AfterMath | Our Minds Are Connected According To Math
ฝัง
- เผยแพร่เมื่อ 7 ก.พ. 2025
- This is the pilot episode of Edward Frenkel’s new TH-cam show/podcast “AfterMath” which will explore revolutionary ideas in mathematics, quantum physics, philosophy, and Jungian psychology, as well as interconnections between these subjects. In this episode, Edward explains in simple and accessible terms - based on mathematics! - that our minds are connected to each other at a much deeper level than is ordinarily understood.
Edward Frenkel is a professor of mathematics at UC Berkeley, member of the American Academy of Arts and Sciences, winner of the Hermann Weyl Prize and the Euler Book Prize, and author of the international bestseller “Love and Math” which has been published in 19 languages.
Listen on Spotify! tinyurl.com/sp...
Coming soon to all other audio steaming platforms!
LINKS:
• Edward Frenkel's Official Website: edwardfrenkel.com
• Edward Frenkel's X/Twitter: x.com/edfrenkel
• Edward Frenkel's LinkedIn / edfrenkel
• Edward Frenkel's Instagram: / edfrenkel
• Edward Frenkel's Facebook: / edfrenkel
• Edward Frenkel’s SoundCloud (DJ Moonstein): / moonstein
Edward Frenkel’s book “Love and Math”: amzn.to/4evbBkS
Erwin Schrödinger's book "Mind and Matter" appears as part of the collection "What is Life?": www.amazon.com...
Lex Fridman's interview of Vladimir Vapnik: • Vladimir Vapnik: Stati...
A good introduction to Jungian psychology (with chapters by Carl Jung and Marie-Louise von Franz) is the book "Man and His Symbols": www.amazon.com...
A good introduction to Euclidean geometry is the book "The King of Infinite Space: Euclid and His Elements" by David Berlinski: www.amazon.com...
Stanley Kubrick's film "2001: A Space Odyssey": www.amazon.com...
On the observable Universe: www.britannica...
For all business inquiries please contact frenkelmath@gmail.com or mike@omegamedia.io
© 2024 by Edward Frenkel
#science #math #mathematics #quantumphysics #philosophy #psychology #podcast
Your feedback will be very much appreciated, and it will make this podcast so much more interactive. The future starts with questions we never had a chance to ask.
Your book just changed my life. Thanks for everything! 💗
I liked the sections where you illustrated the concepts on your iPad! Brings it even more to life!
I am going to Get your book love and math
Interesting! Include fractals (and maybe even knots) into discussion and you earn my subscription. Beauty of fractals is we can have infinite amount of information inside finite volume. Then, for example, fractals to (mathematics of) turbulence. (Beauty of knots is quantisation of continuum mechanics...)
Welcome to the revolution, friend!
The older I get, the more I feel an insatiable hunger for these kind of presentations about the fundamental aspects of human consciousness and it's convergence with the hard sciences. Thank you!
Thanks!
@edfrenkel Edward said this in his book: "Without mathematics there can be no freedom."
I have pointed out the following in response:
A. The entire world financial system is based on math. Is humanity a slave to money?
B. Math has produced the internet, the screen, and everything that is played on the screen. Is humanity helplessly addicted to the screen?
C. Every wall, chain, lock, prison, fence, has math at its core.
Therefore, WHERE THERE IS ENSLAVEMENT THERE IS MATHEMATICS.
Has he rescinded that comment? No. Has he responded at all to me? No.
Edward Frenkel is a delusional coward, as is Curt Jaimungal
Thank you so very much Prof Frenkel. I have always wished I could “speak” maths; I feel like the most mathematically illiterate person I know, and yet if I had half the intelligence those around me do, I would be going through book after book on the subject. I believe maths is the key to unifying all our seperate perceived ways of seeing and understanding our reality and how we have constructed it in our minds. I watched you on Curt Jaimungal’s channel and I was instantly drawn to your passion, your warmth and what you had to share. What you said and what other mathematicians have said about understanding maths, being like having another sense? I’ve always felt that about those mathematically inclined; always wondered just how they “see” “reality”compared to how most of us see it… and very sure that mathematicians see a whole other level/dimension/aspect of reality that we just can’t wrap our minds around, unless we are that way inclined. But this video gave me the distinct sensation that actually, we’re all doing it, we just don’t realise it until someone like yourself points it out so blatantly. You may never read this, but if all minds are connected, then on some level you have anyway :) I feel incredibly privileged and deeply appreciative that you are here, sharing your insights, knowledge and years of experience with us all.
Thank you! 🙏🏻😍
The Return of the Goat
Teach us the way, Aragorn
Curt I’m sure you are some inspiration here!!!
yalls conversations together is among my favorite I've ever seen. Beyond appreciative of the both of you
Edward Frenkel is great guest on your channel theorizes of everything
Fancy seeing you here Curt. Love your work, thank you for the hours of inspiration!!
"Mathematics creates a bridge between physical reality and our minds" is probably one of the best ways I've ever heard mathematics defined.
Though, this is a proposition. ;)
This is a flashy phrase that impressed you because you dont know what mathematics actualy is
This is a great definition. Set Theory especially.
It certain explains math tapping into the logical right hemisphere of the brain
@@СергейИванов-ы1п8э Aw shut up. Take a nap.
Professor @edfrenkel, a small token of my appreciation for taking the world on your epic journey towards unus mundus and the grand Unification of mathematics and physics.
Eagerly awaiting your insights on spacetime emergence and Professor Nima's amplitudehedron, combinatorics & surfaceology.
Looking fwd to continuing our 2020 chat..
Eli
Thanks!
Dr. Frenkel, I was once told under a very unusual circumstance by an architect that if he could do it all over again he would have become a mathematician. Looks like I have 2 books to purchase, a podcast to listen to, and a lot of thinking to do… Your spirit and ideas are a blessing to have stumbled upon
Thanks! 🙏🏻
Everyone is / was invited to mathematics (school). It will receive you all with open arms at any age. The only obstacle is the ego and its hounds, your demons. They must be defeated along the way, even for us mathematicians.
I don't know this host, but I liked him instantly. He has a gentle passion for an immense subject that he wants to share with the widest possible audience. Respect.
