This is the singular-most interesting video on singularities I've seen in awhile. Thanks Sabine!

@area51z63

3 жыл бұрын

So you like science fiction? Me too.

@gentlyschannel4193

3 жыл бұрын

@@area51z63 what is that supposed to mean?

@area51z63

3 жыл бұрын

@@gentlyschannel4193 What do you think it means?

@gentlyschannel4193

3 жыл бұрын

@@area51z63 that you're in the wrong place, the tinfoil hat stuff is in isle 9

@area51z63

3 жыл бұрын

@@gentlyschannel4193 Think less, know more.

I like the way how calm she said “You will die before you reach the singularity.”

@Constellation3232

3 жыл бұрын

There's levels to this 😂

@HamabaJuJu

3 жыл бұрын

Because she is a professional.

@rajarsi6438

3 жыл бұрын

The spirit soul, the true self, is eternal.

@tarmairon431

3 жыл бұрын

@@rajarsi6438 define those things in a meaningful way and demonstrate them to be "eternal". If you can't then why should anyone care what you say?

@pumbaa667

2 жыл бұрын

that's germanly practical ! 👌

I'vevalways been troubled by physicists talking about the black hole singularity seemingly being real. They never differentiate between the mathematical singularity and what really is at the center of a black hole. A neutron star has volume so why wouldn't a black hole have volume at its center. Well the answer comes back, "because the math says so". And while you say we don't know because we can't observe whats inside a black hole, my mind cannot conceive of nothing at its canter. The black hole consumes mass, so there must be mass there, and must have volume. I realize I am trying to visualize something the we can't definatevly know. But its one of those things that hurts this amateur scientists brain. Thank you Sabine for teaching us to question the status quo. Your videos often show me another perspective, in addition to probing deeper into topics than most science videos on youtube. You are a credit to your profession.

@tomashull9805

3 жыл бұрын

Speculation abound in physics until you get Lost in Math...

