Podcasts about Mathematics

Terence Tao is widely considered to be one of the greatest mathematicians in history. He won the Fields Medal and the Breakthrough Prize in Mathematics, and has contributed to a wide range of fields from fluid dynamics with Navier-Stokes equations to mathematical physics & quantum mechanics, prime numbers & analytics number theory, harmonic analysis, compressed sensing, random matrix theory, combinatorics, and progress on many of the hardest problems in the history of mathematics. Thank you for listening ❤ Check out our sponsors: https://lexfridman.com/sponsors/ep472-sc See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. Transcript: https://lexfridman.com/terence-tao-transcript CONTACT LEX: Feedback - give feedback to Lex: https://lexfridman.com/survey AMA - submit questions, videos or call-in: https://lexfridman.com/ama Hiring - join our team: https://lexfridman.com/hiring Other - other ways to get in touch: https://lexfridman.com/contact EPISODE LINKS: Terence's Blog: https://terrytao.wordpress.com/ Terence's YouTube: https://www.youtube.com/@TerenceTao27 Terence's Books: https://amzn.to/43H9Aiq SPONSORS: To support this podcast, check out our sponsors & get discounts: Notion: Note-taking and team collaboration. Go to https://notion.com/lex Shopify: Sell stuff online. Go to https://shopify.com/lex NetSuite: Business management software. Go to http://netsuite.com/lex LMNT: Zero-sugar electrolyte drink mix. Go to https://drinkLMNT.com/lex AG1: All-in-one daily nutrition drink. Go to https://drinkag1.com/lex OUTLINE: (00:00) - Introduction (00:36) - Sponsors, Comments, and Reflections (09:49) - First hard problem (15:16) - Navier–Stokes singularity (35:25) - Game of life (42:00) - Infinity (47:07) - Math vs Physics (53:26) - Nature of reality (1:16:08) - Theory of everything (1:22:09) - General relativity (1:25:37) - Solving difficult problems (1:29:00) - AI-assisted theorem proving (1:41:50) - Lean programming language (1:51:50) - DeepMind's AlphaProof (1:56:45) - Human mathematicians vs AI (2:06:37) - AI winning the Fields Medal (2:13:47) - Grigori Perelman (2:26:29) - Twin Prime Conjecture (2:43:04) - Collatz conjecture (2:49:50) - P = NP (2:52:43) - Fields Medal (3:00:18) - Andrew Wiles and Fermat's Last Theorem (3:04:15) - Productivity (3:06:54) - Advice for young people (3:15:17) - The greatest mathematician of all time PODCAST LINKS: - Podcast Website: https://lexfridman.com/podcast - Apple Podcasts: https://apple.co/2lwqZIr - Spotify: https://spoti.fi/2nEwCF8 - RSS: https://lexfridman.com/feed/podcast/ - Podcast Playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4 - Clips Channel: https://www.youtube.com/lexclips

"Everybody has value to give." “It's not a game breaker, it's a game changer.” “How are you doing that differently? How are you going to stand out from the crowd?”   Episode summary | In this episode of the ROG Return on Generosity podcast, host Shannon Cassidy interviews Yvette Thornton, a registered patent agent and advocate for innovation and women in leadership. Yvette shares her journey from growing up on a farm in Virginia to her career in intellectual property, emphasizing the importance of collaboration, empowerment, and generosity. She discusses her advocacy for the National Down Syndrome Society, her experiences in patent law, and the lessons learned from her upbringing that shape her leadership style. The conversation also touches on navigating career transitions, the power of community, and the significance of recognizing one's own value and strengths.   R.O.G. Takeaway Tips | Leadership is about recognizing and valuing everyone's contributions. Empowering women in leadership roles is crucial for industry transformation. Advocacy for individuals with Down syndrome is about recognizing their abilities. Intellectual property protects innovations and encourages creativity. Listening and asking the right questions are key skills in patent law. Transitioning careers involves self-discovery and recognizing one's strengths. Generosity can come from unexpected places and has a ripple effect. It's important to grieve the loss of a job and give oneself time to heal. You are enough; own your strengths and contributions.   Chapters |  00:00 Introduction to Yvette Thornton and Her Journey 03:20 Growing Up on the Farm: Roots and Values 06:16 Influence of Family and Community on Leadership 08:59 Empowering Women in Leadership through WICT 11:57 Advocacy for Down Syndrome Awareness 14:48 Understanding Intellectual Property and Patents 15:43 The Journey to Becoming a Patent Agent 18:23 Innovations and Patents: The Impact of Ideas 21:21 Listening and Questioning: Keys to Innovation 23:10 Navigating Project Management and Innovation 24:34 Advice for Innovators: Protecting Your Ideas 26:34 Understanding Patents and Intellectual Property 27:48 The Power of Generosity in Professional Transitions 31:14 Embracing Career Transitions and Self-Discovery 35:27 Overcoming Self-Doubt and Embracing Your Value 39:00 The Importance of Asking for Help 42:15 Empowerment and Believing in Your Worth 43:21 Recharge and Leadership Style   Guest Bio | Yvette Thornton, a registered patent agent, is the driving force behind Clarke Innovations LLC, where she advises organizations on innovation strategies, operational improvements and intellectual property (IP).  Her work focuses on the intersection of engineering and IP, expanding access to patenting, and fostering innovation-driven cultures.  In her previous role as Director of Patent Development at Comcast NBCUniversal, Yvette collaborated with engineers and senior leaders to identify and capture innovation across the company. Yvette's impact extended beyond idea generation; she developed internal patent process, launched an Employee Recognition Program and created “Girl Storm” a program supporting women in patenting. Yvette began her IP career as a Primary Patent Examiner at the U.S. Patent and Trademark Office. She holds a M.S.  in Chemistry from the University of Virginia and a B.S. from Norfolk State University, where she was a Dozoretz National Institute for Mathematics and Applied Sciences (DNIMAS) Scholar. Based in the Philadelphia area, Yvette is active in The WICT Network: Greater Philadelphia, an advocate for the National Down Syndrome Society and enjoys reading, drawing, and spending time with her family.   Guest Resources:  https://clarkeinnovations.com/   Bridge Between Resources: 5 Degree Change Course Free N.D.I. Network Diversity Index  Free Generosity Quiz    Credits: Yvette Thornton, Host Shannon Cassidy, Bridge Between, Inc. Coming Next: Please join us next week, Episode 237, Special Guest, Brett Brackett.

Joan Clarke (1917-1996) was a codebreaker for the British armed forces during World War II. Her work alongside famous computer scientist Alan Turing was pivotal in decoding Nazi communications and bringing the war to an end. For Further Reading: Joan Clarke (1917 - 1996) - Biography - MacTutor History of Mathematics 100 Years Ago: Joan Clarke Joan Clarke, woman who cracked Enigma cyphers with Alan Turing - BBC News The Female Codebreakers Of Bletchley Park | HistoryExtra This month we're talking about Outsiders -- women who marched to the beat of their own drum and rejected stereotypes about what women "should" be. They are aesthetic pioneers, norm-benders, and often the only woman in their field. History classes can get a bad rap, and sometimes for good reason. When we were students, we couldn’t help wondering... where were all the ladies at? Why were so many incredible stories missing from the typical curriculum? Enter, Womanica. On this Wonder Media Network podcast we explore the lives of inspiring women in history you may not know about, but definitely should. Every weekday, listeners explore the trials, tragedies, and triumphs of groundbreaking women throughout history who have dramatically shaped the world around us. In each 5 minute episode, we’ll dive into the story behind one woman listeners may or may not know–but definitely should. These diverse women from across space and time are grouped into easily accessible and engaging monthly themes like Educators, Villains, Indigenous Storytellers, Activists, and many more. Womanica is hosted by WMN co-founder and award-winning journalist Jenny Kaplan. The bite-sized episodes pack painstakingly researched content into fun, entertaining, and addictive daily adventures. Womanica was created by Liz Kaplan and Jenny Kaplan, executive produced by Jenny Kaplan, and produced by Grace Lynch, Maddy Foley, Brittany Martinez, Edie Allard, Carmen Borca-Carrillo, Taylor Williamson, Sara Schleede, Paloma Moreno Jimenez, Luci Jones, Abbey Delk, Adrien Behn, Alyia Yates, Vanessa Handy, Melia Agudelo, and Joia Putnoi. Special thanks to Shira Atkins. Original theme music by Brittany Martinez. Follow Wonder Media Network: Website Instagram Twitter See omnystudio.com/listener for privacy information.

What is the role of active versus passive learning for math? How would data science become an avenue of math study for high school students and why isn't it already? Where does change in math education start? At the college level or before?Jo Boaler is a professor of mathematics education at Stanford University and also the author of a number of books, including Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics, Limitless Mind: Learn, Lead, and Live Without Barriers, and Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching.Greg and Jo discuss creativity, diversity, and meaning in math education. Their conversation identifies certain flaws in current math teaching methods, the resistance to educational change, and the importance of metacognition, visual learning, and collaborative problem-solving. Jo shares insights from her journey as a math educator, including her experiences with educational reform and the implications of neuroscience on learning math. They also examine the role of active versus passive learning, the potential of data science in education, and the impact of AI on future teaching practices.*unSILOed Podcast is produced by University FM.*Episode Quotes:How conjectures ignite mathematical thinking17:00: When we ask kids to reason about maths and to come up with their own conjectures, we like to share that word with kids. This is a word that all mathematicians use—a conjecture for an idea they have that you need to test out. It's like a hypothesis in science, but kids have never heard of that word, which is, you know, means there's a reason for that. But anyway, we teach our kids to come up with conjectures and then to reason about them and prove it to each other. And they get these great discussions where they're reasoning and being skeptical with each other. And that's what sparks their interest. They actually feel like they're discovering new things. And it's, like, really engaging for the kids to get into these discussions about the meanings of why these things work in maths. So it's a great route in, not only to engage kids, but have them understand what they're doing. Yeah, it's not that common.Why every kid should learn data science31:02: Data science is really something all kids should be learning in school, before they leave school, and developing a data literacy and a comfort with data and being able to read and analyze data, to some extent, is an important life skill. And it probably is really important to say, if a democracy, as a lot of misinformation is shared now, and if kids aren't leaving able to make sense of and separate fact and fiction, they will be left vulnerable to those misinformation campaigns. So, it's important just to be an everyday citizen.Why estimation is really important34:48: The idea of Math-ish is, estimation is really important. There's a lot of research evidence that we should be getting kids to estimate, but I know that kids in schools hate to estimate, and they resist it, and they will work things out precisely and round them up to make them look like an estimate. But you ask them, what's your ish number? And something magical happens. Like, suddenly they're willing to share their thinking, but it doesn't happen enough.The problem with teaching everything every year14:28: In the US, we have this system of teaching everything every year. So, you start learning fractions in maybe grade three, but you also learn them again in grade four and grade five and grade six. And at the end of that, kids don't understand fractions and everything else. Everything is taught every year. Whereas if you look at very successful countries like Japan, they don't teach in that way. Fractions is taught in one year—one year group—deeply, well, conceptually. So this is why you see kids going around in these massive textbooks that they can hardly carry, because it has all this content. And, of course, when you try and teach everything every year, often kids don't learn any of it well.Show Links:Recommended Resources:Randomized Controlled TrialMetacognitionCompression as a unifying principle in human learningCarol DweckGuest Profile:Faculty Profile at Stanford GSEProfile on WikipediaYouCubedSocial Profile on InstagramSocial Profile on XHer Work:Amazon Author PageMath-ish: Finding Creativity, Diversity, and Meaning in MathematicsLimitless Mind: Learn, Lead, and Live Without BarriersWhat's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire SuccessData Minds: How Today's Teachers Can Prepare Students for Tomorrow's WorldMathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching

Josh Recio from the UT Charles A. Dana Center challenges the mathematical status quo by advocating for quantitative reasoning courses as equally valuable to the traditional calculus pathway. His work with the Dana Center's Launch Years Initiative aims to provide students with math courses aligned to their future careers, emphasizing numeracy, mathematical modeling, and statistical reasoning skills needed in today's workplace.• Students need quantitative reasoning skills for their civic, personal, and professional lives• Traditional push toward calculus causes many students to miss developing crucial analytical skills• QR courses focus on solving relevant, age-appropriate problems using mathematics as a tool• Many QR courses are incorrectly viewed as "lesser than" or "low rigor" alternatives• Changing perceptions requires legitimizing QR through higher standards and recognition from influential institutionsCheck out our future episode where we'll dive deeper into the Launch Years Initiative, exploring how this approach is working to move these ideas into actual practice.