Edward Frenkel is unfailingly engaging and probably the perfect communicator for these ideas. I don’t know about you but I subscribed immediately (which I almost never do).
I find myself not really listening to the words, almost as if this beautiful soul is speaking a language I don’t understand, and yet I am left feeling somehow truly happy just feeling the enthusiasm and joy being expressed here. Thank you fellow travellers for sharing this journey. It may sound trite but I love you 🙏🏼🤗🌈🐝
OMG I am cannot believe we are able listen to these fascinating people, this is so beautiful, I love you all
Love you back.
One of my favorite Einsteinian quotes from Walter Russell goes something like, "Gravity is time's conversion of the simultaneous into the sequential." If one views simultaneity in the context of symmetry-breaking, then the origin of mass in the weak bosons (Z, W, Higgs) can be tied to prime reciprocal's "Midy Property" that serves to discretize the positive and negative frequency amplitudes that Penrose was just talking about on Kurt Jaimungal's show, claiming it as the most important aspect of quantum theory he learned from Engelbert Schuking in 1962.
Mathematical entities are the only truly objective abstractions. That’s how I define mathematics, but I never realized this would mean they are, in a way, the only 'things' that genuinely connect our minds. It’s great to have you back on TH-cam, Professor Frenkel. Greetings from Nuevo Leon, Mexico.
Considering:
...values, truths and faiths.... coming forth and going forward.
Hi Dear Edward,
Thanks So Much, for Your Amazing Work & Benefiting So Many People!
I’m Not Educated academically, Born X-Gen, I Totally Understand Your Teachings & I’m Extremely Grateful for you Posting on YT.
Math & Physics really does help one understand the Emptiness of Phenomena, Impermanence & Selflessness of the I.
William James Is someone to Study too.
It would be awesome If you could Chat with B. Alan Wallace who Lives In Santa Barbra.
You & Alan Would’ve amazing Convo’s about everything you both teach for benefit of the world.
Thanks Again Edward 🙏💞
Look Forward To you next Vid.
Big Love from 🇦🇺
Thank you! 🙏🏻😍 I'm a big fan of William James, and I have also seen lectures by Alan Wallace -- it's good idea to record a conversation with him. Thanks!
How fortunate are we to be gifted with the generosity of such a titan who is sharing such precious knowledge, normally available only in the most privileged classrooms of highly respected universities, where one has to pay big bucks to access it... Thank you for gifting us Peofessor ! ❤
Man, where have you been? How did i not find such a brilliant man earlier in my life. You have a gift. Your introduction about the topics being discussed, were BANG ON the same ones I am passionate about!
Wow, I've spent so long with compartmentalised interests, without fully comprehending their connectivity.
Thank you!
@edfrenkel Edward said this in his book: "Without mathematics there can be no freedom."
I have pointed out the following in response:
A. The entire world financial system is based on math. Is humanity a slave to money?
B. Math has produced the internet, the screen, and everything that is played on the screen. Is humanity helplessly addicted to the screen?
C. Every wall, chain, lock, prison, fence, has math at its core.
Therefore, WHERE THERE IS ENSLAVEMENT THERE IS MATHEMATICS.
Has he rescinded that comment? No. Has he responded at all to me? No.
Edward Frenkel is a delusional coward, as is Curt Jaimungal
@@Nonconceptuality😮 wow!
The binary bits of 1 and 0 traversing our cyberdigitalvirtuality are also encoding the credits and debits of our financial accountancy.
This is only a subset of what mathematics is beginning to offer up....
Your passion for exploring the intersection is truly a breath of fresh air, professor. So many stale and stuffy comments that seem so certain and closed-minded. There is a mysterium that the mystics have known all along.. that which the hard sciences can only fathom. The level of omniscience and omnipotence is usually not granted to those who refuse to expand their limited thinking. Wisdom is found in kaleidoscopic fusions where the superconscious highway of the cosmic mind and heart intersect in profound and often mysterious ways. If you know, you know. Thank you for embarking on this delightful expedition in traversing the journey towards the (third) transcendant function - which Jungians know of very well.
Thank you!
The paradigm is shifting in front of our ‘I’s and Prof. Frenkel is at the forefront of this imminent change among other contemporary geniuses and deeply humans. He has the unique ability to talk about complex subjects using language that everybody can relate to and understand. I am eager to hear about source of creativity in the next episodes but I am sure it’s been planned anyway ❤🙏
iThink (TM) he should interview Ken Wilber and Max Tegmark....😎
I mentioned on X that I am a C student in math, had to take college algebra 2x, had to change my major because there was no way, at the time, I could get thru calculus. Yet, I had a greeat career on Wall Street, suddenly when the $ sign was in front of numbers, the numbers made more sense. My dad was a Mechanical Engineer, so it was frustrating for me and probably for my dad. I've always had an interest in astronomy and the unexplained in our atmosphere and space. Despite a constant struggle in math from grade school to college, I have a deep fascination with math that I can't explain. Maybe a right brain/left brain thing. I am all in with AfterMath !
Ahh amazingg!!! Im sooo excited and ready for some INTENSEE math and physics!!! All the best Ed! :)
Thanks!
Hi Edward, thank you very much for this podcast and please keep it going, I found it very inspring.
I would like to particularly thank you as you have the particular characteristics of making me smile everytime I see you speak as I am inundated with a particularly healthy light.
A question for you and everyone else: What is your favorite question?
I start! I find my self alternating between, basically what you discussed, "why does mathematics works so well for our physical world" and "why I find hard to accept the love of the people around me"
As a fellow mathematician you are to me a treasure beyond words.Thank you Professor Frenkel.
You are one of my maths heroes, Edward! i read your book while studying Theoretic Physics at University of Birmingham, 2011-2015 and it changed me!
Incredible presentation. Filled with love of wisdom! Your accent and handwriting are wonderful also. Keep it coming friend!
Thank you!
Prof. Edward Frenkel ,
You are one my most favorite mathematicians,( essentially , all Number Theorists are my favorite mathematicians,because of obvious nature of Number Theory, but it doesn’t mean that I don’t have inclination towards other branches of math , rather all branches of math & physics are the ones I live for )
By the way , I love your book
“”Love & Math_ the heart of hidden reality “”…!