Crazy how in 8 mins, you explain this stuff more clearly than hour long lectures

@frankdimeglio8216

3 жыл бұрын

THE CLEAR UNDERSTANDING OF THE MOTION OF WHAT IS THE MOON AND OF FALLING OBJECTS (AND THE FALLING MAN), AS E=MC2 IS CLEARLY PROVEN TO BE F=MA: Think about the BALANCE of BODILY/VISUAL EXPERIENCE. Consider what is the FULL DISTANCE in/of SPACE AND what is the MIDDLE DISTANCE in/of SPACE IN BALANCE. So, consider the man who IS standing on what is the Earth/ground. Touch AND feeling BLEND, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE. The EARTH/ground CLEARLY proves ON BALANCE that E=mc2 IS F=ma. Time DILATION ULTIMATELY proves ON BALANCE that ELECTROMAGNETISM/energy is gravity, as E=mc2 IS F=ma. OVERLAY what is THE EYE in BALANCED RELATION to/WITH what is THE EARTH. Notice the black space of THE EYE. The stars AND PLANETS are POINTS in the night sky. THE DOME of a person's EYE is ALSO VISIBLE. Now, carefully consider what is the semi-spherical, translucent, QUANTUM GRAVITATIONAL, AND BLUE SKY. Gravity IS ELECTROMAGNETISM/energy, as E=mc2 IS F=ma. SO, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites. This NECESSARILY represents, INVOLVES, AND, DESCRIBES what is possible/potential AND actual IN BALANCE. Accordingly, TIME is NECESSARILY possible/potential AND actual IN BALANCE; as E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The Sun is E=mc2 AND F=ma. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. So, E=mc2 AS F=ma clearly requires and involves invisible AND VISIBLE SPACE in fundamental equilibrium AND BALANCE; as ELECTROMAGNETISM/ENERGY IS GRAVITY. (The EARTH is ALSO BLUE, as it CLEARLY proves ON BALANCE that E=mc2 is F=ma.) ACCORDINGLY, the MIDDLE DISTANCE in/of SPACE AND the FULL DISTANCE in/of SPACE are NECESSARILY LINKED and BALANCED; as E=mc2 IS F=ma; as ELECTROMAGNETISM/energy is gravity. Great. Therefore, INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience; as E=mc2 IS F=ma; as ELECTROMAGNETISM/ENERGY IS GRAVITY. THE EYE is the body ON BALANCE, as E=mc2 IS F=ma. INDEED, the balance of being AND EXPERIENCE is essential. (BALANCE and completeness go hand in hand.) SO, objects (including what is the falling man) fall at the SAME RATE (neglecting air resistance, of course); as ELECTROMAGNETISM/energy is gravity; as E=mc2 IS F=ma. Indeed, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; as ELECTROMAGNETISM/energy is gravity. Great. Therefore, the rotation of WHAT IS THE MOON necessarily matches it's revolution; as E=mc2 IS F=ma. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity. The Earth AND the Sun are linked AND BALANCED opposites, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Great. Therefore, the rotation of WHAT IS THE MOON NECESSARILY matches it's revolution. Great. E=mc2 IS CLEARLY proven to be F=ma !!!! The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. GREAT !!!!! The EARTH and the Sun constitute and comprise the MIDDLE AND THE FULL DISTANCE in/of SPACE (IN BALANCE) in full and BALANCED compliance and conformity with the CLEAR and universal fact that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Great !!!!!! Hence, it is CLEARLY proven, in fact, that the rotation of WHAT IS THE MOON NECESSARILY matches it's revolution. Great. Obviously, what is THE MOON is subject to and constitutive of both E=mc2 AND F=ma. E=mc2 IS CLEARLY proven to be F=ma. "Mass"/energy involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. The following constitutes even further proof of the fact that ELECTROMAGNETISM/energy is gravity. Very importantly, in dream experience, BODILY/VISUAL EXPERIENCE is invisible AND VISIBLE IN BALANCE. Dream experience is/involves true/real QUANTUM GRAVITY, as ELECTROMAGNETISM/energy is gravity; as E=mc2 IS F=ma. By Frank DiMeglio

@frankdimeglio8216

3 жыл бұрын

Hossenfelder is knowingly and deceitfully lying about physics.

@stevenk-brooks6852

3 жыл бұрын

@@frankdimeglio8216 Without explanation, and with no examples, this comment is worthless.

@frankdimeglio8216

3 жыл бұрын

THE QUANTUM GRAVITATIONAL UNIFICATION OF PHYSICS/PHYSICAL EXPERIENCE: "Mass"/ENERGY is necessarily gravitational/electromagnetic (IN BALANCE) in conjunction with INSTANTANEITY AND the fact that E=mc2 IS F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, as ELECTROMAGNETISM/energy is gravity. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. Accordingly, the rotation of WHAT IS THE MOON necessarily matches it's revolution; as gravity is ELECTROMAGNETISM/energy. The Sun, the Moon, AND WHAT IS THE EARTH are thus CLEARLY representative of the fact that E=mc2 IS F=ma. Indeed, the stars AND PLANETS are POINTS in the night sky. By Frank DiMeglio