This episode of the Bitcoin Infinity Academy covers Sovereignty Through Mathematics Chapter 12: The Years Ahead In this episode, we discuss the final chapter of 'Sovereignty through Mathematics' titled 'The Years Ahead.' We discuss predictions and insights related to Bitcoin's future, including the Lindy Effect, Bitcoin's scarcity, and the role of quantitative easing. We also cover significant events like the block size wars, the advent of the Lightning Network, and the importance of vigilance in the Bitcoin community. This chapter reflects on Bitcoin's growth, historical context, and the increasing importance of adopting Bitcoin as sound money in an inflating fiat world. We wrap up by discussing the potential future developments in Bitcoin and what they mean for users and adopters. Read the chapter on Nostr: https://primal.net/infinity/the-years-ahead--sovereignty-through-mathematics-chapter-12  Join the academy at our Geyser page: https://geyser.fund/project/infinity  You can also support us by sending some sats to our Alby Hub at bitcoininfinity@getalby.com  The Bitcoin Infinity Academy is an educational project built around Knut Svanholm's books about Bitcoin and Austrian Economics. Each week, a whole chapter from one of the books is released for free on Highlighter, accompanied by a video in which Knut and Luke de Wolf discuss that chapter's ideas. You can join the discussions by signing up for one of the courses on our Geyser page! Connect with Us: https://www.bitcoininfinityshow.com/  https://bitcoininfinitystore.com  https://primal.net/infinity  https://primal.net/knut  https://primal.net/luke  https://twitter.com/BtcInfinityShow  https://twitter.com/knutsvanholm  https://twitter.com/lukedewolf 

Introduction The Best Textbooks on Every Subject is the Schelling point for the best textbooks on every subject. My The Best Tacit Knowledge Videos on Every Subject is the Schelling point for the best tacit knowledge videos on every subject. This post is the Schelling point for the best reference works for every subject. Reference works provide an overview of a subject. Types of reference works include charts, maps, encyclopedias, glossaries, wikis, classification systems, taxonomies, syllabi, and bibliographies. Reference works are valuable for orienting oneself to fields, particularly when beginning. They can help identify unknown unknowns; they help get a sense of the bigger picture; they are also very interesting and fun to explore. How to Submit My previous The Best Tacit Knowledge Videos on Every Subject uses author credentials to assess the epistemics of submissions. The Best Textbooks on Every Subject requires submissions to be from someone who [...] ---Outline:(00:10) Introduction(01:00) How to Submit(02:15) The List(02:18) Humanities(02:21) History(03:46) Religion(04:02) Philosophy(04:29) Literature(04:43) Formal Sciences(04:47) Computer Science(05:16) Mathematics(05:59) Natural Sciences(06:02) Physics(06:16) Earth Science(06:33) Astronomy(06:47) Professional and Applied Sciences(06:51) Library and Information Sciences(07:34) Education(08:00) Research(08:32) Finance(08:51) Medicine and Health(09:21) Meditation(09:52) Urban Planning(10:24) Social Sciences(10:27) Economics(10:39) Political Science(10:54) By Medium(11:21) Other Lists like This(12:41) Further Reading--- First published: May 14th, 2025 Source: https://www.lesswrong.com/posts/HLJMyd4ncE3kvjwhe/the-best-reference-works-for-every-subject --- Narrated by TYPE III AUDIO.

In this episode of Innovation and the Digital Enterprise, Patrick and Shelli talk to Jeff Miller, Vice President of Engineering at LinenMaster. Jeff discusses his journey in the tech industry and his role at LinenMaster, a leading laundry management solutions provider. He delves into his previous roles at various prominent Chicago technology companies focusing on his work to modernize platforms and streamline operations. We talk about his earlier interest in tech; he built a computer when he was a kid. Then Jeff shares insights into this hands-on approach, the challenges of transforming legacy systems, and the importance of iterative development. He discusses his leadership philosophy of roadmapping transformation with the customer in mind, and building trust through execution.(00:00) Introducing Jeff Miller, VP of Engineering at LinenMaster(01:14) Jeff Miller's Career Journey(04:38) Roadmapping Strategy at LinenMaster(06:24) Technological Transitions and Innovations(09:36) Leadership and Decision-Making(09:37) Jeff's Early Interest in Technology(12:58) Rebuilding Trust and Modernizing Software(25:02) Advice for Tech Professionals and Founders(28:47) Conclusion and FarewellJeff Miller is Vice President of Engineering at LinenMaster. Previously he moved up through a variety of roles at Yello.co culminating in a position as Chief Technology Officer. Before that he was Vice President Of Engineering at Fooda and he launched his career at Enova International. He earned a Bachelors degree in Computer Science and Mathematics from the University of Wisconsin-Madison, where he was also President of the Madcity Skydiving Club.If you'd like to receive new episodes as they're published, please subscribe to Innovation and the Digital Enterprise in Apple Podcasts, Spotify, or wherever you get your podcasts. If you enjoyed this episode, please consider leaving a review in Apple Podcasts. It really helps others find the show.Podcast episode production by Dante32.

In this conversation, Rufus interviews Zak about his early learning journey, exploring the corruption of graduate education, the sacredness of measurement for ancient man & what kind of new wise agency is needed amidst existential risk and all pervasive information warfare.Listen above or watch the episode here:About the episode:In their second interview, Rufus explores Dr. Zak Stein's formative experiences of education, music and standardised testing. They explore the sacred and esoteric history of measurement in the pre-modern world compared with today. Zak Shares on what he learned conducting research into the all-pervasive landscape of propaganda and information warfare for the Consilience Project. They close exploring the possibility of 'a new archetype of wise agency' which, unlike previous monastic wisdom traditions, is deeply responsive and engaged with worldly agency, politics, power and strategy.This conversation supports the recent book First Principles and First Values: Forty-Two Propositions on CosmoErotic Humanism, the Meta-Crisis, and the World to Come. See detailed notes on the book and our summary here.Chapters00:00 Zak's Early Education Experience 09:46 Zak's Journey Through Jazz Musicians 14:33 Ken Wilber and Developmental Psychology 17:44 The Creation of Lectica & Entering Harvard Without a GPA 24:02 What Happened to Developmental Psychology at Harvard? 28:00 The Academy Is Broken & the Frame of Institutional Decay 31:47 Government and Industry Cannibalize Graduate Education 39:29 The Problem of Metrication & Civilizational Collapse 45:35 The Magic of Measurement for Ancient Man & Measurement as a Sacred Act 58:18 Consilience Project's Findings on Psychological Warfare 1:01:00 Rufus: Culture War, Printing Press, and the Modern Age 1:03:45 Information War Erodes the Possibility of Truth 1:20:00 How Can a Second Renaissance Counter Propaganda Culture? 1:22:45 The “Long Game” of Wisdom in the Past vs. the Need for Active Engagement in the Metacrisis 1:24:12 The New Archetype of “Wise Agency”1:32:00 How Do We Use Power Wisely? About Zak SteinDr. Zachary Stein is co-founder of the Civilizational Research Institute, the Center for World Philosophy and Religion and Lectica, Inc, and is a widely sought after and award winning speaker. Zak is a leading authority on the future of education and contemporary issues in human development. He was trained at the interface of philosophy, psychology, and education, and now works in fields related to the mitigation of global catastrophic risk. Dr. Stein is the author of several books and many peer-reviewed papers, including most recently First Principles and First Values: Forty-Two Propositions on CosmoErotic Humanism, the Meta-Crisis, and the World to Come, by Zak Stein, Marc Gafni and Ken Wilber writing under the name David J. Temple.About Rufus PollockRufus Pollock is an entrepreneur, activist and author as well as a long-term zen practitioner. He is passionate about finding wiser, weller ways to live together. He has founded several for-profit and nonprofit initiatives including Life Itself, Open Knowledge Foundation, and Datopian. His book Open Revolution is about making a radically freer and fairer information age. Previously he has been the Mead Fellow in Economics at the University of Cambridge as well as a Shuttleworth and Ashoka Fellow. A recognized global expert on the information society, he has worked with G7 governments, IGOs like the UN, Fortune 500s as well as many civil society organizations. He holds a PhD in Economics and a double first in Mathematics from the University of Cambridge. Find out more about his work on his website: rufuspollock.com. This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit news.lifeitself.org

Career Crossroads: Episode 2 - High School Mathematics Teacher by 2mfm

In this episode of the IoT For All Podcast, Eystein Stenberg, CTO and co-founder of Northern.tech, joins Ryan Chacon to discuss the critical role of device lifecycle management and over-the-air (OTA) updates for OEMs in today's software-driven world. The conversation covers the five stages of device lifecycle management, the challenges OEMs face when transitioning to software-driven models, how OTA updates maintain cybersecurity and system resilience, the impact of regulations and the EU Cyber Resilience Act, and insights from Northern.tech's latest report.The State of Industrial IoT Device Lifecycle Management: https://northern.tech/dlm-industry-report-2025Eystein Stenberg is the CTO and co-founder of Northern.tech. With over 15 years of experience in security and systems management, Stenberg has served on the frontlines of some of the largest production environments and possesses in-depth knowledge on solving real-world system security challenges. An expert in embedded system security and IoT device management, Stenberg routinely shares his insights at industry conferences. Stenberg holds a Master's degree in Mathematics with a focus on cryptography from the University of Tromsø in Norway.Northern.tech is the leader in device lifecycle management with a mission to secure the world's connected devices. Established in 2008, Northern.tech showcases a long history of enterprise technology management before lloT and loT became buzzwords. Northern.tech is the company behind CFEngine, the pioneer in server configuration management, to automate large-scale IT operations and compliance. In 2015, Northern.tech released the first version of Mender, the market leader in over-the-air software update management. Mender offers robust, secure, and customizable OTA software updates for smart devices. Mender boasts a proven track record with Fortune 1000 clients, including Airbus, Lyft, Volkswagen, Siemens, Thales, and ZF Group.Discover more about IoT at https://www.iotforall.comFind IoT solutions: https://marketplace.iotforall.comMore about Northern.tech: https://northern.techConnect with Eystein: https://www.linkedin.com/in/eysteinstenberg/(00:00) Intro(00:10) Eystein Stenberg and Northern.tech(00:41) Why is device lifecycle management essential?(02:18) What is device lifecycle management?(04:42) Challenges OEMs face in becoming software-driven(07:26) Are over-the-air updates more than a feature?(09:28) Real-world examples of DLM and OTA impact(11:43) Risks of neglecting device lifecycle management(13:21) Impact of regulatory compliance(14:29) Advice for OEMs to future proof devices(15:27) The role of AI in device management(16:48) Insights from Northern.tech's reportSubscribe on YouTube: https://bit.ly/2NlcEwmJoin Our Newsletter: https://newsletter.iotforall.comFollow Us on Social: https://linktr.ee/iot4all

If you are spending more time staring at your windshield instead of looking into your customers' eyes, you are doing field sales wrong.  Over the past couple of years, there's been a resurgence in field sales. Businesses everywhere are adding field salespeople and sending representatives out into the territory to meet with customers face-to-face.  And for good reason—human beings buy from human beings. The most powerful way to anchor relationships, solve problems, and sell more is to get in front of your customers. With AI creating so much noise in the system, it's getting harder to prospect via email and social media. Going out and knocking on doors has become an easier way to connect with people, build relationships, and open up opportunities in your pipeline.  And the good news, at least for now, is that prospects are happy to see field sales pros and inviting them in to their businesses and homes.  But with the resurgence of outside sales comes an age-old problem: Field salespeople have got to travel to get to customers. And here's the brutal reality—the single greatest waste of time for field sales professionals is staring at a windshield. On this Money Monday segment of the Sales Gravy Podcast I'm going to teach you exactly how to minimize windshield time and maximize face time. Because at the end of the day, you don't get paid to drive. You get paid to sell. The Windshield Time Delusion Too many reps delude themselves into believing that driving from one place to another is "working." Let's get something straight: Driving is not an accomplishment. I don't care if you put 100 miles on your vehicle in a day. That doesn't mean you accomplished anything meaningful. It just means you drove from one place to the next, burning dinosaurs and wasting time. I see this all the time. Reps will drive to one customer, then drive all the way across their territory to another customer, instead of concentrating their work in a single geographic area.  They'll dead-head out to an appointment, then drive all the way back to the office, passing up dozens of prospects they could have walked into along the way. Don't confuse activity with productivity.  Just because you drove all over creation, that doesn't mean you had a productive day.  Your job is to be in front of customers, not behind a steering wheel. Every minute you spend staring at your windshield is a minute you're not building relationships, solving problems, putting new opportunities in the pipe or closing deals. The Mathematics of Effective Field Sales Territory Management  Let me put this in perspective with some simple math that will blow your mind. Let's say you're a typical field sales rep working in a moderate-sized territory. You make 5 customer visits per day, and between poor route planning and territory management, you spend an average of 45 minutes driving between each appointment. That's 3 hours and 45 minutes of windshield time daily. Over a 5-day work week, that's 18 hours and 45 minutes of non-productive driving time. That's nearly half of your work week spent accomplishing absolutely nothing. Now, let's say you tighten up your territory management and reduce that drive time to 20 minutes between appointments through better planning. You're now down to 1 hour and 40 minutes of windshield time daily, or 8 hours and 20 minutes weekly. You just freed up more than 10 hours per week. That's enough time for 15 to 20 additional customer visits or prospect calls. Over a month, that's 60-80 more customer touchpoints. Over a year, that's 720-960 additional opportunities to build relationships and generate revenue. The reps who figure out how to minimize windshield time don't just have better work-life balance—they absolutely dominate their territories and blow past their quotas while their competitors are still driving around wastefully. Map Your Territory Into Quadrants This is why the first rule of field sales is get...