Secondly,
in one of the podcasts with Curt Jaimungal ( TOE)
u spoke about,
quotes extracted from
Hindu sacred scripture , ie
“The Bhagwad Gita” , which made me to follow u consistently…on every social media…
U are a mathematician of highest class, because you appreciate something which is not from current modern Math, u are a mathematician of S.Ramanujan type …
ie Not only rigorous is important but intuition is far far superior in mathematics…& intuition can come from anywhere.. mathematics, philosophy or even from sacred scriptures..!
Bhagwad Gita itself, is a practical sacred book in Hinduism…!
Please make more videos to connect maximum branches of mathematics…
Thanking you…
With regards,
Thank you!
@@edfrenkel
Considering:
an unfoldment of ...impulse, instinct, intelligence, and intuitiveness.... with integrally greater ...insights and illuminations....
It is nice to know that there are others that see what I see. Unity in reality beautiful!
Considering:
Transformative Mathematical Communities of integrally greater ...Sense, Science, and Salience.... coming forth and going forward.
Thank you Professor Frenkel for starting this podcast. I have read your "Love and Math" and heard you on all your appearances in Theories of everything ". The excitement you bring to the topic is infectious.
As a mathematician (albeit of a modest standing) I fully resonate with the idea that there is a mental realm beyond the physical reality where mathematical objects reside. We access it when we think that we have introduced a new mathematical object or prove a new theorem.
There is an interesting discussion in the great Hindu philosophical treatise Upanishad on who we really are. We clearly not our body nor our mind because the body changes drastically and our mentor state also changes during a lifetime, yet our sense of self endures. The final conclusion is that at the deepest level of reality we are all one: the source or god consciousness. Various medical studies now show that near death experiences are a reality. Too many people report vivid details of their experiences in a higher realm at a time when their heart flatlined and brains shut down. I think establishment science, in its bigotry of materialism and reductionism has missed out on multiple layers of reality inaccessible to the five senses. Materialism is really incompatible with the findings of Quantum Mechanics. Your thoughts sir?
I agree with you that materialism is incompatible with modern science. And I've also been influenced by the Upanishads (and other sacred tests of the Eastern tradition). As was Erwin Schrödinger, by the way. Thanks for your comment!
@@edfrenkel
What integrally greater ...sense, science, and salience.... may come as our technological know how and technologically interconnecting advance ventures further into what we deem is ...true, truth and more truthful.... coming forth and going forward?
You're among the mathematicians who inspire me to keep going. I've gotten as far as the basic idea of homology and a few simple applications from linear algebra, and it's an eye-opener. I may not have enough years left to go much farther, but at least this helps me understand whence your joy in this work originates. Your Math 53 lectures (delivered as you said "to a worldwide audience") were a real launching pad for me. So, thank you!
🙏🏻❤
@edfrenkel Edward said this in his book: "Without mathematics there can be no freedom."
I have pointed out the following in response:
A. The entire world financial system is based on math. Is humanity a slave to money?
B. Math has produced the internet, the screen, and everything that is played on the screen. Is humanity helplessly addicted to the screen?
C. Every wall, chain, lock, prison, fence, has math at its core.
Therefore, WHERE THERE IS ENSLAVEMENT THERE IS MATHEMATICS.
Has he rescinded that comment? No. Has he responded at all to me? No.
Edward Frenkel is a delusional coward, as is Curt Jaimungal
@@Nonconceptuality
Why do you seem to be trolling?
Are you attempting to describe some mathematical sorcery or mathematical sorcery itself?
@Michael-nt1me I'm not trolling, I'm telling the truth and Edward is avoiding it
@
As far as i can tell from your limited texting you are trolling your truth and/or 'a truth' without any apparent sense of truthfulness coming forth and going forward 🤦♂️
I am merely a layman, but I have been interested these issues for a lifetime. Every time I see you contributing to some other TH-cam I find your insights and enthusiasm stimulating. Your new channel is an immediate follow from me.
Thank you!
Loved it and looking forward to next episodes. Schrödinger puts it beautifully when he says "Conscience is a singular of which the plural is unknown... What if plurality is only a series of the different aspects of one single thing?"
Thank you!
This is my new favourite podcast. I will be sharing this with anyone I think who would be interested.
Feedback: keep this podcast exactly as it is! I love that it felt like I was having a personal conversation with you rather than watching something highly edited with cool graphics.
Also, a big thank you, Edward. I’ve been investigating the nature of mind for a while through personal experience, and Zen practice, but I was raised as a materialist and am now open to considering that it is false. However, having an intelligent person like yours, and others, bring the subject of a non-personal consciousness to light, gives real power behind this, even to my own biases in my mind. I am very much looking forward to your future podcasts!
Thank you very much!
"[Mathematics] is this vast reservoir of timeless, persistent, objective knowledge, which is accessible to all of us." I like that statement a lot.
As a math teacher i accept your provocation that our minds are all connected but i must push back a bit. It's easy while studying math at a high level to be surrounded by people who have a high enough knowledge of math tu understand "infinite line" or "a line with no width" but not everyone is able to. Some people need the phisical object to understand the mathematical concept, i have students who cannot understand negative numbers until i talk about debt, and then they carry this "negative numbers are debt" into their lives without seeing the bigger picture. Maybe i am just a bad teacher, but i truly believe that some people are uncapable of (or unwilling to) truly think in abstract.
P.s.
I don't know if you will read this but your book love and math is what inspired me to pursue when i was only 16 years old, so thank you from the bottom of my heart
Everyone thinks in the abstract all the time. No one could possibly think in physical-material terms, since no one has a clue what physical substrate there is to reality, only that there is something. The only obstacle to a mathematical understanding is a grasp of the basic concepts. As your example shows, the negative numbers require some sort of abstraction about "deficit". Once that is understood, the analogy to numbers becomes natural. But the students had that understanding already latent, or they would never have understood the abstract concept of deficit in the first place.
Other examples: everyone understands "love" (and the feeling of absence of love). Even though no one knows where that understanding comes from, nor what "true love" really means. Everyone understands kindness and honesty, with similar qualifying remarks about the incomprehensibility of associated notions.
Thank you!
@@Achrononmaster That's a good point!