@frankdimeglio8216

3 жыл бұрын

@@stevenk-brooks6852 WHY AND HOW E=MC2 IS F=MA, AS ELECTROMAGNETISM/ENERGY IS GRAVITY: Time DILATION ULTIMATELY proves ON BALANCE that ELECTROMAGNETISM/energy is gravity, as E=mc2 IS F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Ultimately and truly, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. OVERLAY what is THE EYE in BALANCED RELATION to/WITH what is THE EARTH. Notice the black space of THE EYE. The stars AND PLANETS are POINTS in the night sky. THE DOME of a person's EYE is ALSO VISIBLE. Now, carefully consider what is the semi-spherical, translucent, QUANTUM GRAVITATIONAL, AND BLUE SKY. Great. E=mc2 IS F=ma. It is CLEAR. Time DILATION ULTIMATELY proves (ON BALANCE) that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=mc2 IS F=ma; as ELECTROMAGNETISM/energy is gravity. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light; as E=mc2 IS F=ma; as ELECTROMAGNETISM/ENERGY IS GRAVITY. The stars AND PLANETS are POINTS in the night sky. The EARTH and the Sun constitute and comprise the MIDDLE AND THE FULL DISTANCE in/of SPACE (IN BALANCE) in full and BALANCED compliance and conformity with the CLEAR and universal fact that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Great !!!!!! Hence, it is CLEARLY proven, in fact, that the rotation of WHAT IS THE MOON NECESSARILY matches it's revolution. Great. Obviously, what is THE MOON is subject to and constitutive of both E=mc2 AND F=ma. E=mc2 IS CLEARLY proven to be F=ma. "Mass"/energy involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. This CLEARLY explains why objects fall at the SAME RATE (neglecting air resistance, of course), AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. THE EARTH is ALSO F=ma AS E=mc2. The Sun is both F=ma AND E=mc2. The BLUE SKY is E=mc2 AND F=ma. What is THE MOON is NECESSARILY F=ma AS E=mc2. THINK. It ALL CLEARLY makes perfect sense. (BALANCE and completeness go hand in hand.) VERY IMPORTANTLY, outer "space" involves full inertia; AND it is fully invisible AND black. Great !!! INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. (THOUGHTS ARE INVISIBLE.) GREAT. THE DOME of a person's EYE is ALSO VISIBLE. The balance of being AND EXPERIENCE is essential. The EARTH is ALSO BLUE (as water). Alas, the ULTIMATE unification of physics/physical experience combines, BALANCES, AND INCLUDES opposites; as ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. Gravity IS ELECTROMAGNETISM/energy. By Frank DiMeglio

Excellent video! Just one point: the function f(x)=e^(-1/×^2) has a removable singularity at 0 (for real x) since we can define f (0)=0 to preserve continuity. The singularity of sin (1/x) is essential since its values come arbitrarily close to every real number between -1 and 1 infinitely often as x approaches 0 (more on singularities of different types on the new KZread channel infinity manifestations).

@stevenfallinge7149

Жыл бұрын

No, it still won't be continuous when you let x=ia, where i is the imaginary constant as you let a->0. Then f(x) gets infinitely large. Usually we are thinking about complex functions when talking about singularities. There's a theorem that around an essential singularity, the function takes on almost every possible value in a neighborhood of the singularity, the Big Picard theorem.

I love how you explain physics without trying to amplify the gee-wiz factor. It's refreshing to see a scientist that doesn't worship science.

Thank you Sabine, I enjoyed this a lot. I find I have to really concentrate to understand this, and I still miss some of it, but it's a pure joy to listen to someone who really knows what they're talking about, and can express it so clearly. I now find that, at 71, I can still learn. This is a good thing! Thanks again.

I remain skeptical on the possibility of a singularity being discovered in nature , and if it were, I'd look very closely at the instrument of measure. Great video as always Sabine.

@brandonwilliams3788

3 жыл бұрын

You are using that singularity right now. A true singularity in nature would also be infinity at the same time

@marvinhacking5777

Жыл бұрын

@@brandonwilliams3788 An erection is a singularity that hopes for a big bang ... but sadly infinity is not part of the equation.

@Yawndr

Жыл бұрын

One could argue "Now" in the time axis is a singularity since it's impossible to go the other direction, no?

I'm glad I found this channel, incredible descriptions of interesting topics and editing sprinkled with some comedy here and there, it's fantastic thank you so much.

Excellente! There's so much good stuff to think about here.

Thank you! I have been thinking about singularities for the last hour and this put a lot of things in place for me. Great video!

Incredible clarity of thought. Thank you Sabine !!

Sabine, thank you for making the world a smarter place! Excellent video as always

A pleasure to watch, as always.

thanks for taking the time, to present numerous topics

Video by video,knowledge expands...Thank you Sabine

I love your videos since they are so professional.