En este episodio Jota y Luis reseñan el último disco de Wu-Tang Clan junto al productor Mathematics, Black Samson, the Bastard Swordsman. Mencionan lo que esperaban del disco, analizan su música y dicen la importancia que ocupa este álbum en su catálogo.www.patreon.com/acordesyrimas

This episode of the Bitcoin Infinity Academy covers Sovereignty Through Mathematics Chapter 11: A New Form of Life In this episode, we discuss the intriguing concept of Bitcoin as a new form of life. From its open system and homeostasis to its cellular structure and lifecycle, the conversation challenges conventional thinking about life and Bitcoin. We also touch on topics like privacy measures, fungibility of Bitcoin, and the importance of self-custody.  Read the chapter on Nostr: https://primal.net/infinity/a-new-form-of-life-%7C-sovereignty-through-mathematics-chapter-11  Join the academy at our Geyser page: https://geyser.fund/project/infinity  You can also support us by sending some sats to our Alby Hub at bitcoininfinity@getalby.com  The Bitcoin Infinity Academy is an educational project built around Knut Svanholm's books about Bitcoin and Austrian Economics. Each week, a whole chapter from one of the books is released for free on Highlighter, accompanied by a video in which Knut and Luke de Wolf discuss that chapter's ideas. You can join the discussions by signing up for one of the courses on our Geyser page! Connect with Us: https://www.bitcoininfinityshow.com/  https://bitcoininfinitystore.com  https://primal.net/infinity  https://primal.net/knut  https://primal.net/luke  https://twitter.com/BtcInfinityShow  https://twitter.com/knutsvanholm  https://twitter.com/lukedewolf 

In this episode, listeners will learn about Actantial Networks—graph-based representations of narratives where nodes are actors (such as people, institutions, or abstract entities) and edges represent the actions or relationships between them.  The one who will present these networks is our guest Armin Pournaki, a joint PhD candidate at the Max Planck Institute for Mathematics in the Sciences and the Laboratoire Lattice (ENS-PSL), who specializes in computational social science, where he develops methods to extract and analyze political narratives using natural language processing and network science.  Armin explains how these methods can expose conflicting narratives around the same events, as seen in debates on COVID-19, climate change, or the war in Ukraine. Listeners will also discover how this approach helps make large-scale discourse—from millions of tweets or political speeches—more transparent and interpretable, offering tools for studying polarization, issue alignment, and narrative-driven persuasion in digital societies. Follow our guest Armin Pournaki's Webpage Twitter/X Bluesky Papers in focus How influencers and multipliers drive polarization and issue alignment on Twitter/X, 2025 A graph-based approach to extracting narrative signals from public discourse, 2024  