"Negative numbers" remain very problematic in many ways, and part of the general still unresolved foundational crisis of mathematics. Maybe they could be best seen as a special, contextually defined case of the general phenomenonon of inverse relation, which has also other unresolved problems.
My own experience of intuiting the meaning of Euclid's first definitions suggests that mathematical intuition requires also some ability of self-transformation, e.g. to transfrom your perspective to that of an flat-lander.
Plato was, however, very optimistic in this regard. His classic example of 'anamnesis''is a teacher giving instructions for an uneducated servant to intuite a theorem based on geometric relation. To visualize purely intuitively without any aid from external sense representations is very hard for most, and according to Proclus mathematics is an intermediary science, dianoia and dialectic between holistic Nous and external sense representations/projections.
@@santerisatama5409
Imagine:
...Ashen, Black, White, Color and Clear.... Numbers coming forth and going forward.
This was amazing to learn! Thank you so much👏👏!
I was reading Kant’s Prolegomena so I couldn’t help thinking of him while listening to your ideas. Kant says that in pure math and pure reason we use concepts a priori, ideas that make possible our understanding of material and abstract thoughts but these concepts aren’t themselves subject to our analysis, they are like axiomatic principles. Though we can always enlarge our conceptual modelling of nature, it remains out of our reach. There are limits to our understanding but we keep reaching for completeness, the Absolute (which makes me think of Gödel theorems).
Congratulations for the video and channel.
Considering
an open and ongoing, integrally developing, and conscientiously advancing ...sense, reason, and imagination.... coming forth and going forward.
The idea of connectivity is captivating! I'm delighted you're bringing these thoughts to life through a podcast, can't wait to listen to more!
Thank you!🙏🏻😍
You're welcome! 😊 @@edfrenkel
he's bringing these thoughts to life directly through our minds! didn't you listen to his theory?! 😉
Some people think the world is prickles.
Some people think the world is goo.
But in reality, when you really dig down deep, it's gooey prickles and prickly goo.
To paraphrase Alan Watts....
Such a fascinating topic, but I'm a physicist turned artist, so I've always been interested in this intersection of science, math, and consciousness.
I love thinking about how everything is connected, even from a purely physical perspective.
There are no such things as things.
In fact, we might be better off to describe nature using only verbs, as everything is pattern in process.
And it's all part of some larger infinite happening that we can never really grasp entirely.
In some sense, we are all part of this infinity, whatever it happens to be.
Looking forward to this podcast!
Another one you might enjoy watching/listening to is called INFINITE NOW.
It's right up the same alley and it's wonderfully produced
In 2013 I was privileged with the chance to start a career in accelerator physics. I found inspiration in your book and interviews in Numberphile. Thanks for everything you do! 🖤
Happy to hear this!
Can't wait for the next EP. Would love to hear your thoughts on Buddhist philosophy and mathematics.
Finally! I was missing new content from you!! Thanks!! Amazing program. Excited for the next episodes
Thank you!
@edfrenkel Edward said this in his book: "Without mathematics there can be no freedom."
I have pointed out the following in response:
A. The entire world financial system is based on math. Is humanity a slave to money?
B. Math has produced the internet, the screen, and everything that is played on the screen. Is humanity helplessly addicted to the screen?
C. Every wall, chain, lock, prison, fence, has math at its core.
Therefore, WHERE THERE IS ENSLAVEMENT THERE IS MATHEMATICS.
Has he rescinded that comment? No. Has he responded at all to me? No.
Edward Frenkel is a delusional coward, as is Curt Jaimungal
I don’t know much about math, but I enjoy learning about it from someone who does. I will have to listen to this podcast again. 💖
В моей библиотеке есть книга из детства занимательная алгебра. Я хотела решить там все задачки но споткнулась с самого начала. Но очень хотела. Я обожала математику, числа по модулю и прогрессии…Слушала вас с таким вдохновением, а когда подкаст закончился слезы потекли из глаз. Расчувствовалась.
Вашим роликом поделилась. 👍🏻
Спасибо!
Love and Math was a really good book. The history and introduction to the Langland's Program was very interesting. If they clone Professor Frenkel, and install clones in every high school, math literacy would jump tremendously. Watch him talk about the Riemann Hypothesis on Numberphile. His love of math is infectious.
Thank you Edward! You are a gifted teacher not just mathematician. What a blessing to learn from you for free without the crumbling structure of academia in between us.
🙏🏽❤️🙏🏽❤️
Thank you! 🙏🏻❤
Your enthusiasm is contagious! Dying to watch the next episode
don't
This is the pilot episode and this is now 2 month ago. When is the next episode due? This is really great and I look forward to the rest of them. Thanks
Thank you! Working on Episode 2 and hope to release it later this month. And there will be more, you can be sure of that!
Large parts of our structure are common with all humans. Given that our brains and nervous systems contain the abstract structures that give rise to mathematics, it is not surprising that we understand each other when discussing abstract mathematical concepts.
...brain, mind and psi....
Professor Frenkel it's nice to see the use of social media in a positive way. To share knowledge. And that is done with bravado and passion. It triggered me and left me puzzled.
This pod cast got me reading “Love and Math.”
If math is somewhere in a platonic reality (PR), outside of observed reality (OR) (space and time).
Then all letters and symbols in the book L&M are a representation/ interpretation in the OR of the PR.
In the OR we do not find the idealized shapes/constructs of the PR. We find approximations of these shapes.
Isn't this necessary for us to have a (self)conscious experience?
Is the PR a static construct?
a²+b²=c² didn't change since it was discovered/ revealed.
So is time possibly not present in the PR?
We need time in the OR to observe different states of a system. We also need finite to make an observation in OR. If we should observe an infinite line in OR it would take forever....
I still have lots of questions.
But to summarize: it left me puzzled.
Thank you very much for sharing your knowledge.
Great first episode! 👏Carl G. Jung believed that novel archetypes emerge over time, and listening to your conclusion at the very end of the video, it made me wonder if the latest discovered Mersenne prime number (the 52nd in that order) qualifies as such. Thank you for the great insights. 🙏 Looking forward to the next episode.
Thank you! That's a good point.