I’m so ready for this

Hi Sabine ,I will put it down to coinesidence that you chose to do Singularities this week because last week you covered infinity.I'm glad you chose to cover this topic this week see next post ,I enjoy your videos very much as they really challenge my theoritical work.

Thank you for your videos. I learn alot. Keep up the great work

Dr. Hossenfelder, many thanks for this video, and indeed all of your videos. They introduce me to aspects of the universe I had little idea of. I am in my 8th decade so your career should last long after I have passed away. May I wish you all success in your researches.

@SabineHossenfelder

3 жыл бұрын

Happy you find my videos of interest!

@gugisagara4489

3 жыл бұрын

@@SabineHossenfelder Dear Sabine, I hope you will talk about different kind of singularity as popularized by Ray Kurzweil (Google's engineering director)...

I was updating KZread application in Google Play while watching this video. At 5:29 the screen went black and the application restarted. For a while, I was genuinely thinking that this is some kind of intended illustration of what happens in singularity. The speech was perfectly aligned: "There's just ". Just wanted to share to you all... 😀

@aurelienyonrac

3 жыл бұрын

That just made my day. At the same time that the screen went dark you realise it was just a little black thing in a colorful and alive universe.

So fortunate to have learned about this woman, even if only recently. Sabine, you are amazing! I am watching your videos regularly and enjoy every one. Thank you!

Always so great and so clear about so hard topic!

Sabine, I have a question that has always interested me. When you look through a magnifying lens and hold it at a distance the image flips. Does this not mean that the light at some point becomes a singularity? For it to flip it must go through a point of nothing, neither the right way up or inverted. This to me is exactly what happens in the explanation of a black hole. To me it seams impossible but it must happen somewhere in its journey.

@johnlshilling1446

3 жыл бұрын

Orange Manstan, interesting. Let me know when you've got proof... It seems that the water droplet analogy applies, that is, if photons exist as discreet particles. Wouldn't individual photons need to also be shrunkteded to a singularity and also share space with other photons? Space that is also required to shrinktenen itself into a singularity? Hhhmmm.. 🤔 "Houston, we h....."

@OrangeManStan

3 жыл бұрын

@@johnlshilling1446 I'm no scientists unfortunately but it's just something that's always baffled me. As for the image to reverse there has to be a point in time when there is nothing there because if there wasn't you would be able to magnify to a point when it is either one or the other way up, so in my mind the light must become a singularity. I'd love for someone like Sabine to explain if this is the case. This to me is here on earth and open for research but I'm probably barking up the wrong tree 😁

@johnlshilling1446

3 жыл бұрын

@@OrangeManStan Me, too. I'm nowhere near being a scientist, either. It is an interesting observation. I would love to have my thoughts analyzed and rejected, as long as my mutilation was described in a way that I could understand...

I like that she explains things in such a way, that we can actually understand them. It's like she's not trying to waste our time.

@hyperduality2838

3 жыл бұрын

The big bang singularity is a Janus point (two faces) = Duality! Points, singularities represent limits or boundaries -- Immanuel Kant. Poles (infinities) are dual to zeroes -- Optimized control theory. The positive curvature singularity is dual to the negative curvature singularity -- General relativity, Einstein. Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Elliptic or spherical geometry is dual to hyperbolic geometry (dark energy). Curvature or gravitation is therefore dual. Potential energy is dual to kinetic energy -- gravitational energy is therefore dual. Apples fall to the ground because they are conserving duality. Concepts are dual to percepts -- the mind duality of Immanuel Kant. The intellectual mind/soul (concepts) is dual to the sensory mind/soul (percepts) -- The mind duality of Thomas Aquinas. Mind is dual to matter -- Descartes. Bosons are dual to fermions -- Matter duality. Active matter (life) is dual to passive matter (atoms, forces) -- matter duality. Mind duality is dual to matter duality Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. "Always two there are" -- Yoda. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality). Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Duality creates reality.