This episode we look at time and direction and the influence of geomancy--theories of Yin and Yang and a little bit of how people viewed the world through that lens.  For more, check out the blog page:  https://sengokudaimyo.com/podcast/episode-127 Rough Transcript Welcome to Sengoku Daimyo's Chronicles of Japan.  My name is Joshua, and this is episode 127: Time and Direction in Ancient Yamato   Officers of the court stood in the pavilion.  The soft trill of water could be heard trickling from one reservoir to the next.  They watched closely, as the figure of a court official, one hand out, pointing at a measuring stick, slowly rose along with the water.  Eventually, the figure's outstretched arm indicated a line with a single character next to it. On cue, one of the officials began to beat the large drum that was nearby.  The rhythm was slow, but deliberate, and the sound was loud, echoing out to the mountains and back, showering the nearby palaces in a layer of sound.  Across the palace, people briefly paused, took note of the number of strokes, and by that they knew the time of day.  Without giving it much more thought, they then went about their business.     This episode we find ourselves partway through the reign of Naka no Oe, aka Tenji Tennou—his formal reign started in 668, but he had been pretty much running things since the death of Takara Hime in 661 and, arguably, for much longer than that.  668, however, saw Naka no Oe ascend the throne in his new palace of Otsu no Miya, officially making him the sovereign.  And although 645 is the year Naka no Oe and others had started the Taika Reforms, it's not wrong to say that  that 668 and the start of Naka no Oe's official reign, brief as it would be, that he finally had the ability to bring it all together and set it into stone. We've talked about many of these reforms before on the podcast, but a lot of them were associated with the continued push to incorporate continental concepts into Yamato society, covering everything from court ranks to how to organize agricultural production.  Of course, there was also Buddhism, which we've covered numerous times, but there were other concepts coming across as well, including ideas about history and writing, as well as ancient STEM—Science, Technology, Engineering, and Mathematics.  This included architects, and new ways of constructing buildings.  And it also meant ways of seeing the world, including things like directions and time.  And this is what I want to focus on this episode, taking a break from the primary narrative to spend some time on what we might call Yamato concepts of science, especially how they thought about the structure of reality organization of time and the universe – their cosmology, as it were.  After all, to better understand the reasoning and motives of people, it is helpful to try and understand how they saw the world, not just for translation—understanding what it means when an entry says something like the “Hour of the Horse” on an “Elder Wood” day—but also for understanding how things actually worked in their eyes.  For instance, the idea of ”auspicious” and “inauspicious” times and directions is something that most listeners probably don't incorporate much into their daily lives, but the Chroniclers and the people of Yamato absolutely did, so understanding concepts like this can sometimes be the key to unlocking why historical people may have taken the actions that they did.  In particular, we'll talk about things like yin and yang, five elements, ten stems and twelve earthly branches, and what all this meant for the Yamato ideas of organizing time and space. A large part of Yamato cosmology is tied to something called Onmyoudou, literally the Way of Yin and Yang, which in the organization of the Ritsuryo state fell under a particular ministry, known as the Onmyo-ryo.  If you've heard of Onmyoudou before, you likely have heard about the “Onmyouji”, practitioners who studied the flow of yin and yang—and who could reportedly do miraculous things with that.  A 10th century Onmyoji, the famous Abe no Seimei, is perhaps the most well-known, with numerous stories about his exploits, which were then turned into a fantastical series of stories by the award-winning author, Baku Yumemakura.  Those were then turned into Manga, movies, and more.  Abe no Seimei is like Japan's Merlin, or Gandalf, at least in the stories. Back to the organization we mentioned, the Onmyou-ryou was responsible for Yin-Yang theory, or Onmyou-dou, which included divination, as well as astronomy, or Tenmon-dou, and calendar making, or reki-dou.  While some of this was based on straight up natural observances, a lot of it was explained through older concepts of Yin and Yang theory.  Today, you might encounter a lot of this in the theories around Feng Shui, and this can also be referred to as “geomancy”, or earth divination.   To give a broad overview of Onbmyoudou and its origins, it is part of a large corpus of concepts focused around a concept of energy known as qi or ki—which forms the basis for a lot of Chinese and Japanese cosmology, or their concept of how the world worked.  Much of this is tied up in concepts that are modernly broadly called “Daoist” or associated with so-called Daoist practices.  That term can be a bit misleading, as strictly speaking, Daoism refers to the teachings of the legendary philosopher Laozi, in his book, the Dao De Jing, as well as works attributed to later authors, like the Zhuangzi. There is some controversy as to when and to what extent this strict Daoism came to Japan.  However, in the broader sense, the category of “Daoist “ practices includes an entire panoply of various folk practices, including concepts of Yin and Yang – and in the archipelago, many of these concepts were imported with the various books that people had acquired on the mainland, even if they weren't strictly tied to Daoist religious practice.  For example, there were aspects that were borrowed by various Shinto shrines, and others formalized into ritual practices under the new government.  And of course many of these became linked to various Buddhist teachings and practices, as well.   But what did this actually look like in concept and practice for practitioners of Onmyoudo in Japan? Let's start with the idea of yin and yang.  One of the earliest references comes from the Zhou Yi, the Zhou Book of Changes, the core of what we also know as the Yijing, the Book of Changes.  Here we see the idea that the universe began with a single force that split into two, and those two forces make up all of creation in one way or another.  Yin and Yang, or In and You—or even Onmyou—refer to these forces, which are characterized as shadow and light, moon and sun, female and male, cold and hot, etc.  So these forces are opposites, but it should be noted that they are not necessarily good or evil.  After all, too cold is just as bad as too hot.  Likewise too much darkness is as blinding as too much light. As most people have seen, yin and yang are often depicted as a circle divided into two comma shapes, with a smaller circle in each.  One side is white with a black circle and the other is black with a white circle.  This is the “Tai Chi” diagram, but the diagram itself doesn't seem to have been depicted like this prior to the 11th century, at least that we are aware. But the concepts are much older.    Now if you've heard of the Yijing, where it came from is something of a mystery.  One theory is that it started as a written account of folk wisdom, and may have even given instructions for things like when to plant and when to harvest, based on changes in various heavenly phenomena.   But overall it is organized into 64 chapters, each associated with a particular hexagram.  Start with a line, that can either be a full line – representing yang – or a broken line representing yin.  Stack three of these on top of one another and you get a trigram.  If you chart out every single possible combination of yin and yang lines, you get 8 unique trigrams, sometimes referred to as the baqua.  Stack two trigrams atop one another and you get a hexagram, a combination of 6 lines that can have 8 by 8 or 64 unique variants.   It's theorized that the Yijing resulted from taking all of the collected sayings or aphorisms and bits of advice and cataloguing and dividing them into 64 chapters, each one associated with a given hexagram. Going further, each line of the hexagram is  associated with particular line in Yijing, and various meanings are ascribed to it and its association.  It's a complex and fascinating system and I don't have time to go into it fully, but I would note that this was used as a form of divination—yarrow stalks or other means of random lot drawing that gives you a binary outcome – zero or one, yin or yang – could be used to determine the six lines of any given hexagram.  This, in turn, would reference a chapter in the Yijing which was then interpreted as a sign as to how to read a given situation that you might find yourself in. What's really important to understanding the worldview of the time is this idea, represented by the hexagrams in the Yijing, that you can encompass everything about the universe by making and cataloging different amounts and arrangements of yin and yang. It's a science, as it were – a systematic approach to understanding the differences in the world by breaking it into component parts.    And if this seems preposterous, consider this:  today we understand that all things are made up of tiny atoms.  And these atoms are all made up of the same material—protons, neutrons, and electrons.  And yet, how those atomic particles combine create atoms with wildly different qualities.  And how those atoms then combine into molecules and so on and so forth describe how we explain everything around us.  So is it really so far-fetched? I'm not saying that we should suddenly start to figure out the measurements of yin and yang in everything, but if we want to understand how the people of the time saw their world, it may be helpful to hold an open mindand understand the assumptions that they were working from and where they came from.  As human beings, we naturally look for connections in the world around us, and this was no exception.  People would observe facts, know how that it worked, and often then would back into the reason for it.  This is a tale told across cultures, and we still see it, today.  At the same time, we've developed structured approaches to test out our theories, empirically. So for the moment, let's leave the trigrams and hexagrams, and talk about another idea that also gained traction as people were trying to figure out how the world worked.  This was the five elements theory also known as Wuxing, or Gogyou, in Japanese.  The five elements in this case are Fire, Water, Wood, Metal, and Earth.  Some may notice that these, along with the sun and the moon, are used in Japanese for the days of the week:  Nichi (sun), getsu (moon), ka (fire), sui (water), moku (wood), kin (metal), do (earth). Buddhists, by the way, also had an elemental system with only four elements,  Fire, Water, Air, and Earth, possibly connected with some Greek influence, and brought along with Buddhist practice.  For now, however, let's focus on the five elements. The idea in wuxing is similar to that of yin and yang in that everything in creation is made up of these five elements in some degree and configuration.  Furthermore, there are creation and destruction cycles.  So fire creates ash, or earth.  Earth gives birth to metal.  Metal creates water—look at a cold piece of metal in a warm environment and see how the water droplets form on it, and imagine what that looks like without understanding humidity and how there could be water vapor in the air.  And then water creates wood, or plants—any farmer could tell you that without water the plants die.  And wood is where we get fire from. Of course, the reverse cycle is the opposite.  Fire eats the wood.  Wood drinks up the water.  Water rusts metal.  Metal tools plough the earth. And Earth can be used to douse fire. Finally, there is another cycle of weakening. ,. Because fire heats and weakens metal, metal chops down wood, the trees roots break up rocks, the earth soaks up water, and water likewise puts out or weakens fire. So the theory went, if these elements make up all matter, these relationships continue on a more complex scale in everything.  So if something was thought to contain a lot of “fire” element, then it would be potentially helpful if you needed “Earth” but destructive or at least weakening to metal and wood.  Properly accounting for these elements was important to achieve the results you were looking for, whatever that may be.   These were the kinds of things that were incorporated into traditional medicine practices, but also applied to auguries or divination about things like where and how to build a building.  Even today, Shrines will sell calendars that help people know the prominence of certain elements, and some folk remedies may look to balance elements, much as medieval European medicine was often designed to balance the four humors that ancient physicians believed were present in the human body. The chart of these five elements and their relationships is something you may have seen.  It is a five pointed star, often inside of a circle.  Of course this is also similar to a western pentagram, though typically drawn with the point of the star up, but it has nothing to do with Christian values or Satan, or anything similar.  Rather, it is just a way to represent these five elements, and you'll see it frequently in reference to Onmyoudou. The elements were used to categorize many different areas into groupings of five.  This includes grouping the various directions into five directions.  Of course, you may be wondering about that, since most societies usually mark four cardinal directions, and in this case, they did the same, but added the fifth as “center”.  And so you get things like the north is water.  It is related to cool, or cold weather.  It is represented with the color black. To the south, opposite of the north, is fire.  It is hot, and the color is red.  Of course, this probably doesn't take a huge leap to see the connections they drew: since these civilizations are in the northern hemisphere, the farther north you go, the colder it gets, and the farther south you travel, the warmer it gets, generally speaking, at least until you reach the equator. Meanwhile, the west was related to metal, and the color white, while the east was related to woods and forests, and the color…. Blue.  Alright, that last one, in particular, probably doesn't make sense to a lot of us.  After all, we likely associate blue with water, and wood, or trees, would be associated with brown or, possibly, green.  Well, in this case, it goes beyond that.  The north is water, but it is also associated with darkness—shorter days in the winter, and things like that Sothe association of north with black makes sense, but many also look at the ocean and don't necessarily see it as “blue”, or dark or even black, like Homer's famous “wine-dark sea”. Furthermore, although they have a word for it (midori), “green” was not a primary color in Japan, instead  considered more of a shade of “aoi”, or blue.  Even today they refer to a “green” traffic light as an “aoi shingo, not “midori” shingo.  So if you asked someone in the Asuka period to describe the wooded hills and fields, they would have likely used “aoi”.  And of course, we are missing the fifth element.  In the center we have the element earth and the color yellow. A lot of these different concepts were brought together during the Han period, when they were trying to syncretize all of the various philosophies and attempts to describe the world and bring them all together into a single system.  This meant that the Yijing, the wuxing theory, and others were mixed together with various other philosophies and theories of how the world work.  Things like the Shanhaijing, the Classic of Mountain and Seas, along with stories about immortals, the Queen Mother of the West, and more were all rolled together, and basically assumed to be true.  This included various real-world observations.  Therefore, there were many attempts to try and reconcile these various theories together. One of the other concepts, which we've discussed before, was the system of ten heavenly stems and the twelve earthly branches.  We've mentioned this before regarding the sexagenary style of counting the years, but we'll recap here.  The ten heavenly stems and the twelve earthly branches are concepts that go back to at least the legendary Shang period, and even show up in various bronzes Andit wasn't until later that they would be associated with other ideas.  The ten heavenly stems were each associated with one of the five elements, with each element being represented by a greater and lesser, or elder and younger, stem.  And then each of the twelve earthly branches were associated with animals—what we often call the Chinese Zodiac. We talked about how this applied to the calendar, in that it was used to track years in 60 year cycles, but also it was used to track days of the year.  The twelve earthly branches were also used for earthly directions.  The first, the rat, was in the north, and the order continued clockwise to the east, the south, west and then back to the north.  Now this means that the four cardinal directions—north, south, east, and west—all match up nicely with one of the twelve earthly branches, but as for northeast, southeast, southwest, and northwest?  Those were all combinations of two branches.  So, for instance, the northeast was a combination of the ox and the tiger, or ushi-tora. Speaking of eight directions, where have we also heard the number eight come up recently? That's right: the eight trigrams, or bagua.  So each one of those trigrams, each representing a different concept, got associated with a direction as well.  This makes it easier to see where practices of geomancy came from.   You had a system with complex, overlapping associations between concepts and the physical world, and in the Tang dynasty, they used all of this  to understand not only  how things had happened, but also how the world would be in the future—in other words, they tried to use it to make predictions.  Hence the “mancy”. In the Yamato state, all of this became an official part of the government under the Onmyoryou: a branch of the government whose job is to make observations and figure things out from there, for the good of the state and the people.  They made observations of the heavens to figure out how the calendar should be aligned—which months should come at what time, and when there should be “leap months”, or intercalary months, to keep various astronomical phenomena in the correct seasons, which were also further divided up into 24 periods.  They also kept track of the movement of bodies like the various planets, because those planets were also assigned values, and thought to affect the flow of energy within this framework.  And so comets, storms, eclipses, and more were all important because of the theory that everything in the heavens impacted and were reflections of how things were happening on the earth.  Similarly, these various discussions of white animals and other omens were likely captured and catalogued by these officials as well, attempting to figure out what they meant. All of this also influenced things like how palaces, buildings, and even capitals, would be built and laid out.  For the palace, it was important the the sovereign be in the north, looking south.  In fact, many maps would have south at the top because that is how a sovereign would be viewing it, were it stretched out before them.  And one would need to consider various features, including mountains and streams, as all of those things carried various meanings, but it wasn't as simple as just finding the one thing that could affect a person.  As they observed differences they would also have to catalogue what happened and try to determine what the cause could be, based on their understanding of the world.  And in the archipelago this would also include an understanding of Buddhist and local kami-based wisdom and knowledge as well. One of the things in the Chronicles that inspired this episode was something I actually mentioned last time,  a record from 666  talking about Chiyu, a Buddhist priest of the Yamato no Aya family, who presented a south-pointing chariot to the sovereign, Naka no Oe.  this appears to be the same Chiyu from a similar record in 658, which also refers to him building a south pointing chariot.  So did it take him eight years, or is he just now presenting it to the sovereign?  And what, exactly, is a south-pointing chariot? Well, as the name implies, a south-pointing chariot is a two-wheeled chariot that always points south.  More appropriately stated, it is a wheeled device with a figure on top, much like a weather vane, which always points south.  This is usually described as the figure of a person or an official pointing in the appropriate direction.  This was a mechanical, rather than a magnetic compass. As the chariot, or carriage, is wheeled around, the two wheels spin.  The wheels themselves are independently connected to a series of gears.  If the wheels spin at the same rate, then their movement cancels each other out.  However, if one wheel turns more than the other, then it will cause the figure on the top to rotate.  Of course, as the chariot turns to the right, the left wheel, traveling along the outer diameter, will travel farther than the right.  This will cause the figure to turn counter-clockwise to the left, but from an outside observer's perspective, it will continue to point in the same direction, even as the chariot itself turns.  Turning to the left would cause the opposite effect. Though it may have been used earlier, there appears to be reliable written evidence of a South Pointing chariot starting from the third century.  The first one was based on much earlier stories of a similar device, but it is unclear if it was a chariot, some other device, or even just a legend that was told as historical fact.  From the third century on the design appears to have been continuously improved upon. I should point out that all we have is descriptions—we don't have any actual south pointing chariots, let alone diagrams showing how the mechanisms worked.  There is the possibility that it used a kind of differential gear to work automatically, but we don't have any actual evidence.  There are other theories that it may have required some kind of manual switch, so that it would attach to one wheel or the other as needed.  That would require that the chariot be moving in either a straight direction or turning in one particular direction, which seems rather unwieldy. I noted some of the problems with this, and even moreso in a place like Japan, where 70% of the terrain is mountains.  Up and down hills, along paths that are likely anything but the smooth, paved surface we have for roads today—and even those have plenty of irregularities and potholes that could throw off any such device. And if you want to use it for any real distance, then you have to factor in other things, including the curvature of the earth.  After all, with the earth being a sphere, any chariot traveling due west to east or east to west, other than at the equator, would have one wheel traveling farther than the other one.  Granted, at the scale we are talking about, it probably is all but negligible, and the rough terrain and simple slippage of what were most likely wooden gears probably entered a lot more variability than the earth's curvature. One of the other issues is that the chariot only points “south” if you set it up to do so.   And if you know that, well, why do you need a south-pointing chariot?  Ultimately, it seems that this is more of a novelty item, good for impressing crowds and demonstrating some engineering principles, rather than an actual, useful invention.  After all, it was forgotten about and recreated multiple times, often centuries apart.  Had it been a truly useful invention, it probably would have been kept in constant use.  Meanwhile, I suspect that there were a fair number of farmers and others who knew that you could more easily and reliably use the sun and stars, as long as the weather was clear. There is also some evidence of an understanding of magnetic compasses since at least the 2nd Century BCE.  Early Han sources suggest that a spoon made of naturally magnetized ore could be placed on top of a polished bronze surface, and it would align itself north to south.  We don't have any actual surviving examples, however—there are later versions that you can find, where the plate is divided up into various directions, and then a magnetized “spoon” is placed on top, but nothing has actually come from Han tombs.  Furthermore, this seems to mostly be for geomantic purposes.  A more practical compass, with a magnetized needle, seems to have been developed by the 11th century, which could then be used for actual navigation. By the way, the “spoon” as a compass pointer may be in reference to the “Big Dipper” constellation, which was envisioned as a spoon, or ladle, in shape.  The seven stars were often used in geomancy, likely because of their importance, at least in the northern hemisphere, of pointing to the north.  So there's some thought that the “needles” of these early compasses weren't litterally  spoon shaped, but symbolically representive of the Big Dipper or the Northern Ladle.  Quick astronomy lesson, here.  If you are in the northern hemisphere, particularly from the 35th parallel to the north pole, you can see the seven stars that make up the constellation or asterism we know as the Big Dipper.   In English we sometimes also refer to this as Ursa Major, though technically the familiar seven stars are just a part of that larger constellation.  In Japan, the same constellation is often referred to as Hokuto Shichisei, the Seven Stars of the Northern Ladle.  It can be seen further south, but parts of it may dip below the horizon during the autumn season. It is important for several reasons.  One is that it is made up of particularly bright stars, which you can generally see even when other stars may not be visible.  Second, its distinctive shape lends itself to being easy to find in the sky.  And finally, if you draw a line between two of the stars at the end of the “cup” of the ladle, you can follow that line to find Polaris or hokkyokusei, the north star, which means you know which direction is north- and once  you know that, you can use it to figure out any other direction.  And Polaris is less than a degree off of true north, making it even more accurate than most magnets, as the magnetic pole can be quite different, depending on its current position, and magnetic north changes over time as the magnetic field around the earth fluctuates. That said, this was not necessarily the case in ancient times.  Four thousand years ago, the star closest to true north would have been the star Thuban, in the constellation Draco, a star that most of us probably haven't heard of.  Polaris, in the constellation Ursa Minor (the Little Bear, also known as the Little Dipper) apparently took over as the north star around 500 CE.  However, even before then, the mouth of the dipper could still be used to indicate north.  In fact, if you draw a line between two of the stars in the back of the constellation, then you also end up finding Thuban.  So even if the north star itself wasn't accurate, finding the dipper would still help you orient yourself, especially if you can find true north during the day and then compare that with the constellation at night. Which helps to understand why astronomy, or Tenmondou, was so important in the Onmyouryou.  Though it wasn't just a study of stars, but of the way of the heavens in general.  And the changes in the heavens, brings us to another important concept—the flow of energy across the seasons.  From the bright days of summer, filled with sunshine and yang energy, to the dark yin energy of winter's long, cold nights. It wasn't enough to just know what happened, and where, but when was also important. Obviously you need to know when to sow seeds, flood the fields, and harvest the rice.  Beyond that, though, you have other concepts, such as how the the day and hour of an event could be symbolically important. And of course, all of these had their own associations with various concepts of the flow of yin and yang energy. Now knowing the year, the month, and even the day is largely just a matter of counting.  But let's talk about something a little more tricky:  How do you know the hour? This brings us to the vignette at the top of the episode, about the clepsydra, or water clock, that Naka no Oe is said to have built. Now we talked about some of the fountains and similar things that have been discovered in the Asuka region back in episode 118.  One thing that they believe they also found evidence of is something called a water clock, which is, as its name suggests, a clock powered by water.  It is typically depicted as a series of three or more boxes or reservoirs that each hold an amount of water.  Water is placed in the top reservoir, and then a hole towards the bottom is unplugged and it is allowed to drain into the box beneath.  The hole is of a particular size, and thus the water flows at a constant rate, filling up the container below, which has a similar hole, etc. all the way to a reservoir at the very bottom.  The multiple boxes mean that the water level in the intermediate boxes stays relatively constant, resulting in relatively consistent pressure and flow rate.  The last reservoir has a measuring stick on a float, so that as the last box is filled with water, the measuring stick raises up.  Since it is rising at a constant rate, one can use that to tell how much time has passed, regardless of anything else.  Thus you can keep time even at night. There is a record of Naka no Oe making one in the fifth month of 660, and he would have another one built in 671, which we will discuss later.  It is interesting that both of these inventions appear twice in the narrative—once during the reign of Naka no Oe, aka Tenchi Tenno, and once during the previous reign, that of Takara Hime, aka Saimei Tenno.  In this case it is said that 671 is the first time that the water clock, or roukoku, was actually used. From what I can tell, there is nothing that definitively indicates that the Mizuochi site in Asuka was definitely the site of Naka no Oe's water clock.  There isn't much in the Chronicles telling us what it was like or where, exactly, it was built, and there wasn't anything found at the site naming it as the location of the roukoku.  However, the site is in a prominent enough place, with channels for water and a pavilion of some sort.  They definitely found evidence of pipes, remnants of lacquered wood, and reservoirs for water, among other things, that suggest something to do with moving water happened in this area.  So it seems a very strong choice, as it all fits with theoretical archeological reconstructions. A water clock like this is excellent for keeping accurate time at all hours of the day.  However, it does have a slight problem in that anyone without a clock is still going to have to use the sun and similar heavenly cues to know what time it is.  So how do you let them know?  Well, it turns out that the continent had an answer for that as well, and instituted various systems of drums and bells to let people know the hour.  In fact, some of these practices continued, in one form or another, right up to the modern day—with or without a water clock.  After all, the key was to give the community some sense of the passing of time, but I doubt anyone was using it to time things more precisely than a general idea of an hour—though they did have the concept of their own minutes and seconds.  Which brings us to just how they saw time back then. The system of time that the Chronicles seems to use also came over from the continent, where there appear to have been several different methods for telling time prior to accurate clocks.  And while there was an idea of dividing the entire day into twelve segments, the time as it was announced was not always consistent with those twelve segments, or hours.  Rather, time was based around the key parts of the day.  So, for instance there was sunrise, noon, sunset, and midnight.  And while noon and midnight remain exactly twelve hours apart, sunrise and sunset change with the seasons.  So if you call out sunrise, and then divide the time between sunrise and noon into equal segments of time, the size of those time segments change with the seasons.  On top of that, because of the tilt of the earth and our slightly irregular orbit around the sun, the sun appears to “move” across the sky faster or slower throughout the year, with a difference of about 30 minutes total between the extremes.  This isn't going to affect most people's daily lives, but would have been noticeable to those taking accurate measurements. In ancient Han, this appears to have been common in cities and towns, with a watch that would call out as they progressed on their rounds at set points in the day and night, relying largely on heavenly cues—which I suspect did not lead to the most accurate timekeeping, but it was sufficient for what most people needed.  The telling of time in this manner was partly to help with keeping track of the time of day, but was just as much an announcement that the watch was on duty and a warning to would-be criminals. Now a water clock was an excellent device for keeping track of a standard, absolute time, such as it were, but it required constant maintenance.  If you already have a watch calling out the time, perhaps they can also keep the water clock properly set, but you did have to have someone constantly filling it up and draining it at known points of the day.  Plus there was the problem that you only knew the time if you could check it, and this wasn't like a clock tower or something similar. And so in 671 it appears that Nak no Oe instituted the continental idea of drums and bells to announce the time to the people—or at least to those at the court.  We don't have a record of exactly how they were, used, but we can infer from other sources on the continent, and what we do know that some tradition of announcing the time with drums and bells continued to be employed in Japan until the Meiji era, though perhaps not without interruption:  Temples and the like had bell or drum towers, and as the day progressed they would beat out the time.  It was not, however, telling time as we might think of it, with one stroke at the first hour, two on the second, etc..  In fact, in many ways they counted backwards, and they only counted 12 hours, not our modern 24.  By the Edo period it seems that it was common practice to toll the bells nine times at noon and at midnight.  From there, they would count down, with 8 bells at roughly 2 o'clock, 7 bells at 4 o'clock, and 6 bells at 6 o'clock.  That would be another issue.  From 6 o'clock, the number of bells that would be tolled continued to decrease, so that at 8 o'clock it would be 5 bells, then 4 bells at 10 o'clock.  It would then jump back up to 9 and start over again. Why these numbers were used for the different hours we are not entirely sure, and I have no idea if these numbers were the same ones used back in the 7th century—though it does seem to match similar continental traditions.  Even the hours themselves were known by the twelve signs that came to be associated with the zodiac:  the hour of the rat, the hour of the ox, the hour of the tiger, etc.  Midnight fell in the middle of the hour of the rat, and noon fell in the middle of the hour of the horse, with each hour being almost exactly 2 hours by modern reckoning. There were other systems in use as well.  One divided the entire day up by 100 and then each of those divisions by another 10.  The key was whether or not it was an absolute or relative measurement. Something like the roukoku would indicate an absolute measurement.  After all, the fall of water from one reservoir to another was not affected by the change in seasons—at least as long as the water didn't freeze.  The flow was constant, as was the measurement of time. For those using other forms of reckoning, such as celestial phenomena or even a sundial, things might be a bit less accurate.  This was especially true when using concepts like “sunrise” and “sunset”.  Still, through observing the changes over the year, people eventually figured out charts and rules to help reconcile absolute forms of measurement with solar time.  There were other methods for telling time, as well.  Perhaps one of the more pleasant was the use of incense sticks.  By the time of the Tang dynasty, incense in stick form was relatively common, and it had been noticed that sticks of incense could burn at a fixed rate.  This meant that you could use incense sticks like candles were used in Europe, counting down how far they had burned to tell what time it was.  If you were really fancy, you could make a single stick out of different types of incense, so that as it hit a new hour, the scent would change, alerting you to the time through your olfactory senses. Speaking of time, we are coming to the end of ours for this episode.  We do have some more information on this on our website, Sengokudaimyo.com, and we'll have links to those sections of the website accompanying our blog. Next episode we will focus more on the reign of Naka no Oe, aka Tenji Tennou, from his seat at Otsu no Miya. Until then, thank you once again for listening and for all of your support. If you like what we are doing, please tell your friends and feel free to rate us wherever you listen to podcasts.  If you feel the need to do more, and want to help us keep this going, we have information about how you can donate on Patreon or through our KoFi site, ko-fi.com/sengokudaimyo, or find the links over at our main website,  SengokuDaimyo.com/Podcast, where we will have some more discussion on topics from this episode. Also, feel free to reach out to our Sengoku Daimyo Facebook page.  You can also email us at the.sengoku.daimyo@gmail.com.  Thank you, also, to Ellen for their work editing the podcast. And that's all for now.  Thank you again, and I'll see you next episode on Sengoku Daimyo's Chronicles of Japan.  