Professor Frenkel, I am so excited for this podcast! I would love to hear your thoughts and philosophy regarding Gödel's Incompleteness theorems. How do you reconcile using axiomatic systems as a fundamental basis for mathematics? Also, since quantum physics will be a topic, I'd be interested in if you have any interest in complexity theory and how Quantum Computing may change our understanding of "hard" problems like optimization. Thank you.
Thank you! Yes, I am definitely planning to talk about the Gödel's Incompleteness theorems - fairly soon. Quantum Computing is not an area of my expertise, but I am fascinated with this topic, so perhaps it will make an appearance at a later point.
Current views of Quantum Computing (QC) are mostly based on statistical mechanics and thus semiclassical instead of genuine Quantum Computing, as e.g. done by photosynthesis. Yup, trees etc. are far more mathematically advanced than academic mathematics at least in some areas. :)
In Pure Math approach to QC we can give it a fairly simple general definition: parallel reversible computing.
Thus we can observe that QC is already present in everyday mathematical language, pretty much like water to fish. I mean the everyday use of parenthesis as the most common everyday phenomenon of parallel reversible computing. Dirac was very much on the right track to realizing this simple truth with his Bra-Ket notation.
Very important to note in this context that in the relative order of operations of standard field arithmetics, the brackets are solved first. Then exponents, multiplication and addition (with their inverse operations). The order of operations is thus top-down order, and brackets of QC are at the top of the hyperoperation tower:
TOP:
Brackets
(...)
Pentation
Tetration
Exponantiation
Multiplication
Addition
BOTTOM
Based on the naturally reversible chiral symmetry of Dyck language pairs, we can construct holistic foundations of mathematics from just relational operators < and > in our toolbag of marked characters, starting from constructing genuine "quantum" metric" in the form of an operator language eigenform, from which also number theory can be derived in holistic manner in Stern-Brocot style. I can show how if there is interest.
@@santerisatama5409 you are probably aware of the sublimely simple syntax of the lisp language in its pervasive parentheses.
@@jondor654 Actually not, thanks for the hint. All I know about Lisp is that it's the first functional programming language - after Schönfinkel's combinators and Lambda calc.
In my study of foundations, I've found also the inverse Dyck language very interesting. Meaning, instead of just the symbol pair < >, also the inwards pointing relational operators are very important. Lisp has similar feature?
Dirac was onto something similar with his Bra-Ket notation. .
this dude is my all time fav mathematician/scientist/physicist!
a very ...good, great, and groovy.... podcast 😎 thank you for sharing.
Thanks!
The current state and potential of ...Money, Propaganda, and Visioneering.... resides among the elite ...Oligarchic Blood Lines, Corporatistic Money Lines, and Ascensionalistic Power Lines.... and their versions of ...Family Values, Freedom Values, and Functional Values.... playing out in The World.
An open and ongoing, integrally developing, and conscientiously advancing human ...sense, science, and salience.... from the bottom-up needs an authentic developing 'peer review science' to flourish alongside it.
...as a greater goodness for a greater number across a greater span.... emerges how may it evolve coming forth and going forward?
When I imagine an infinite line I can't really manifest in my mind an infinite object. I merely imagine a line without a specific property (the two ends). I think this is a crucial distinction because everyday we use conceptual objects with a set of properties without imagining the objects in their entirety. From the POV of philosophy of language we share the same imagined line because its entire existence is a set of properties expressed in a few claims. In reality objects are far too complex to be described in their entirety in the same way. For example a mere rock has unbelievably many properties because most of them are the product of it's relation to everything else that exists. Mathematics describes some underlying functions of physics which in turns shapes biology. Our evolutionary success is largely the product of cooperation and intelligence so it make sense for us to share the same genetic predisposition for our brains to form the neuronal structures necessary for mathematical concepts. Regarding the quote about underlying intelligence of the world (or at least many levels of biology which is just complex physics) I strongly suggest the work of Michael Levin. I'm so glad I just discovered your channel!
I'm so excited for this series. I've been a fan since I've seen you on numberphile while I was in undergrad. I'm glad you started on the idea of axioms and Euclidean geometry. I hope you do a similar episode on the godel incompleteness theorem and your interpretation in it's significance
Thank you!
Excellent. I very much look forward to the next installments.
So happy you decided to launch this podcast, specially in times of chaos… really love your passion! would love to hear your thoughts on the idea of our ability, as mental constructs, to change/affect the one mind. Does a real change in consciousness creating also new math ? For example relativity theory- instead of me versus something outside of me, me versus me. Not competition and lack but game of infinite possibilities of creation. Don’t know if I explain myself clear enough 😅.
By the way, i think that sticking to 30 min is the best length for such podcast.
Thank you for your passion and knowledge sharing 🙏
Thank you! I'd like to rephrase your question as follows: What do I identify with: the "construct" with a name and other attributes that is supposedly confined to this body OR the "universal mind"? It seems to me that when we create, when we truly connect, when we love -- we always do it on behalf of the latter. But what if I could also be consciously aware of it? I would think that in this case the potential for impact (and hence for positive change) goes up ten-fold. Do you see what I mean? :)
@ i do. The challenge is how to get there when we are so programmed to the mental construct..so you also imply that there is no need to new math since math represents the one consciousness, it is more our ability to understand it that way? The depth of it? In physics it is more easy for me to understand how it develops and represents new ideas regarding consciousness and creation
Finally! I was looking for a source for this type of channel to connect all these disciplines into one! More of a macro view of everything. Subscribed!
Yes! Waiting for the next episode! I loved math in high school and I miss it!
I loved what you said about us being connected because we can talk about the same math ideas and understand each other. Good luck with your podcast.
Thanks!
Thank you, Professor! Your ability to weave together different subjects offers such a beautifully clear perspective on the world.
Thank you!
I love it! The blend of wonder and logic. Can’t wait for more. Thank you for making me think.
Thank you!
I have been waiting for a podcast like this for the longest time. So excited!!
I would love to hear your thoughts on the philosophical implications of quantum entanglement!
Thank you!🙏🏻😍 Noted (for future episodes).
So far you have shown that our minds may be connected in one particular way: that we can share certain mental constructs of the sort used in geometry. I have been fascinated by the idea of a universal consciousness and I look forward to your discussing other types of mental constructs that you believe can be shared between our minds. Thank you for an excellent first episode!