@erikparent8176

3 жыл бұрын

@@hyperduality2838 There is a reality deeper than duality and that projects the duality! There is a "quantum leap" between the two which cannot be understood ( ever) by any human mind.( now that's difficult to rap ones mind around)

@hyperduality2838

3 жыл бұрын

@@erikparent8176 Stereographic projection is duality! Noumenal (rational, analytic) is dual to phenomenal (empirical, synthetic) -- Immanuel Kant. Concepts are dual to percepts -- the mind duality of Immanuel Kant. Thesis is dual to anti-thesis creates converging thesis or synthesis -- the time independent Hegelian dialectic. Being is dual to non-being creates becoming -- Plato. Projection (mathematics) is prediction (syntropy) in physics. I would tend to disagree with you as I discovered the 4th & 5th laws of thermodynamics:- Syntropy (prediction) is dual to increasing entropy -- the 4th law. The conservation of duality (energy) is the 5th law, energy is duality, duality is energy. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality). Energy is dual to mass -- Einstein Space is dual to time -- Einstein. Certainty is dual to uncertainty -- the Heisenberg certainty/uncertainty principle. The deeper reality is duality in physics. The big bang is a Janus point (two faces). The "quantum leap" is the mind duality of Immanuel Kant and also Thomas Aquinas! The intellectual mind/soul (concepts) is dual to the sensory mind/soul (percepts) -- the mind duality of Thomas Aquinas. Dark energy is dual to dark matter -- The mind/soul or the Janus point. Percepts project into concepts and concepts project into percepts, Immanuel Kant understood this -- stereographic projection (spinors).

@erikparent8176

3 жыл бұрын

@@hyperduality2838 I diverge from Kant's Noumenon in that the deeper reality cannot be labled "The thing in itself" or "object" I'm more in line with Buddhists "no thing" Kant is working in the right direction but lables Noumenon as a concept.

@hyperduality2838

3 жыл бұрын

@@erikparent8176 Yes I agree with you but there is still a dual pattern at work here which many people do not accept especially physicists. This dual pattern leads to the idea/concept of a 4th law of thermodynamics because you can ask the question what is dual to entropy? Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics. The observer is dual to observed -- David Bohm, physicist. Syntropy is rational, noumenal (mind). Entropy is empirical, phenomenal, (matter, physics). There is a dual pattern through out Kant's metaphysics which I was not aware of until I started to read his books. Philosophy is not encouraged in physics. "Philosophy is dead" -- Stephen Hawking. If you ignore philosophy you have a "dark age" in physics!

Simple, quick and clear explanation about singularities. Thanks!

Brilliantly explained. I wish I had teachers like you when I was in school. Thanks Sabine. It is not too late for me to understand the concepts.

@area51z63

3 жыл бұрын

So you think that you learned something. OK detail what you learned?

Really, really interesting! Thank you, Sabine! 😊 Merry Christmas and a fantastic new year! Keep Krampus away! 😊 Stay safe there with your family! 🖖😊

@SabineHossenfelder

3 жыл бұрын

Merry Christmas to you too!

@theoreticalphysicistzeinaq2753

3 жыл бұрын

@@SabineHossenfelder hello I am 12 years old and my dream is to be an astrophysicist and solve the quantum gravity theory, but please can you answer me this question please !!!!!!! If graviton boson really exist, can it develop string theory/loop quantum gravity and can this boson complete the general relativity or there will be a new theory????? And Thank you🌷

@theoreticalphysicistzeinaq2753

3 жыл бұрын

@@SabineHossenfelder please can you answer that question 🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷🌷

@Hermetics

3 жыл бұрын

@@SabineHossenfelder kzread.info/dash/bejne/gJimm85pib2WcZM.html There, the end of science, the beginning of LOVE :*

Wishing you a very merry Christmas and a happy new year in advance Sabine 🎉☄️✨💫

@SabineHossenfelder

3 жыл бұрын

Same to you!!

@tomashull9805

3 жыл бұрын

@@SabineHossenfelder I didn't know atheists, like Sabine, celebrate Christmas ? It's kind of hypocritical to pick and choose beliefs....