There's little doubt that music is an integral part of what it means to be human. But how did it first arise, how did musical instruments and compositions become ever more sophisticated and why does listening to or playing music bring us so much joy? In this episode, we speak to science writer and music producer David Darling about his latest book A Perfect Harmony: Music, Mathematics and Science. He tells us how the oldest pitched musical instrument found so far is thought to be more than 40,000 years old, the role music has played in the evolution of human culture, and what the impact AI-generated music may have on the work of human musicians and composers in the near future. Learn more about your ad choices. Visit podcastchoices.com/adchoices

1/ Bas, The Hics, Ab-Soul. Norbit.2/ Knowledge the Pirate. 1 On me.3/ FRESH DAILY AND PARENTAL. Plaid patterns. feat. DEBONAIR P y Awon. 4/ WU-TANG & MATHEMATICS. Dolemite.5/ BERNADETTE PRICE. Now ain’t the time. feat.TERROR VAN POO.6/ SUPREME CEREBRAL. Find a way. feat YOLANDA SARGENT.7/ AGALLAH THE DON. Albizu. feat M Tundra. 8/ BOOG BROWN, SLOPFUNKDUST & SPONATOLA. Flight Journey. 9/ KOOL KAT. When the lala hits. feat AWON.10/ TERMANOLOGY & BRONZE NAZARETH. Fargo. feat WAIS P.11/ LORDS OF THE UNDERGROUND. Circle of life.12/ RIM AND VANDERSLICE. If it’s hot. featt PLANET ASIA, MAFFEW. 13/ WHITE SHADOW & SON OF SATURN. Encephalon fluxx. feat Silkroad Gunmen.14/ SHYLOW. D&A.15/ MINDSONE. Blank slate.16/ RECOGNIZE ALI AND STU BANGAS. Most dangerous. 17/ BLACKLIQ & DUB SONATA. Much Given, much tested.Escuchar audio

This episode of the Bitcoin Infinity Academy covers Sovereignty Through Mathematics Chapter 10: The Environment In this episode, we discuss the intersection of Bitcoin and the environment , delving into how Bitcoin incentivizes the use of renewable energy sources and improves energy efficiency. We explore the misconceptions about Bitcoin's energy usage and how it compares to other industries, the economic incentives for producers, and the importance of sound money. Additionally, we touch on political and social aspects, the rise of environmental movements, and the role of Bitcoin in providing equality of opportunity. Read the chapter on Nostr: https://dev.primal.net/infinity/the-environment-%7C-sovereignty-through-mathematics-chapter-10 Join the academy at our Geyser page: https://geyser.fund/project/infinity You can also support us by sending some sats to our Alby Hub at bitcoininfinity@getalby.com The Bitcoin Infinity Academy is an educational project built around Knut Svanholm's books about Bitcoin and Austrian Economics. Each week, a whole chapter from one of the books is released for free on Highlighter, accompanied by a video in which Knut and Luke de Wolf discuss that chapter's ideas. You can join the discussions by signing up for one of the courses on our Geyser page! Connect with Us: https://www.bitcoininfinityshow.com/ https://bitcoininfinitystore.com https://primal.net/infinity https://primal.net/knut https://primal.net/luke https://twitter.com/BtcInfinityShow https://twitter.com/knutsvanholm https://twitter.com/lukedewolf

Episode: 1379 Frank and Peter Griffin: teaching calculus.  Today, an obituary brings back memories.

Head on over to https://cell.ver.so/TOE and use coupon code TOE at checkout to save 15% on your first order. Get ready to witness a turning point in mathematical history: in this episode, we dive into the AI breakthroughs that stunned number theorists worldwide. Join us as Professor Yang-Hue Hi discusses the murmuration conjecture, shows how DeepMind, OpenAI, and EpochAI are rewriting the rules of pure math, and reveals what happens when machines start making research-level discoveries faster than any human could. AI is taking us beyond proof straight into the future of discovery. As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe Join My New Substack (Personal Writings): https://curtjaimungal.substack.com Listen on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e Timestamps: 00:00 Introduction to a New Paradigm 01:34 The Changing Landscape of Research 03:30 Categories of Machine Learning in Mathematics 06:53 Researchers: Birds vs. Hedgehogs 09:36 Personal Experiences with AI in Research 11:44 The Future Role of Academics 14:08 Presentation on the AI Mathematician 16:14 The Role of Intuition in Discovery 18:00 AI's Assistance in Vague Problem Solving 18:48 Newton and AI: A Historical Perspective 20:59 Literature Processing with AI 24:34 Acknowledging Modern Mathematicians 26:54 The Influence of Data on Mathematical Discovery 30:22 The Riemann Hypothesis and Its Implications 31:55 The BST Conjecture and Data Evolution 33:29 Collaborations and AI Limitations 36:04 The Future of Mathematics and AI 38:31 Image Processing and Mathematical Intuition 41:57 Visual Thinking in Mathematics 49:24 AI-Assisted Discovery in Mathematics 51:34 The Murmuration Conjecture and AI Interaction 57:05 Hierarchies of Difficulty 58:43 The Memoration Breakthrough 1:00:28 Understanding the BSD Conjecture 1:01:45 Diophantine Equations Explained 1:03:39 The Cubic Complexity 1:19:03 Neural Networks and Predictions 1:21:36 Breaking the Birch Test 1:24:44 The BSD Conjecture Clarified 1:26:21 The Role of AI in Discovery 1:30:29 The Memoration Phenomenon 1:32:59 PCA Analysis Insights 1:35:50 The Emergence of Memoration 1:38:35 Conjectures and AI's Role 1:41:29 Generalizing Biases in Mathematics 1:44:55 The Future of AI in Mathematics 1:49:28 The Brave New World of Discovery Links Mentioned: - Topology and Physics (book): https://amzn.to/3ZoneEn - Machine Learning in Pure Mathematics and Theoretical Physics (book): https://amzn.to/4k8SXC6 - The Calabi-Yau Landscape (book): https://amzn.to/43DO7H0 - Yang-Hui's bio and published papers: https://www.researchgate.net/profile/Yang-Hui-He - A Triumvirate of AI-Driven Theoretical Discovery (paper): https://arxiv.org/abs/2405.19973 - Edward Frenkel explains the Geometric Langlands Correspondence on TOE: https://www.youtube.com/watch?v=RX1tZv_Nv4Y - Stone Duality (Wiki): https://en.wikipedia.org/wiki/Stone_duality - Summer of Math Exposition: https://some.3b1b.co/ - Machine Learning meets Number Theory: The Data Science of Birch–Swinnerton-Dyer (paper): https://arxiv.org/pdf/1911.02008 - The L-functions and modular forms database: https://www.lmfdb.org/ - Epoch AI FrontierMath: https://epoch.ai/frontiermath/the-benchmark - Mathematical Beauty (article): https://www.quantamagazine.org/mathematical-beauty-truth-and-proof-in-the-age-of-ai-20250430/ SUPPORT: - Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join - Support me on Patreon: https://patreon.com/curtjaimungal - Support me on Crypto: https://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - Support me on PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 SOCIALS: - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs #science Learn more about your ad choices. Visit megaphone.fm/adchoices

My guest today is Dr. Aditya Nagrath, who holds a PhD in Mathematics and Computer Science. With over 30 years of industry experience as a software engineer, author, and entrepreneur, he's worked on everything from atomic clocks to Amazon's Kindle Fire. As founder of Elephant Head Math software and the Elephant Learning Math Academy, he's developed an online system that helps children learn about a year and a half of math in just 10 weeks when used 30 minutes per week.   In our conversation, Dr. Nagrath outlines three distinct steps to master new math concepts – define, recognize, and produce. He explains the crucial "language gap" in mathematics, and explores the difference between recognizing math symbols on paper versus truly understanding and applying mathematical concepts. Most importantly, we discuss math anxiety and what children need to overcome it.   Get full show notes, transcript, and more information here: https://planningplaytime.com/101

In this episode of The Research Files podcast, Teacher editor Jo Earp chats to Jenni Ingram, Professor of Mathematics at the University of Oxford, about the OECD's Unlocking High-Quality Teaching report. Alongside insights from 150 schools in 50 countries, it explores 20 practices that teachers draw on to achieve 5 key teaching goals. Host: Jo Earp Guest: Professor Jenni Ingram

In this episode of the Additive Snack Podcast, host Fabian Alefeld explores the critical role of mathematics in additive manufacturing with guest Harshil Goel, founder, and CEO of Dyndrite. Harshil shares his unconventional entry into the additive manufacturing industry, driven by his deep background in mathematics and mechanical engineering. The conversation delves into how Dyndrite's software provides solutions for complex additive manufacturing challenges, from data preparation to materials and process development. Harshil also discusses various customer success stories and how their software helps streamline qualification processes, ultimately enhancing productivity. Additionally, they discussed the upcoming Dyndrite roadshow aimed at educating users on advanced additive manufacturing techniques, featuring hands-on sessions and practical demonstrations.Comments about the show or wish to share your AM journey? Contact us at additive.snack@eos-na.com. The Additive Snack Podcast is brought to you by EOS. For more information about Dyndrite's innovative solutions, visit their website and connect with Harshil Goel on LinkedIn.     01:17 Meet Harshil Go: From Mathematics to Additive Manufacturing02:33 The Birth of Dyndrite: Solving Software Challenges05:22 Understanding Dyndrite's Core Offerings09:53 Dyndrite's Unique Approach to Build Preparation15:07 Customer Success Stories and Real-World Applications19:47 Empowering Engineers with Python Integration23:04 Learning and Adapting to Dyndrite's Tools26:51 Multilingual Proficiency and Family Background27:36 Transitioning to Coding and Tool Integration28:17 Optimizing Production with Dendrite30:05 Challenges and Innovations in Qualification33:20 Deep Dive into Aviation Qualification39:17 Additive Manufacturing Industry Trends43:09 The Role of GPUs and AI in Additive Manufacturing45:59 Dyndrite Roadshow and Conclusion 

In this episode of Room to Grow, Joanie and Curtis continue the season 5 series on the Mathematics Teaching Practices from NCTM's Principles to Actions, celebrating its 10th anniversary. This month's practice is “Establish Mathematics Goals to Focus Learning.” This is defined as follows:Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions. In today's conversation, our hosts unpack the key components of this principle. First, they discuss how learning goals, focused on important mathematical understandings, differ from procedural, process goals, which may include skills and procedures that are not directly connected to the underlying mathematical concepts. Next, the discussion turns to situating goals within a learning progression, which helps teachers stay focused on what is relevant to their grade level or course, and provides a venue for students to be active in their progress toward learning. Finally, effective mathematics goals guide instructional decisions, helping educators know which tangents to explore and which are distractions from the intended learning. We hope you enjoy the conversation, and that it extends your thinking on mathematics goals for learning. Additional referenced content includes:·       NCTM's Principles to Actions·       NCTM's Taking Action series for grades K-5, grades 6-8, and grades 9-12·       NCTM's myNCTM forums (membership required).·       How learning goals serve as a guide – NCTM Teaching Children Mathematics blog post·       Rachel Harrington's appearance on the Math Learning Center podcast/blog discussing mathematical goals Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy. 

