C, using the double bob, Archimedean technique. Ferrous iron determinations of 100–200 mg samples, “dip” quenched from high temperature, indicate that all the melts investigated were highly oxidized under these experimental conditions. 57Fe Mössbauer spectra of glasses obtained by drop quenching 80 mg melt samples from loop equilibration runs yield Fe3+/Fe2+ data equivalent to that for the densitometry (dip) samples for all but the most viscous melt, and confirm that all but one melt equilibrated with air during the densitometry measurements. Melt densities range from 2.17 to 2.88 g/cm3 with a mean standard deviation (from replicate experiments) of 0.36%. Least squares regression of the density data at 1300, 1400 and 1500°C, was calculated, both excluding and including excess volume terms (herein named linear and nonlinear fits, respectively) and the root mean squared deviation (RMSD) of each regression was compared with the total experimental error. The partial molar volumes computed for linear fits for Na2O and SiO2 are similar to those previously reported for melts in the Na2O-Al2O3-SiO2 system (Steinet al., 1986). The partial molar volumes of Fe2O3 obtained in these linear fits are equal to those obtained by Shiraishi et al. (1978) in the FeO-Fe2O3-SiO2 system but 5 to 10% lower than reported by Mo et al. (1982) in multicomponent melts. The partial molar volume exhibited by Fe3+ in this system is representative of the partial molar volume of tetrahedrally coordinated Fe3+ in silicate melts.
The densities of 10 melts in the CaO-FeO-Fe2O3-SiO2 system were determined in equilibrium with air, in the temperature range of 1200 to 1550°C, using the double-bob Archimedean technique. Melt compositions range from 6 to 58 wt% SiO2, 14 to 76 wt% Fe2O3 and 10 to 46 wt% CaO. The ferric-ferrous ratios of glasses drop-quenched from loop fusion equilibration experiments were determined by 57Fe Mössbauer spectroscopy. Melt densities range from 2.689 to 3.618 gm/cm3 with a mean standard deviation from replicate experiments of 0.15%. Least-squares regressions of molar volume versus molar composition have been performed and the root mean squared deviation shows that a linear combination of partial molar volumes for the oxide components (CaO, FeO, Fe2O3 and SiO2) cannot describe the data set within experimental error. Instead, the inclusion of excess terms in CaFe3+ and CaSi (product terms using the oxides) is required to yield a fit that describes the experimental data within error. The nonlinear compositional-dependence of the molar volumes of melts in this system can be explained by structural considerations of the roles of Ca and Fe3+. The volume behavior of melts in this system is significantly different from that in the Na2O-FeO-Fe2O3-SiO2 system, consistent with the proposal that a proportion of Fe3+ in melts in the CaO-FeO-Fe2O3-SiO2 system is not tetrahedrally-coordinated by oxygen, which is supported by differences in 57Fe Mössbauer spectra of glasses. Specifically, this study confirms that the 57Fe Mössbauer spectra exhibit an area asymmetry and higher values of isomer shift of the ferric doublet that vary systematically with composition and temperature (this study; Dingwell and Virgo, 1987, 1988). These observations are consistent with a number of other lines of evidence (e.g., homogeneous redox equilibria, Dickenson and Hess, 1986; viscosity, Dingwell and Virgo, 1987,1988). Two species of ferric iron, varying in proportions with temperature, composition and redox state, are sufficient to describe the above observations. The presence of more than one coordination geometry for Fe3+ in low pressure silicate melts has several implications for igneous petrogenesis. The possible effects on compressibility, the pressure dependence of the redox ratio, and redox enthalpy are briefly noted.
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