@Bambabah

3 жыл бұрын

​@@tomashull9805 She probably doesn't "celebrate" it, a greeting is not celebration. Most people actually don't, other than eating yourself fat and visiting family. Also most "atheists" are actually agnostic, they just don't know what "atheism" actually is; although Sabine probably does and might be a real atheist (that is do not believe in God).

@alvaroballon7133

3 жыл бұрын

@@tomashull9805 I mean Christmas comes from the Roman celebration of Saturnalia, which basically celebrates the Winter Solstice: the rebirth of the sun. They changed it to mean Jesus’ Birthday after the Romans shifted to Catholic religion, just to please people and keep celebrating their pagan holidays. If it’s historically a pagan party, I don’t see why Christians should celebrate it either. In the end I think anyone who wants to should celebrate the holiday, either for religious reasons or just to gather with their family and celebrate being together.

@bozo5632

3 жыл бұрын

I celebrate George Washington's birthday and I'm not George Washington, so...

2:57 Fun fact: It is only really understandable in complex analysis (complex as in complex numbers), why this type of singularity is called an "essential singularity". In the real numbers, the function can be continued pretty smoothly (continuously, differentiably, ...), but if one allows z to be a complex number, then in any arbitrarily small circle around 0 (minus the 0, which can not be inserted into the function), the function exp(-1/z^2) takes on every complex value with the exception of possibly one complex number according to the "Great Picard Theorem". So it really goes crazy. On the other hand, the function (exp(z) - 1) / z has a "removable singularity" in 0, it can be continued to a complex differentiable function (also called holomorphic), because (exp(z) - 1) / z = (1 + z + z^2/2 + ... - 1)/z = (z + z^2/2 + ...)/z = 1 + z/2 + ... which tends to 1 as z approaches 0.

Wow. This is one of those "I never thought of that", and better, I now have some insight thanks to you.

I was hoping you would cover this topic. 👍

Whenever I encounter a singularity, I assume it's holomorphic and integrate around it. Problem solved!

@TheReaverOfDarkness

3 жыл бұрын

Isn't that tantamount to assuming that it doesn't have a singularity?

@sjdpfisvrj

3 жыл бұрын

@@TheReaverOfDarkness it's been a really long time since I did this in college, but it's not that you assume the singularity doesn't exist, it's rather that you are able to compute physically meaningful values even though you are operating over singularities. I'm an EE, and there you have the problem that a simple electron already is a singularity (because the electric field is infinite where the electron is). However, the electric field is holomorphic, and thus you can use "analytic continuation" to still integrate over it and get meaningful results.

@hyperduality2838

3 жыл бұрын

The big bang singularity is a Janus point (two faces) = Duality! Points, singularities represent limits or boundaries -- Immanuel Kant. Poles (infinities) are dual to zeroes -- Optimized control theory. The positive curvature singularity is dual to the negative curvature singularity -- General relativity, Einstein. Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Elliptic or spherical geometry is dual to hyperbolic geometry (dark energy). Curvature or gravitation is therefore dual. Potential energy is dual to kinetic energy -- gravitational energy is therefore dual. Apples fall to the ground because they are conserving duality. Concepts are dual to percepts -- the mind duality of Immanuel Kant. The intellectual mind/soul (concepts) is dual to the sensory mind/soul (percepts) -- The mind duality of Thomas Aquinas. Mind is dual to matter -- Descartes. Bosons are dual to fermions -- Matter duality. Active matter (life) is dual to passive matter (atoms, forces) -- matter duality. Mind duality is dual to matter duality Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. "Always two there are" -- Yoda. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality). Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Duality creates reality.

@SamGarcia

3 жыл бұрын

@@hyperduality2838 this is too simplified. matter and energy cannot exist without the space. 2D space cannot exist without 3D. Everything is three, not two.