1/ Knowledge the Pirate. Eating Etiquette.2/ BOLDY JAMES & REAL BAD MAN. Come back around. fear Dreamcastmoe.3/ MAZE OVERLORD. Lo down.4/ DYNAS AND JAH FREEDOM. Callaloo and collards.5/ FRESH DAILY AND PARENTAL. Back at it. feat KELLY MOONSTONE.6/ Westside Gunn, Doechii. EGYPT (Remix).7/ TERMANOLOGY & BRONZE NAZARETH. History lesson. feat. Jon Connor y Nim K.8/ KOOL KAT. Another Day. Asun Eastwood.9/ WU-TANG & MATHEMATICS. The roar of lion. feat KOOL G RAP.10/ BERNADETTE PRICE. Bars. feat. TERROR VAN POO y RUSTE JUXX.11/ SUPREME CEREBRAL. Dart Gallery. feat Ralphiie Reese. 12/ AGALLAH THE DON. Albizu. feat M Tundra.13/ BOOG BROWN, SLOPFUNKDUST & SPONATOLA. What you want.14/ ONYX. Rock Boxx. 15/ RIM AND VANDERSLICE. Stick to the plan.16/ LORDS OF THE UNDERGROUND. U can get it.17 / RASOM BADBONEZ. Can’t Give up. Escuchar audio

In his new book, Blueprints, Marcus du Sautoy traces the connections between mathematics and art and the ways in which creatives use numbers to underpin their work – unconsciously or otherwise. From the earliest stone circles to the unique architecture of Zaha Hadid, du Sautoy shows us that there are blueprints everywhere and how logic and aesthetics are intrinsically intermingled. Sophie Pavelle is also interested in connections and her forthcoming book, To Have or To Hold, explores symbiotic relationships in nature. Focusing on eight key examples, Sophie Pavelle explains how these mutually beneficial connections are crucial for the survival of our natural world and how they play an integral role in regulating ecosystems and strengthening resilience. She asks if we are capable of restoring and nurturing our environment or will we continue to exploit the Earth's resources, till death do us part? The British Museum's new exhibition illuminates the captivating work of the nineteenth-century Japanese artist, Utagawa Hiroshige (from 1st May to 7th September 2025). He was fascinated by the natural world and many of his pictures take flora and fauna as their subject matter. Hiroshige was one of Japan's most talented, prolific and popular artists and his influence was not only felt in his home country, but spread globally – influencing artists such as Vincent Van Gogh and contemporary artists such as Julian Opie. The curator of the exhibition, Alfred Haft, shines a light on the oeuvre of Hiroshige, his techniques and enduring legacy.Producer: Natalia Fernandez

Monday marks what would have been Malcolm X’s 100th birthday. Akinyele Umoja, a professor in the department of Africana Studies at Georgia State University, talks more about the Muslim minister and civil and human rights leader’s life and legacy, from his early years when he was known as “Detroit Red” to his period within the Nation of Islam. Professor Umoja also discusses his own involvement in the Malcolm X Grassroots Movement. INSERT: We continue with WABE’s “Server South” series. Residents in Fayetteville brace for rapid data center development, basically in their backyards, we air WABE Southside reporter DorMiya Vance’s latest report. Plus, for “Closer Look’s” Class of 2025 graduation series, we hear from Winter Jones. The standout graduate is part of Spelman College’s largest-ever graduating class, consisting of 694 students. While earning her degree, Jones became an astronaut scholar and worked with NASA on reducing emissions from supersonic jets. Now, Jones talks with Rose about her academic journey and her dreams of becoming an aerospace engineer.See omnystudio.com/listener for privacy information.

This episode of the Bitcoin Infinity Academy covers Sovereignty Through Mathematics Chapter 9: Money as an Amplifier In this episode, we explore the idea of money as a linguistic tool for expressing value and its role as an amplifier of personality. The discussion covers the flawed nature of fiat money, the societal impacts of sound money, the parallels between Bitcoin and gold, and much more!  Read the chapter on Nostr: https://dev.primal.net/infinity/sovereignty-through-mathematics-chapter-9:-money-as-an-amplifier Join the academy at our Geyser page: https://geyser.fund/project/infinity You can also support us by sending some sats to our Alby Hub at bitcoininfinity@getalby.com  The Bitcoin Infinity Academy is an educational project built around Knut Svanholm's books about Bitcoin and Austrian Economics. Each week, a whole chapter from one of the books is released for free on Highlighter, accompanied by a video in which Knut and Luke de Wolf discuss that chapter's ideas. You can join the discussions by signing up for one of the courses on our Geyser page! Connect with Us: https://www.bitcoininfinityshow.com/ https://bitcoininfinitystore.com https://primal.net/infinity https://primal.net/knut https://primal.net/luke https://twitter.com/BtcInfinityShow https://twitter.com/knutsvanholm https://twitter.com/lukedewolf

Can you hide in plain sight? Katherine Perry, assistant professor of mathematics at Soka University of America, explores if mathematics can. Katherine Perry is a mathematician specializing in graph theory, design theory, and combinatorics. She is especially interested in breaking apart graphs into smaller subgraphs with special properties. She has a BA in mathematics from […]

Tweetable quote from Fr. Seán“Life is a dream that the ego is having, the ego is a dream that the soul is having, and the soul is a dream that spirit is having.”SummaryJoin us for a profound conversation as we explore the depths of spirituality, faith, and the teachings of Christ with Fr. Seán ÓLaoire. He introduces the concept of Christ consciousness as a recognition of the inner divinity present in all beings. The dialogue explores the importance of small, supportive communities in spiritual growth, the significance of understanding sacred texts through a mystical lens, and the transformative power of personal experiences in healing and self-discovery.About our guest:Fr. Seán ÓLaoire, PhD, born in Cork, Ireland, holds a BSc in Mathematics and a PhD in Transpersonal Psychology. Ordained as a Catholic priest in 1972, he spent 14 years serving in East Africa and is fluent in six languages. He is a licensed Clinical Psychologist, author, and researcher focused on the effects of prayer. Fr. Seán is Co-Founder and Spiritual Director of Companions on the Journey, a non-hierarchical spiritual community that honors personal experience, interfaith wisdom, and the divine in all.

Episode: 1375 Leibniz, Newton, and the great calculus dispute.  Today, we throw Leibniz's cat into the super collider.

Stephen Wolfram is a physicists, mathematician, and programmer who believes he has discovered the computational rules that organize the universe at the finest grain. These rules are not physical rules like the equations of state or Maxwell's equations. According to Wolfram, these are rules that govern how the universe evolves and operates at a level at least one step down below the reality that we inhabit. His computational principles are inspired by the results observed in cellular automata systems, which show that it's possible to take a very simple system, with very simple rules, and end up at complex patterns that often look organic and always look far more intricate than the black and white squares that the game started with. We sit down with him for a conversation about the platonic endeavor that he has undertaken, where to draw the line between lived experience and the computational universe, the limits of physics, and the value of purpose and the source of consciousness. MAKE HISTORY WITH US THIS SUMMER:https://demystifysci.com/demysticon-2025PATREON https://www.patreon.com/c/demystifysciPARADIGM DRIFThttps://demystifysci.com/paradigm-drift-show00:00 Go!00:02:07 Entropy and Computational Irreducibility00:09:45 Understanding Observers in Physics00:15:12 The Concept of Time as Computation00:23:00 Neural Networks and Determinism00:30:03 Understanding Space and Its Nature00:39:24 Exploring the Nature of Emergence and Reality00:41:44 Perception and Computational Limitations of Human Minds00:46:18 The Complexity of Existence and Consciousness00:51:58 The Universe's Computation versus Human Understanding00:55:42 Conceptualizing Reality Beyond Physical Actors01:01:11 Computational Irreducibility in Biological Systems01:09:49 The Nature of Experience in Humans and Machines01:14:25 Internal Experiences and the Connection to Purpose01:18:07 Exploration of Purpose in Life and AI01:26:00 The Nature of Human Existence and Purpose01:35:19 Searching for Extraterrestrial Intelligence and Understanding Reality01:41:02 Communication Across Species02:01:13 Emergence of Simple Rules in Physics02:14:47 Observers and the Universe02:19:14 The Role of Mass and Experience02:24:02 Self-Reproduction and Evolution02:30:50 Complexity and Natural Selection02:37:07 Foundations of Medicine02:40:45 Application of Physics Concepts in Other Fields02:49:44 Limits and Possibilities of Travel Through Space02:53:11 Future of Human Civilization and Technology02:55:05 Science and Pre-Existing Questions about the Universe02:58:05 The Intersection of Mathematics and Physical Reality#physics, #computationalphysics, #consciousness, #freewill, #determinism, #spaceexploration, #evolution, #purpose, #futureofhumanity, #complexsystems , #machinelearning, #philosophypodcast , #sciencepodcast, #longformpodcast ABOUS US: Anastasia completed her PhD studying bioelectricity at Columbia University. When not talking to brilliant people or making movies, she spends her time painting, reading, and guiding backcountry excursions. Shilo also did his PhD at Columbia studying the elastic properties of molecular water. When he's not in the film studio, he's exploring sound in music. They are both freelance professors at various universities. PATREON: get episodes early + join our weekly Patron Chat https://bit.ly/3lcAasBMERCH: Rock some DemystifySci gear : https://demystifysci.myspreadshop.com/allAMAZON: Do your shopping through this link: https://amzn.to/3YyoT98DONATE: https://bit.ly/3wkPqaDSUBSTACK: https://substack.com/@UCqV4_7i9h1_V7hY48eZZSLw@demystifysciBLOG: http://DemystifySci.com/blog RSS: https://anchor.fm/s/2be66934/podcast/rssMAILING LIST: https://bit.ly/3v3kz2S SOCIAL: - Discord: https://discord.gg/MJzKT8CQub- Facebook: https://www.facebook.com/groups/DemystifySci- Instagram: https://www.instagram.com/DemystifySci/- Twitter: https://twitter.com/DemystifySciMUSIC: -Shilo Delay: https://g.co/kgs/oty671

On this episode of ID the Future from the archive, Andrew McDiarmid talks with science historian Michael Keas about pioneering mathematical astronomer Johannes Kepler, based on Keas's book Unbelievable: 7 Myths About the History and Future of Science and Religion. Kepler studied theology before turning to math and science, and it was his belief in God that guided his extraordinary discoveries. Kepler is one of several great scientists of early modern science whose convictions about God's nature inspired their groundbreaking investigations. Source

From the earliest stone circles to Mozart's obsession with numbers to the radically modern architecture of Zaha Hadid, maths and creativity are interwoven across time and space. Whether we are searching for meaning in an abstract painting or finding patterns in poetry, there are blueprints everywhere: symmetry, prime numbers, the golden ratio and more. In May 2025 we were joined by award-winning mathematician and Oxford professor Marcus du Sautoy as he looked to the arts to uncover the key mathematical structures that underpin both nature and human creativity. Drawing on his new book, Blueprints, du Sautoy explored how we make art, why a creative mindset is vital for discovering new mathematics, and how a fundamental connection to the natural world intrinsically links these two subjects. ----- If you'd like to become a Member and get access to all our full ad free conversations, plus all of our Members-only content, just visit intelligencesquared.com/membership to find out more. For £4.99 per month you'll also receive: - Full-length and ad-free Intelligence Squared episodes, wherever you get your podcasts - Bonus Intelligence Squared podcasts, curated feeds and members exclusive series - 15% discount on livestreams and in-person tickets for all Intelligence Squared events  ...  Or Subscribe on Apple for £4.99: - Full-length and ad-free Intelligence Squared podcasts - Bonus Intelligence Squared podcasts, curated feeds and members exclusive series … Already a subscriber? Thank you for supporting our mission to foster honest debate and compelling conversations! Visit intelligencesquared.com to explore all your benefits including ad-free podcasts, exclusive bonus content and early access. … Subscribe to our newsletter here to hear about our latest events, discounts and much more. https://www.intelligencesquared.com/newsletter-signup/ Learn more about your ad choices. Visit podcastchoices.com/adchoices Learn more about your ad choices. Visit podcastchoices.com/adchoices

Dr. John Mighton is an award-winning mathematician, playwright, and best-selling author internationally recognized for his ground-breaking work building children's confidence, skills, and success in math. He founded the Canadian charity JUMP Math (Junior Undiscovered Math Prodigies) in 2002 with an equity-driven mission to empower every child to achieve their potential through accessible math education. JUMP Math's K-8 resources currently support thousands of educators and students in North America and other countries to teach, learn, and love math. Dr. Mighton holds a master's degree in philosophy from McMaster University and a PhD in Mathematics from the University of Toronto, where he frequently teaches at the Ontario Institute for Studies in Education. A recipient of the Order of Canada, Dr. Mighton has published three books on math education, given hundreds of talks on the subject, including a TEDx Talk and keynote at the Aspen Brain Forum, and has received many awards and honorary doctorates in recognition of his work. His latest book, All Things Being Equal: Why Math is the Key to a Better World, offers a compelling argument for why accessible math education can and must be available to everyone. In a twist of fate in his early career, Dr. Mighton played Matt Damon's math tutor in the 1997 movie, Good Will Hunting ---- Stay Connected with #CanadasEntrepreneur! Join our growing community of entrepreneurs across Canada! Don't miss out on inspiring interviews, expert insights, and the latest business trends from the people shaping the future of our economy.