Thank you for this podcast, I'm a big fan of yours!
I have a few questions:
1. You mention that people can intuitively understand basic Euclidean geometry. However, maybe not all people can do that, for example uneducated people in India. Is it possible that the intuitive knowledge of math is contingent on certain early life education and cultural upbringing? (and not universal)
2. I found it very interesting when you said that straight lines *can* be found in nature - they are just wiggly lines viewed from a distance! Doesn't that invalidate the claim that mathematical objects exist only in our minds?
3. Another thing that seems to cross sensory and cultural boundaries is music. I think most people would agree that melodious music "sounds good". Do you think music is similar to mathematics in transcending worldly experiences?
Keep up your great work!
Thanks for your questions! Answering:
(1) Yes, this could be dormant in some people, or perhaps less developed. In fact, most likely, these people then have some other abilities more developed. There are outliers in every area. In other words, I am not trying to claim we are the same! In fact, we are different. My point is that there is a big enough sample of people who have no problem conjuring up infinite lines, which have zero width and aren't wiggly; so, let's take this as a hint that our minds are connected.
(2) You seem to have misunderstood me. I was saying the opposite: we can NOT find perfectly straight lines in nature. But they do exist in our minds.
(3) Yes and no. I would say that our experience of music is different (even though the capacity to be moved by music is universal, we are all moved by music differently), but our experience of mathematical objects is the same.
@@edfrenkel Thank you so much for your response! I feel privileged to be able to ask you my questions on this topic, as it is very dear to me.
I wholly agree with your response to questions 1 and 3, but I would like to follow up on my 2nd question.
Maybe perfectly straight lines do not *actually* exist in nature upon careful scrutiny, but to the human eye (or to any visual creature), *approximately* straight lines are observable in nature, which are practically indistinguishable from true straight lines. Couldn't these serve as "inspiration" for the concept of true straight lines?
In that case, it could be sensory experience which is the ultimate source of the concept of straight lines, and they would not be a purely mental (a-priori) construct.
I would love to hear your response!
EDIT - just saw your response to @seamuslowe54 which somewhat clarifies your position on the question.
@@726Twister Hi again! The point is that the statements of Euclidean geometry are simply NOT applicable to those wiggly lines. For example, one of the theorems of Euclidean geometry is that two different lines intersect at no more than 1 point (they are either parallel, in which case they do not intersect, or they intersect at one and only one point). But for wiggly lines that is not the case. Indeed: take a line that has one small wiggle. We can then find a straight line that will intersect it at two points (kind of "latching" onto the wiggle). Do you see this? In other words, statements of Euclidean geometry are NOT true for lines that are not perfectly straight. This is a subtle point (no pun intended!) which not usually mentioned when we learn Euclidean geometry, and it might come as a surprise. But if you look closely, you cannot escape the fact that in math we truly study objects that do NOT exist in physical reality. :)
@@edfrenkel Thank you for your response. I agree that straight lines do not exist in physical reality, and also that Euclidean geometry does not apply to wiggly lines. I just meant to say that I think it is possible that the concept of straight lines is derived from sense experience, specifically from seeing approximately straight lines in our environment. As opposed to being an "innate" concept.
@@726Twister I suppose one could say that wiggly lines are so close to the idealized straight lines that perhaps we could have "derived" the concept of an idealized straight line from our observation of wiggly lines in the physical world. Fine. But what about the other aspect of the absract, idealized lines of Euclidean geometry: the fact that they are INFINITE? We can only observe (wiggly) line segments of FINITE length with our 5 senses, right? But a finite line segment does not approximate an infinite line, because no matter how long a finite line segment is, it's still INFINITELY FAR from being an infinite line. And yet, we have no trouble conjuring up infinite lines in our minds, and that fact that we have no difficulty discussing these lines right now shows that we are conjuring up exactly the same lines, even though neither of us has ever seen them in the physical world around us. :) Thanks again for your thoughtful comments!
Впервые услышав в классе геометрии о двух точках и линии ведутщей в бесконечность порозили мое сознание о себе и о мире ! Тот факт, что есть бесконечность , открыл чуство космического маштаба и первое осознание что Любовь это не индивидуальное чуство ,что это Космическое Начало и всегда присутствует,как невидимый воздух ! Может быть Любовь это прямая линия между двух точек? Спасибо любимый Человек за ваши открытия и книгу, которую буду читать с великим чувством Любви к Вам и Бесконечности Сознания !
Спасибо! 🙏🏻❤
@edfrenkel Вам спасибо , Чудесный Человек,за то, что Вы Есть в моем уме и в моем сердце! Моя Любовь будет с Вами Теперь и Вечно в Инфинити,🙏💖🙏
Thats crazy! After reading your book a couple of weeks back, I thought to myself I wish he had a podcast. And there you are!!!
Thank you for "manifesting" it! :)
Well let's Put it this way: The Distance Between An atom And then it Becoming a Whole Cell, can be interpreted in the distance between 0->1, though Each number Is Specifically Defined and It Uniquely differs from The next or the previous State, The Whole Step to Set A full Distinct Image, Is another Fascinating Phenomenal of all these Realities Combined Together!
Wow so happy your doing this podcast. I am a huge fan!! I love math and the other subjects you describe. I have such passion for learning. Books like Cosmos by Carl Sagan, Infinity and the Mind by Rudy Rucker and yours got me hooked on learning!!!!Look forward to seeing every episode. Thank you so much for doing!!!
Thank you!
I love the theme of interconnections. Thank you for doing this!
Thank you!🙏🏻😍
adding another voice to what sheldrake has been shunned for (on TED).
I just opened my iPad and found you. Wow , it is amazing what is going on with this inner quest to know. Questions and questions from childhood to my elder years and your opening words just made me feel in communion with this presentation . I look so forward to aspiring as now i feel we are angels of flight ; OUR WINGED THOUGHTS. These past days i have been asking “ what is the ONE COORDINATING SYSTEM is there ONE in vastness edgeless shapeless where i ponder what really is Direction -where really is UP OR DOWN - EAST OR WEST . Yesterday i bumped into Plato’s description “ the dodecahedron is the solid that the gods used for embroidering the constellations on the whole heaven” we sort of have set up our little systems of our Flighted minds to this IMAGINARY place of CONCEPTUAL EQUIVALENTS : MATH AND PHYSICS AND GEOMETRY our very own COORDINATING SYTEM ! WE are the little measure bumping into the more perfect ! WOW! Isn’t the universe is the ONE COORDINATE - ONE SPIN! I guess it has established the pure measure - i have been asking why 5 steps in ballet- who came up with this basic when our bodies can move in multiplicity of shapes . I am blown away with a mind that reduces THE ALL to a simplex- E = MC squares ! GOD LIKE , no??? Thank you - look so forward to your lectures .