@hyperduality2838

3 жыл бұрын

@@SamGarcia Duality is more fundamental than triality. Space is dual to time -- Einstein or 4 dimensions. Thesis is dual to anti-thesis creates converging thesis or synthesis -- the time Hegelian dialectic. Hegel's cat: Alive (thesis, being) is dual to not alive (anti-thesis, non-being) -- Schrodinger's cat. Being is dual to non-being creates becoming Plato's cat. Absolute truth is dual to relative truth -- Hume's fork. Reality or the universe is actually a Janus point/singularity. Absolute time (Galileo) is dual to relative time (Einstein) -- time duality. The future is dual to the past -- time duality. My absolute time is your relative time and your absolute time is my relative time -- time duality. Time and space are both dual concepts. Left is dual to right, up is dual to down, in is dual to out -- space duality. Length, distance or space is defined by two dual points -- space duality. Space duality is dual to time duality. Certainty is dual to uncertainty -- the Heisenberg certainty/uncertainty principle. There is a dual process to that of increasing entropy namely syntropy (prediction). "Through imagination and reason we turn experience into foresight (prediction)" -- Spinoza describing Syntropy. Thinking and having thoughts is a syntropic process and rational thinking leads to optimized predictions -- syntropy. Teleological physics (syntropy) is dual to non-teleological physics (entropy). Space/time is synthetic a priori knowledge according to Immanuel Kant -- The Critique of Pure Reason.

Amazing background, so fascinating

Professor, you are a wonderful lecturer. Brilliant video! I have used the sinx function in spectrum analysis. It's an interesting and practical maths function.

I want to support your channel, but I'm already a member of Brilliant.

"Open the U-tube app HAL"..."Sorry Johnny I cannot do that...."

Brilliant information over the year thanks

Also, concise and clear content as usual. Thanks.

Sie könnten ja Alpha Centauri wieder aufleben lassen. Toller Kontent 👍😀

The statements about "reaching the the other side" could be a more pinned down by explicitly using the topological terminology of continuity and smoothness. I'm also surprised there were no chicken jokes.

@crystalgiddens7276

3 жыл бұрын

If the value of the function becomes infinitely large does infinity exist or not?

@mikel4879

3 жыл бұрын

Crystal G / The infinity can never be achieved. So the stupid and erroneous explanation is this : "when it does achieve infinity then this goes to zero". Pure stupidity !

@crystalgiddens7276

3 жыл бұрын

@@mikel4879 Right! Clear as mud! Gotta love the mental "exercise" i.e. gymnastics.

While perhaps not strictly within the scope of this channel, hearing your thoughts and commentary on the technological singularity that you touched on in this video would be really interesting!

Best, more balanced discussion of singularities I’ve read. Thank you very much.

@hyperduality2838

3 жыл бұрын

The big bang singularity is a Janus point (two faces) = Duality! Points, singularities represent limits or boundaries -- Immanuel Kant. Poles (infinities) are dual to zeroes -- Optimized control theory. The positive curvature singularity is dual to the negative curvature singularity -- General relativity, Einstein. Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Elliptic or spherical geometry is dual to hyperbolic geometry (dark energy). Curvature or gravitation is therefore dual. Potential energy is dual to kinetic energy -- gravitational energy is therefore dual. Apples fall to the ground because they are conserving duality. Concepts are dual to percepts -- the mind duality of Immanuel Kant. The intellectual mind/soul (concepts) is dual to the sensory mind/soul (percepts) -- The mind duality of Thomas Aquinas. Mind is dual to matter -- Descartes. Bosons are dual to fermions -- Matter duality. Active matter (life) is dual to passive matter (atoms, forces) -- matter duality. Mind duality is dual to matter duality Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. "Always two there are" -- Yoda. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality). Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Duality creates reality.

@5:15 "You die and tidal forces rip you to pieces..." imagine if Dr Sabine was a medical doctor and had to deliver bad news to a patient...

@rajarsi6438

3 жыл бұрын

She talks tough but is only an ignorant & fearful girlie.

Love you my best physics professor! Loves from Brazil

Thank you Sabine!

Thanks, Sabine!