From the earliest stone circles to Mozart's obsession with numbers to the radically modern architecture of Zaha Hadid, maths and creativity are interwoven across time and space. Whether we are searching for meaning in an abstract painting or finding patterns in poetry, there are blueprints everywhere: symmetry, prime numbers, the golden ratio and more. In May 2025 we were joined by award-winning mathematician and Oxford professor Marcus du Sautoy as he looked to the arts to uncover the key mathematical structures that underpin both nature and human creativity. Drawing on his new book, Blueprints, du Sautoy explored how we make art, why a creative mindset is vital for discovering new mathematics, and how a fundamental connection to the natural world intrinsically links these two subjects. ------ This is the first instalment of a two-part episode. If you'd like to become a Member and get access to all our full ad free conversations, plus all of our Members-only content, just visit intelligencesquared.com/membership to find out more. For £4.99 per month you'll also receive: - Full-length and ad-free Intelligence Squared episodes, wherever you get your podcasts - Bonus Intelligence Squared podcasts, curated feeds and members exclusive series - 15% discount on livestreams and in-person tickets for all Intelligence Squared events  ...  Or Subscribe on Apple for £4.99: - Full-length and ad-free Intelligence Squared podcasts - Bonus Intelligence Squared podcasts, curated feeds and members exclusive series … Already a subscriber? Thank you for supporting our mission to foster honest debate and compelling conversations! Visit intelligencesquared.com to explore all your benefits including ad-free podcasts, exclusive bonus content and early access. … Subscribe to our newsletter here to hear about our latest events, discounts and much more. https://www.intelligencesquared.com/newsletter-signup/ Learn more about your ad choices. Visit podcastchoices.com/adchoices Learn more about your ad choices. Visit podcastchoices.com/adchoices

From Buffalo Bob to the NSA, we cover it all with magician and mathematician S. Brent Morris … and then jump into the next chapter of “The Linking Rings.” Brent Morris Interview starts at 00:05:44"I Love That" starts at 00:55:57Chapter Nine of "The Linking Rings" starts at 01:03:52 LINKSThe Eli Marks Mystery Series: http://www.elimarksmysteries.com/Get yourself a Free Eli Marks Short Story: https://dl.bookfunnel.com/jj1r1yaavjListen to an Eli Marks Audio Short Story: https://BookHip.com/LZBPPMDEmail John at jgaspard (at) earthlink (dot) netThe Tour Guy: https://thetourguy.com/Five Hours of The Shipping News: https://youtu.be/CxHa5KaMBcMCheck out the Occasional Film Podcast: https://www.fastcheapfilm.com/the-podcast

Is AI a big scam? In their co-authored new book, The AI Con, Emily Bender and Alex Hanna take aim at what they call big tech “hype”. They argue that large language models from OpenAI or Anthropic are merely what Bender dubs "stochastic parrots" that produce text without the human understanding nor the revolutionary technology that these companies claim. Both Bender, a professor of linguistics, and Hanna, a former AI researcher at Google, challenge the notion that AI will replace human workers, suggesting instead that these algorithms produce "mid" or "janky" content lacking human insight. They accuse tech companies of hyping fear of missing out (FOMO) to drive adoption. Instead of centralized AI controlled by corporations, they advocate for community-controlled technology that empowers users rather than exploiting them. Five Takeaways (with a little help from Claude)* Large language models are "stochastic parrots" that produce text based on probability distributions from training data without actual understanding or communicative intent.* The AI "revolution" is primarily driven by marketing and hype rather than groundbreaking technological innovations, creating fear of missing out (FOMO) to drive adoption.* AI companies are positioning their products as "general purpose technologies" like electricity, but LLMs lack the reliability and functionality to justify this comparison.* Corporate AI is designed to replace human labor and centralize power, which the authors see as an inherently political project with concerning implications.* Bender and Hanna advocate for community-controlled technology development where people have agency over the tools they use, citing examples like Teheku Media's language technology for Maori communities.Dr. Emily M. Bender is a Professor of Linguistics at the University of Washington where she is also the Faculty Director of the Computational Linguistics Master of Science program and affiliate faculty in the School of Computer Science and Engineering and the Information School. In 2023, she was included in the inaugural Time 100 list of the most influential people in AI. She is frequently consulted by policymakers, from municipal officials to the federal government to the United Nations, for insight into into how to understand so-called AI technologies.Dr. Alex Hanna is Director of Research at the Distributed AI Research Institute (DAIR). A sociologist by training, her work centers on the data used in new computational technologies, and the ways in which these data exacerbate racial, gender, and class inequality. She also works in the area of social movements, focusing on the dynamics of anti-racist campus protest in the US and Canada. She holds a BS in Computer Science and Mathematics and a BA in Sociology from Purdue University, and an MS and a PhD in Sociology from the University of Wisconsin-Madison. Dr. Hanna is the co-author of The AI Con (Harper, 2025), a book about AI and the hype around it. With Emily M. Bender, she also runs the Mystery AI Hype Theater 3000 series, playfully and wickedly tearing apart AI hype for a live audience online on Twitch and her podcast. She has published widely in top-tier venues across the social sciences, including the journals Mobilization, American Behavioral Scientist, and Big Data & Society, and top-tier computer science conferences such as CSCW, FAccT, and NeurIPS. Dr. Hanna serves as a Senior Fellow at the Center for Applied Transgender Studies and sits on the advisory board for the Human Rights Data Analysis Group. She is also recipient of the Wisconsin Alumni Association's Forward Award, has been included on FastCompany's Queer 50 (2021, 2024) List and Business Insider's AI Power List, and has been featured in the Cal Academy of Sciences New Science exhibit, which highlights queer and trans scientists of color.Named as one of the "100 most connected men" by GQ magazine, Andrew Keen is amongst the world's best known broadcasters and commentators. In addition to presenting the daily KEEN ON show, he is the host of the long-running How To Fix Democracy interview series. He is also the author of four prescient books about digital technology: CULT OF THE AMATEUR, DIGITAL VERTIGO, THE INTERNET IS NOT THE ANSWER and HOW TO FIX THE FUTURE. Andrew lives in San Francisco, is married to Cassandra Knight, Google's VP of Litigation & Discovery, and has two grown children.Keen On America is a reader-supported publication. To receive new posts and support my work, consider becoming a free or paid subscriber. This is a public episode. If you'd like to discuss this with other subscribers or get access to bonus episodes, visit keenon.substack.com/subscribe

This episode of the Bitcoin Infinity Academy covers Sovereignty Through Mathematics Chapter 8: Changing the Rules In this episode, we explore the intricacies of altering the Bitcoin protocol,t he concepts of hard forks and soft forks, and more. We also touch on historical events such as the block size wars, the difference between Bitcoin and crypto, and the idea of Bitcoin as absolute digital scarcity. Read the chapter on Nostr: https://primal.net/infinity/sovereignty-through-mathematics-chapter-8:-changing-the-rules Join the academy at our Geyser page: https://geyser.fund/project/infinity You can also support us by sending some sats to our Alby Hub at bitcoininfinity@getalby.com The Bitcoin Infinity Academy is an educational project built around Knut Svanholm's books about Bitcoin and Austrian Economics. Each week, a whole chapter from one of the books is released for free on Highlighter, accompanied by a video in which Knut and Luke de Wolf discuss that chapter's ideas. You can join the discussions by signing up for one of the courses on our Geyser page! Connect with Us: https://www.bitcoininfinityshow.com/ https://bitcoininfinitystore.com https://primal.net/infinity https://primal.net/knut https://primal.net/luke https://twitter.com/BtcInfinityShow https://twitter.com/knutsvanholm https://twitter.com/lukedewolf

Episode109-Marta Garcia, "Redefining Mathematics For Belonging"

Stephen Wolfram answers questions from his viewers about the future of science and technology as part of an unscripted livestream series, also available on YouTube here: https://wolfr.am/youtube-sw-qaTopics discussed: Fusion energy and nuclear fuel design - AI reasoning, learning and scientific roles - Mathematics, computation and physical reality - Jobs and fields at risk from AI - Philosophy of knowledge and future roles