The distinction - the complementary relation e.g. between directions R and L is also their "unity".
The inferences one can make from mathematical axioms, whether geometric or otherwise, is the same general structure that we see in Jungian symbolic theory; given a set of symbols seen in a patient we can generate a range of possible inferential structures, of which we need to see which path the person themselves resonates with.
I truly believe that the mathematical is as Jungian as the Jungian is mathematical, which is to say that the logic of math and of symbol more generally need to be recognised on the same standing.
Very similar indeed, and one could say both are rooted in archetypes. Thanks for your comment!
Thank you 🦋 I love non-euclidean geometry, I'm really looking forward to more!
Thank you for this initiative!
I realized I listened all the episode only once it's finished: I was working on some scripts on data, and the time passes very fast listening to you, in what somebody would call "the zone" 🙂
Being addicted to graph-based representations, I like very much your stile of connecting concepts, I hope we will detout with you, to a deeper knowledge of some of the ideas :-)
Edward this is so important. Your own podcast was definitely missing from TH-cam. I hope you remember my comments when this channel has millions of views because I need to talk to you some day!
Thank you!
Thank you, Edward for doing this. Always a master class in communicating passion with unpretentious passion.
Thank you!
It's great to see you posting a new video after such a long time. You're an excellent speaker! That said, I feel the word "connected" is a bit too strong in this context. Based on your points, it seems like a more accurate conclusion would be something along the lines of "we share some knowledge and thanks to our brain similarities, we can often achieve the same conclusions using that knowledge". It’s similar to having two nearly identical neural networks (structurally similar) but trained separately with different, large datasets of dogs and cats. Running them in parallel will almost always produce the same results when classifying, but they are surely not "connected".
My thoughts exactly: our minds must be connected! :) Joking aside, that's what I was thinking too, only that you came up
with a better way of putting it with your neural network example. There are lots of independent mechanisms giving rise
to very similar results without their being directly connected. If one subscribes to the idea that a brain is "just" a complicated
machine subject to the laws of physics it's not surprising that we can compare experiences and thoughts. It's also not clear to me
that my understanding and views about, say, p-adic numbers really match any others' (let alone professor Frenkel's!). For instance,
I have a tin ear, and I am pretty sure that my "music objects" are just a shadow of a musician's, yet we can talk about them and
compare and draw conclusions about them just all right (but maybe that fact shows that there's a deeper "connection"?).
But if one thinks that working according to the same laws shows a connection, then, yes, of course.
BTW, our thoughts also coincide regarding what an excellent speaker Dr Frenkel is! A pure delight, thanks a lot for this, professor.
Dr Frenkel, I facilitate the learning of Math wirh children where some elementary students below 15 years old study up to Calculus. With undersranding.
Encounters with thinking children who ask philosophical questions have been fascinating. Your information is useful in crafting interesting answers to keep my curious students interested in pursuing compkex math.
Thankyou!
Thank you!
Literally, our bodies are just a bunch of assembled particles, and our minds just dwells somehow "around" that bunch of particles..
Fabulous exposition, thank you!!
👏👏👏
So beautiful lecture.
Thank you, Professor.
and
With luck and more power to you.
hoping for more videos.
Thank you! I'll do my best.
Mathematics, Quantum Physics, Phylosophy and Psicology. I am so excited to be part of this podcast. I read your book, watched some interviews. Thanks to you I am deeply bounded to math. What are some concepts of math that can actually change the way we see the world (like dimensions)? and Why is that?
Why logic is used in phlylosophy? How does language appeared is linked to math?How ? How AI can predict the next word of an idea? Does it think? or not ?
How someone can exprees his ideas trough math? Why in advanced math topics you don´t see numbers? From War and Peace, there is an idea that says that you can see the history of the sum of the wills of the people, and also can approximate it as an integral? It is possible ? . Greetings from Peru😄
Great questions, thank you! Hope to address some of them on this podcast.
Wonderful first episode! Thank you for encouraging interactive questions - I promise to work on providing thoughtful feedback!
Recently, I have heard the name of Pythagoras mentioned in connection with the early practice of Theurgy. I never knew he was associated with this practice and would love for you to explore that connection! 🎉 🙏
Thank you! I will definitely talk about Pythagoras and Pythagoreans, and perhaps we will explore their Orphic/Dionysian practices.
@@edfrenkel Thank you, looking forward to it!
This is gold. I hope the series progresses. Many thanks for it.
Thank you!
@edfrenkel ward said this in his book: "Without mathematics there can be no freedom."
I have pointed out the following in response:
A. The entire world financial system is based on math. Is humanity a slave to money?
B. Math has produced the internet, the screen, and everything that is played on the screen. Is humanity helplessly addicted to the screen?
C. Every wall, chain, lock, prison, fence, has math at its core.
Therefore, WHERE THERE IS ENSLAVEMENT THERE IS MATHEMATICS.
Has he rescinded that comment? No. Has he responded at all to me? No.
Edward Frenkel is a delusional coward, as is Curt Jaimungal
I could argue that even though our perception of a mathematical (unlike a physical) object is the same for everyone, it still can be less or more different in the depth of understanding it depending on our intelectual (mental) strength. Like a math professor would possess much deeper and wider knowledge related to, say, an infinite plane than an average person 🙂
I agree. But the same is true for any ability that human beings have: some are more proficient than others. My point was not that we all have exactly the same ability to perceive the mathematical objects but that we all have this ability to some degree.
What a great start to your podcast journey, professor! SUBSCRIBED!