William Zahner, Understanding the Role of Language in Math Classrooms ROUNDING UP: SEASON 3 | EPISODE 17 How can educators understand the relationship between language and the mathematical concepts and skills students engage with in their classrooms? And how might educators think about the mathematical demands and the language demands of tasks when planning their instruction?  In this episode, we discuss these questions with Bill Zahner, director of the Center for Research in Mathematics and Science Education at San Diego State University. BIOGRAPHY Bill Zahner is a professor in the mathematics department at San Diego State University and the director of the Center for Research in Mathematics and Science Education. Zahner's research is focused on improving mathematics learning for all students, especially multilingual students who are classified as English Learners and students from historically marginalized communities that are underrepresented in STEM fields. RESOURCES Teaching Math to Multilingual Learners, Grades K–8 by Kathryn B. Chval, Erin Smith, Lina Trigos-Carrillo, and Rachel J. Pinnow National Council of Teachers of Mathematics Mathematics Teacher: Learning and Teaching PK– 12 English Learners Success Forum SDSU-ELSF Video Cases for Professional Development The Math Learning Center materials Bridges in Mathematics curriculum Bridges in Mathematics Teachers Guides [BES login required] TRANSCRIPT Mike Wallus: How can educators understand the way that language interacts with the mathematical concepts and skills their students are learning? And how can educators focus on the mathematics of a task without losing sight of its language demands as their planning for instruction? We'll examine these topics with our guest, Bill Zahner, director of the Center for Research in Mathematics and Science Education at San Diego State University.  Welcome to the podcast, Bill. Thank you for joining us today. Bill Zahner: Oh, thanks. I'm glad to be here. Mike: So, I'd like to start by asking you to address a few ideas that often surface in conversations around multilingual learners and mathematics. The first is the notion that math is universal, and it's detached from language. What, if anything, is wrong with this idea and what impact might an idea like that have on the ways that we try to support multilingual learners? Bill: Yeah, thanks for that. That's a great question because I think we have a common-sense and strongly held idea that math is math no matter where you are and who you are. And of course, the example that's always given is something like 2 plus 2 equals 4, no matter who you are or where you are. And that is true, I guess [in] the sense that 2 plus 2 is 4, unless you're in base 3 or something. But that is not necessarily what mathematics in its fullness is. And when we think about what mathematics broadly is, mathematics is a way of thinking and a way of reasoning and a way of using various tools to make sense of the world or to engage with those tools [in] their own right. And oftentimes, that is deeply embedded with language.  Probably the most straightforward example is anytime I ask someone to justify or explain what they're thinking in mathematics. I'm immediately bringing in language into that case. And we all know the old funny examples where a kid is asked to show their thinking and they draw a diagram of themselves with a thought bubble on a math problem. And that's a really good case where I think a teacher can say, “OK, clearly that was not what I had in mind when I said, ‘Show your thinking.'”  And instead, the demand or the request was for a student to show their reasoning or their thought process, typically in words or in a combination of words and pictures and equations. And so, there's where I see this idea that math is detached from language is something of a myth; that there's actually a lot of [language in] mathematics. And the interesting part of mathematics is often deeply entwined with language. So, that's my first response and thought about that.  And if you look at our Common Core State Standards for Mathematics, especially those standards for mathematical practice, you see all sorts of connections to communication and to language interspersed throughout those standards. So, “create viable arguments,” that's a language practice. And even “attend to precision,” which most of us tend to think of as, “round appropriately.” But when you actually read the standard itself, it's really about mathematical communication and definitions and using those definitions with precision. So again, that's an example, bringing it right back into the school mathematics domain where language and mathematics are somewhat inseparable from my perspective here. Mike: That's really helpful. So, the second idea that I often hear is, “The best way to support multilingual learners is by focusing on facts or procedures,” and that language comes later, for lack of a better way of saying it. And it seems like this is connected to that first notion, but I wanted to ask the question again: What, if anything, is wrong with this idea that a focus on facts or procedures with language coming after the fact? What impact do you suspect that that would have on the way that we support multilingual learners? Bill: So, that's a great question, too, because there's a grain of truth, right? Both of these questions have simultaneously a grain of truth and simultaneously a fundamental problem in them. So, the grain of truth—and an experience that I've heard from many folks who learned mathematics in a second language—was that they felt more competent in mathematics than they did in say, a literature class, where the only activity was engaging with texts or engaging with words because there was a connection to the numbers and to symbols that were familiar. So, on one level, I think that this idea of focusing on facts or procedures comes out of this observation that sometimes an emergent multilingual student feels most comfortable in that context, in that setting.  But then the second part of the answer goes back to this first idea that really what we're trying to teach students in school mathematics now is not simply, or only, how to apply procedures to really big numbers or to know your times tables fast. I think we have a much more ambitious goal when it comes to teaching and learning mathematics. That includes explaining, justifying, modeling, using mathematics to analyze the world and so on. And so, those practices are deeply tied with language and deeply tied with using communication. And so, if we want to develop those, well, the best way to do that is to develop them, to think about, “What are the scaffolds? What are the supports that we need to integrate into our lessons or into our designs to make that possible?”  And so, that might be the takeaway there, is that if you simply look at mathematics as calculations, then this could be true. But I think our vision of mathematics is much broader than that, and that's where I see this potential. Mike: That's really clarifying. I think the way that you unpack that is if you view mathematics as simply a set of procedures or calculations, maybe? But I would agree with you. What we want for students is actually so much more than that.  One of the things that I heard you say when we were preparing for this interview is that at the elementary level, learning mathematics is a deeply social endeavor. Tell us a little bit about what you mean by that, Bill. Bill: Sure. So, mathematics itself, maybe as a premise, is a social activity. It's created by humans as a way of engaging with the world and a way of reasoning. So, the learning of mathematics is also social in the sense that we're giving students an introduction to this way of engaging in the world. Using numbers and quantities and shapes in order to make sense of our environment.  And when I think about learning mathematics, I think that we are not simply downloading knowledge and sticking it into our heads. And in the modern day where artificial intelligence and computers can do almost every calculation that we can imagine—although your AI may do it incorrectly, just as a fair warning [laughs]—but in the modern day, the actual answer is not what we're so focused on. It's actually the process and the reasoning and the modeling and justification of those choices. And so, when I think about learning mathematics as learning to use these language tools, learning to use these ways of communication, how do we learn to communicate? We learn to communicate by engaging with other people, by engaging with the ideas and the minds and the feelings and so on of the folks around us, whether it's the teacher and the student, the student and the student, the whole class and the teacher. That's where I really see the power. And most of us who have learned, I think can attest to the fact that even when we're engaging with a text, really fundamentally we're engaging with something that was created by somebody else. So, fundamentally, even when you're sitting by yourself doing a math word problem or doing calculations, someone has given that to you and you think that that's important enough to do, right?  So, from that stance, I see all of teaching and learning mathematics is social. And maybe one of our goals in mathematics classrooms, beyond memorizing the times tables, is learning to communicate with other people, learning to be participants in this activity with other folks. Mike: One of the things that strikes me about what you were saying, Bill, is there's this kind of virtuous cycle, right? That by engaging with language and having the social aspect of it, you're actually also deepening the opportunity for students to make sense of the math. You're building the scaffolds that help kids communicate their ideas as opposed to removing or stripping out the language. That's the context in some ways that helps them filter and make sense. You could either be in a vicious cycle, which comes from removing the language, or a virtuous cycle. And it seems a little counterintuitive because I think people perceive language as the thing that is holding kids back as opposed to the thing that might actually help them move forward and make sense. Bill: Yeah. And actually that's one of the really interesting pieces that we've looked at in my research and the broader research is this question of, “What makes mathematics linguistically complex?” is a complicated question. And so sometimes we think of things like looking at the word count as a way to say, “If there are fewer words, it's less complex, and if there are more words, it's more complex.” But that's not totally true. And similarly, “If there's no context, it's easier or more accessible, and if there is a context, then it's less accessible.”  And I don't see these as binary choices. I see these as happening on a somewhat complicated terrain where we want to think about, “How do these words or these contexts add to student understanding or potentially impede [it]?” And that's where I think this social aspect of learning mathematics—as you described, it could be a virtuous cycle so that we can use language in order to engage in the process of learning language. Or, the vicious cycle is, you withhold all language and then get frustrated when students can't apply their mathematics. That's maybe the most stereotypical answer: “My kids can do this, but as soon as they get a word problem, they can't do it.” And it's like, “Well, did you give them opportunities to learn how to do this? [laughs] Or is this the first time?” Because that would explain a lot. Mike: Well, it's an interesting question, too, because I think what sits behind that in some ways is the idea that you're kind of going to reach a point, or students might reach a point, where they're “ready” for word problems.  Bill: Right. Mike: And I think what we're really saying is it's actually through engaging with word problems that you build your proficiency, your skillset that actually allows you to become a stronger mathematician. Bill: Mm-hmm. Right. Exactly. And it's a daily practice, right? It's not something that you just hold off to the end of the unit, and then you have the word problems, but it's part of the process of learning. And thinking about how you integrate and support that. That's the key question that I really wrestle with. Not trivial, but I think that's the key and the most important part of this. Mike: Well, I think that's actually a really good segue because I wanted to shift and talk about some of the concrete or productive ways that educators can support multilingual learners. And in preparing for this conversation, one of the things that I've heard you stress is this notion of a consistent context. So, can you just talk a little bit more about what you mean by that and how educators can use that when they're looking at their lessons or when they're writing lessons or looking at the curriculum that they're using? Bill: Absolutely. So, in our past work, we engaged in some cycles of design research with teachers looking at their mathematics curriculum and opportunities to engage multilingual learners in communication and reasoning in the classroom. And one of the surprising things that we found—just by looking at a couple of standard textbooks—was a surprising number of contexts were introduced that are all related to the same concept. So, the concept would be something like rate of change or ratio, and then the contexts, there would be a half dozen of them in the same section of the book. Now, this was, I should say, at a secondary level, so not quite where most of the Bridges work is happening. But I think it's an interesting lesson for us that we took away from this. Actually, at the elementary level, Kathryn Chval has made the same observation.  What we realized was that contexts are not good or bad by themselves. In fact, they can be highly supportive of student reasoning or they can get in the way. And it's how they are used and introduced. And so, the other way we thought about this was: When you introduce a context, you want to make sure that that context is one that you give sufficient time for the students to understand and to engage with; that is relatable, that everyone has access to it; not something that's just completely unrelated to students' experiences. And then you can really leverage that relatable, understandable context for multiple problems and iterations and opportunities to go deeper and deeper.  To give a concrete example of that, when we were looking at this ratio and rate of change, we went all the way back to one of the fundamental contexts that's been studied for a long time, which is motion and speed and distance and time. And that seemed like a really important topic because we know that that starts all the way back in elementary school and continues through college-level physics and beyond. So, it was a rich context. It was also something that was accessible in the sense that we could do things like act out story problems or reenact a race that's described in a story problem. And so, the students themselves had access to the context in a deep way.  And then, last, that context was one that we could come back to again and again, so we could do variations [of] that context on that story. And I think there's lots of examples of materials out there that start off with a core context and build it out. I'm thinking of some of the Bridges materials, even on the counting and the multiplication. I think there's stories of the insects and their legs and wings and counting and multiplying. And that's a really nice example of—it's accessible, you can go find insects almost anywhere you are. Kids like it. [Laughs] They enjoy thinking about insects and other icky, creepy-crawly things. And then you can take that and run with it in lots of different ways, right? Counting, multiplication, division ratio, and so on. Mike: This last bit of our conversation has me thinking about what it might look like to plan a lesson for a class or a group of multilingual learners. And I know that it's important that I think about mathematical demands as well as the language demands of a given task. Can you unpack why it's important to set math and language development learning goals for a task, or a set of tasks, and what are the opportunities that come along with that, if I'm thinking about both of those things during my planning? Bill: Yeah, that's a great question. And I want to mark the shift, right? We've gone from thinking about the demands to thinking about the goals, and where we're going to go next.  And so, when I think about integrating mathematical goals—mathematical learning goals and language learning goals—I often go back to these ideas that we call the practices, or these standards that are about how you engage in mathematics. And then I think about linking those back to the content itself. And so, there's kind of a two-piece element to that. And so, when we're setting our goals and lesson planning, at least here in the great state of California, sometimes we'll have these templates that have, “What standard are you addressing?,” [Laughs] “What language standard are you addressing?,” “What ELD standard are you addressing?,” “What SEL standard are you addressing?” And I've seen sometimes teachers approach that as a checkbox, right? Tick, tick, tick, tick, tick. But I see that as a missed opportunity—if you just look at this like you're plugging things in—because as we started with talking about how learning mathematics is deeply social and integrated with language, that we can integrate the mathematical goals and the language goals in a lesson. And I think really good materials should be suggesting that to the teacher. You shouldn't be doing this yourself every day from scratch. But I think really high-quality materials will say, “Here's the mathematical goal, and here's an associated language goal,” whether it's productive or receptive functions of language. “And here's how the language goal connects the mathematical goal.”  Now, just to get really concrete, if we're talking about an example of reasoning with ratios—so I was going back to that—then it might be generalized, the relationship between distance and time. And that the ratio of distance and time gives you this quantity called speed, and that different combinations of distance and time can lead to the same speed. And so, explain and justify and show using words, pictures, diagrams. So, that would be a language goal, but it's also very much a mathematical goal.  And I guess I see the mathematical content, the practices, and the language really braided together in these goals. And that I think is the ideal, and at least from our work, has been most powerful and productive for students. Mike: This is off script, but I'm going to ask it, and you can pass if you want to.  Bill: Mm-hmm. Mike: I wonder if you could just share a little bit about what the impact of those [kinds] of practices that you described [have been]—have you seen what that impact looks like? Either for an educator who has made the step and is doing that integration or for students who are in a classroom where an educator is purposely thinking about that level of integration? Bill: Yeah, I can talk a little bit about that. In our research, we have tried to measure the effects of some of these efforts. It is a difficult thing to measure because it's not just a simple true-false test question type of thing that you can give a multiple-choice test for.  But one of the ways that we've looked for the impact [of] these types of intentional designs is by looking at patterns of student participation in classroom discussions and seeing who is accessing the floor of the discussion and how. And then looking at other results, like giving an assessment, but deeper than looking at the outcome, the binary correct versus incorrect. Also looking at the quality of the explanation that's provided. So, how [do] you justify an answer? Does the student provide a deeper or a more mathematically complete explanation?  That is an area where I think more investigation is needed, and it's also very hard to vary systematically. So, from a research perspective—you may not want to put this into the final version [laughs]—but from a research perspective, it's very hard to fix and isolate these things because they are integrated. Mike: Yeah. Yeah. Bill: Because language and mathematics are so deeply integrated that trying to fix everything and do this—“What caused this water to taste like water? Was it the hydrogen or the oxygen?”—well, [laughs] you can't really pull those apart, right? The water molecule is hydrogen and oxygen together. Mike: I think that's a lovely analogy for what we were talking about with mathematical goals and language goals. That, I think, is really a helpful way to think about the extent to which they're intertwined with one another. Bill: Yeah, I need to give full credit to Vygotsky, I think, who said that. Mike: You're— Bill: Something. Might be Vygotsky. I'll need to check my notes. Mike: I think you're in good company if you're quoting Vygotsky.  Before we close, I'd love to just ask you a bit about resources. I say this often on the podcast. We have 20 to 25 minutes to dig deeply into an idea, and I know people who are listening often think about, “Where do I go from here?” Are there any particular resources that you would suggest for someone who wanted to continue learning about what it is to support multilingual learners in a math classroom? Bill: Sure. Happy to share that.  So, I think on the individual and collective level—so, say, a group of teachers—there's a beautiful book by Kathryn Chval and her colleagues [Teaching Math to Multilingual Learners, Grades K–8] about supporting multilingual learners and mathematics. And I really see that as a valuable resource. I've used that in reading groups with teachers and used that in book studies, and it's been very productive and powerful for us. Beyond that, of course, I think the NCTM [National Council of Teachers of Mathematics] provides a number of really useful resources. And there are articles, for example, in the [NCTM journal] Mathematics Teacher: Learning and Teaching PK– 12 that could make for a really wonderful study or opportunity to engage more deeply.  And then I would say on a broader perspective, I've worked with organizations like the English Learners Success Forum and others. We've done some case studies and little classroom studies that are accessible on my website [SDSU-ELSF Video Cases for Professional Development], so you can go to that. But there's also from that organization some really valuable insights, if you're looking at adopting new materials or evaluating things, that gives you a principled set of guidelines to follow. And I think that's really helpful for educators because we don't have to do this all on our own. This is not a “reinvent the wheel at every single site” kind of situation. And so, I always encourage people to look for those resources.  And of course, I will say that the MLC materials, the Bridges in Mathematics [curriculum], I think have been really beautifully designed with a lot of these principles right behind them. So, for example, if you look through the Teachers Guides on the Bridges in Mathematics [BES login required], those integrated math and language and practice goals are a part of the design. Mike: Well, I think that's a great place to stop. Thank you so much for joining us, Bill. This has been insightful, and it's really been a pleasure talking with you. Bill: Oh, well, thank you. I appreciate it. Mike: And that's a wrap for Season 3 of Rounding Up. I want to thank all of our guests and the MLC staff who make these podcasts possible, as well as all of our listeners for tuning in. Have a great summer, and we'll be back in September for Season 4.  This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2025 The Math Learning Center | www.mathlearningcenter.org  

Learning to teach math teachers better with Dr. Gina Wilson, Knowles Teacher Initiative Program Officer of Teacher Development and Dr. Ayanna Perry, Director of Outreach and Dissemination, as we discuss supporting early career mathematics teachers and the professional development of teachers outside of higher education. Links from the episode Knowles Teacher Initiative (https://knowlesteachers.org/) Knowles Teaching Fellowship (https://knowlesteachers.org/teaching-fellowship) Knowles Academy (https://knowlesteachers.org/professional-learning) Knowles Annual Conference (https://knowlesteachers.org/annual-conference) Five to Thrive Series from Corwin (https://www.corwin.com/landing-pages/five-to-thrive-series?srsltid=AfmBOooIErSKqgBQnpGPBSfApHlKXHdCVHQTzCibmd8OdhLstekAxbi1) The Art of Coaching: Effective Strategies for School Transformation (https://www.google.com/books/edition/The_Art_of_Coaching/m_kZ7eO2q9UC?hl=en&gbpv=0) Mathematics Teacher Education Partnership (https://linktr.ee/mtep2.0) Special Guests: Ayanna Perry and Gina Wilson.

Dr. Theresa Bullard delves into the history of the split between physics and metaphysics, exploring its implications for our understanding of reality. She examines the laws of science that limit our perceptions and discusses her transformative shift from classical to quantum physics. She explains the mathematics of the universe, the 7 steps of the alchemical process, and how to embrace a quantum mindset. Try MUDWTR & Get Up to 43% off + a free frother:https://mudwtr.com/knowthyselfAndrés Book Recs: https://www.knowthyself.one/books___________0:00 Intro2:07 History of the Split between Physics & Metaphysics 7:32 Laws of Science that Limit Us10:54 Her Shift from Classical to Quantum Physics 17:00 The Implicate Order (New Science)27:00 Mathematics of the Universe31:41 (Mindset) Transcend Limitation, Embrace Quantum Possibility38:35 Embracing the Uncertainty of Life44:27 Ad: Mudwtr Save 43%46:05 How New Age Spirituality Mis-uses Quantum Terms56:53 The Science of Alchemy1:01:56 7 Steps of Alchemy (Personal Transformation) 1:17:28 Honoring Your Past While Moving Forward1:23:08 Our Inner Alchemical Process1:26:16 The Transformations that Shaped Her Life1:29:17 How Our DNA Evolves as we Awaken1:36:33 Science of Extra Sensory Perceptions1:46:36 Creating Coherence in Body, Mind & Soul1:51:29 Entrainment: Take Your Future Into Your Hands1:58:39 Practices to Becoming an Alchemist 2:05:12 Activate Your Divine Potential2:12:00 Conclusion ___________Episode Resources: https://theresabullard.comhttps://modernmysteryschoolint.com www.quantumlearningacademy.co https://www.instagram.com/andreduqum/https://www.instagram.com/knowthyself/https://www.youtube.com/@knowthyselfpodcasthttps://www.knowthyself.oneListen to the show:Spotify: https://spoti.fi/4bZMq9lApple: https://apple.co/4iATICX

Producer and long time Wu Tang Clan DJ Mathematics breaks down the creative process behind his new album Black Samson, the Bastard Swordsman. We also dive into why ranking hip hop whether playlists or all-time lists is so tough, with too many angles and no clear rules.Follow The Show:PatreonDiscordYoutubeInstagramX(Twitter)Follow Cipha Sounds:InstagramX(Twitter)TikTokFollow Rosenberg:InstagramX(Twitter)TIkTokThis podcast is sponsored by Monster Energy and Monster Music. Hosted on Acast. See acast.com/privacy for more information.

Episode: 3040 Leonardo and Borelli.  Today, two hemispheres come together.

Episode: 2579 Music and Mathematics.  Today, UH Math Professor Krešo Josić talks about music and mathematics.