We all share cells that divided in the same encapsulated space time at some point in the past; we are deeply connected. Also, abstract concepts can exist outside of the mind, inside instructions for computation, assuming you set aside the halting problem. Mathematics gave rise to universal computation, which unlocked the fact that what we call reality is an approximation, full of optimisations, and a hint of what is "running" underneath. I'm old enough and dealt with enough complex systems to see pretty clearly what I like to call "information coalescence" - situations arising beyond coincidence. You touched on this quite a bit.
Love this, would be great to have an episode on the philosophy of mathematics!
Thank you. I loved your book. I'm skeptical of mystical imaginings, but will stay tuned to see how you treat the subjects you are so expert in.
I can not emphasize how excited I am for this. I think about the aforementioned topics separately and collectively all the time. Even just yesterday I was talking to my friends about this…it’s almost as if you read my mind lol
I almost want to say: "Thanks for manifesting it!" :)
I'm tremendously excited he started his own channel.
ooh Edward, I'm an(armchair) Jungian scholar and currently up to my knees in 137 and the work that Jung was doing at the end of his life on archetypal numbers and mapping the psychoid and the acausal connecting principle mathematically. I'm engineering software and using semantic text embeddings of books(actually "Aion" at the moment by Jung) and mapping them to 3D space using different kinds of matrices and interesting experiments involving coupling the Hamiltonian of the semantic embedding space to alpha. I've been turning out some significant findings and results, but intersection between psyche and matter carries with it the feeling of embarrassment due to the unknown nature of the connection, but I persist. I would absolutely love to talk to you, but I know you're a busy man! I knew there was something special about you man! Can't wait to get into your videos. Awesome.
First and foremost, I warmly thank you for your initiative.
I firmly believe that you are bringing us to cross the “Acte de Penser’s frontier “ to navigate the Intelligible world when you mentioned it at 30:58.
…We can discuss it, exchange ideas about it, and move to the next Frontiers about the subjects, which is how mathematics has been developing…
I will be pleased to learn more about our mind's unity with Brouwer’s intuitionistic mathematics ideas, which are fundamentally differentiated from classical mathematical language, from one of the future episodes.
Namely by the following fact: it masters the "elusive infinities" of the standard description of a continuum of time, Euclidean/non-Euclidean space, the interactions of elementary particle Forces and in particular, the propagation of mechanical-electromagnetic-gravitational waves as an infinite collection of real numbers carrying the "intrinsic randomness" of deterministic chaos of the unknowns of initial conditions in matter.
Thank you for being there for us.
Professor Frenkel, you are one of the most extraordinary people I ever met online.
Your (set of) interests are the same as mine. I did subscribe to this channel (and liked this video) the very moment I saw your face.
I was reminded of the 'missing square puzzle' in geometry today and maybe I'm way off it seems to me that it conveys the wiggliness of experience you were talking about quite well, since it depends on that very wiggliness/imperfect human perception to work. The (neo-)Platonic truths of geometry do not fall victim to the same error.
thanks really, this is very appreciated
Edward, would you say the senses are necessary to developing an understanding of mathematics in the first place? Or, put another way maybe, would it be possible for a being without senses to discover logical/mathematical truths? As you mention, mathematical objects don’t exist in space-time. But is it our ability to experience space-time that somehow leads us to discover mathematical objects? Or can “math” be fundamentally decoupled from space-time? Any thoughts you can share along these lines would be very interesting to hear!
Good question! I think the two abilities are largely independent from each other, and our experience of math as intertwined with our perceptions of the physical reality is a kind of synesthesia. For example, there have been great blind mathematicians. And on the other hand, there may well be very visually imaginative people who may have difficulties conjuring up abstract mathematical objects that they can't easily visualize. But this is just my intuition. I'm not sure of it. It may well be that the two abilities are more closely connected to each other than I imagine them to be.
In my view, the best approach is to consider also intuition and reasoning senses, instead of making strict boundary between "internal" and "external" senses and call only the latter "senses".
@@santerisatama5409I think they have something in common perhaps inextricable .
Amazing. You’re a natural so glad you’re pursuing this!! Can’t wait for the next episode!
Thank you!🙏🏻😍
Just finished “love and math” and now watching this channel. Incredible book and video, excited for more of the podcast!
Wow!!! That`s it for the moment.
And thank you.
I'm no mathematician or could ever be but this talk fascinated me because I've always believed in a universal conciousness. Not because I'd ever made a study but purely intuitive feelings. I've talked to many other ordinary people about this and many have agreed with me 😊
OK. But how does that square with the privacy of each self?
I am curious if you will talk about the mandala, a symbol of the interconnectedness of mind, and how it relates to mathematical structure. Also, your discussion reminded me of Yogacara Buddhist philosophy, which argues that the seeming intrinsic or objective existence of the external world is actually a projection of the mind. I did not know that Jung connected numbers with archetypes, so I'm existed to hear more about that. I loved the clarity of your explanations and how you left questions open for critical thinking.
Thank you! Yes, I'll probably talk about mandalas in the future.
Edward … I am loving your life’s work. Thank you for choosing to dive into the Nature of nature. ☀️🤝🙏
Thank you!
Dear Sir,
Thank you very much for this podcast.
When you (and Darwin) mentioned that mathematics can be viewed as an additional sense, it brought back to mind an old question of mine. We often think of this extra sense as one that sits atop the others; from our sensory experiences, we reach an abstract world that can explain what we perceive. This mathematical sense holds a unique status-it gives us the "why" behind things, where our other senses merely provide a "how," passively describing our surroundings.
Returning to my old question, I've often wondered how mathematics might look today if we had different senses. For instance, if we lacked vision, I can’t imagine we would have discovered the Pythagorean theorem as early as we did. Why would we even consider dividing a line (the hypotenuse) into two seemingly arbitrary smaller lines, whose main interest is that the sum of their squares equals the square of the hypotenuse? It seems likely that our first coordinate system would have been polar coordinates, and the Pythagorean theorem might have remained a cute mathematical curiosity, much like the fact that 1+2+3=1×2×3.
With a brain unaccustomed to vision, imagine the faith or even madness required to accept the fifth postulate: that given a point and a line, there exists another line passing through that point that will never intersect the first line. Infinite lines that never intersect-can you imagine? This might have felt as incomprehensible as the statement, "A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force."
I could go on endlessly with this question, and I’d love to hear your thoughts on it. Thank you again for everything!