I thought if you fell into a singularity of a black hole you would enter the fifth dimension of love and travel back in time to see your loved ones.

@mayuryewale4057

2 жыл бұрын

Haha like in interstellar movie

@Reth_Hard

2 жыл бұрын

Why aren't we just sending a probe inside a black hole and take pictures inside of it?

@phandinhthanh2295

2 жыл бұрын

@@Reth_Hard bc nothing comes out of a black hole even EM wave.

@Reth_Hard

2 жыл бұрын

@@phandinhthanh2295 OK, but if the probe entering the black hole was deploying an antenna long enough to stick out of the event horizon, shouldn't be able to send the pictures to an orbiter?

@phandinhthanh2295

2 жыл бұрын

@@Reth_Hard no, the crazy gravitational force of the black hole will crumble any antenna, bone, metal, ... I think the whole black hole subject is just a waste of time.

The First Rule of Black Holes: When in one, yo dead.

@loganwolv3393

3 жыл бұрын

I'd like to die like that...Would be cool to know that eventually i'll reach the singularity if it exists

@SpecialistBR

3 жыл бұрын

Unless it is a rotating one.

@u.v.s.5583

3 жыл бұрын

Unless it's Interstellar.

@shatterthemirror8563

3 жыл бұрын

But how can you be dead if nothing can escape the singularity (including your soul)?

@TerraPosse

3 жыл бұрын

@@shatterthemirror8563 No such thing as a 'soul'.

The analogy with the drop of water is very useful. Thanks for the videos

Thank you for this topic..

Keep up the good work :)

@SabineHossenfelder

3 жыл бұрын

I'm trying! Watch out for a channel update end of the year.

@siddharthadasgupta3564

3 жыл бұрын

@@SabineHossenfelder of course I will :)

In a nutshell: "Are Singularities Real?" "Well we have not found singularities in nature, but... who knows?". THE END.

@brandonwilliams3788

3 жыл бұрын

We are in the natural singularity. This is what a true singularity looks like

Very informative. Thank you.

Always amazing insight and explanations! As time slows to almost a stop at the center of a black hole, matter becomes trapped in yesteryear creating a seemingly bottomless "Time well" similar to the example here but the bottom of the well is far in the past and pinches off very gradually instead. Time Factor Theory Channel

The so-called technological singularity is really more like an event horizon.

@aniksamiurrahman6365

3 жыл бұрын

Nah. It's more like cashing in on a term made popular by something else.

@quantumtacos

3 жыл бұрын

I don't think so. Maths predicts exactly where spacetime leads upon crossing the event horizon. In a way that's the exact opposite of a singularity.

@clmasse

3 жыл бұрын

It's more like BS.

@catcatcatcatcatcatcatcatcatca

3 жыл бұрын

its the moment in chaotic system where we lose the ability to keep it in keep the system inside some parameters. Which is just another way to state the more understandable reality: this side of point in time we can take certain actions, and after that point we lose that ability, so the system becomes possibly unpredictable and at least in steerable. Which sounds super dramatic, until you realise that similar singularity is between running and jumping. Really the singularity is not the interesting point alone. It is the absence of known landing that makes it scary. There could be a technological singularity where computers can better themselves yet we can still control them. Or a where we regain control after some time has passed. Maybe the computers at first can improve themselves faster than humans, but later humans increase their speed faster then computers, catching up again.

@user-hk8yp7cw1v

3 жыл бұрын

No it+s just trivial.

"There's nothing particularly interesting happening at the horizon, it's just the boundary beyond which you cannot get out." I think if I was in that situation I would find it of massive interest to me tbh. So interesting, in fact, that it would be pretty much all I could think about, although not for very long as then I would soon expire.

@monad_tcp

3 жыл бұрын

Horizon is just like a point of no return in a trip where you can't go back home because you spent more gas than what you need to return and there's no refueling stations.

@juanausensi499

3 жыл бұрын

@@monad_tcp Good analogy.

@moartems5076

3 жыл бұрын

Actually if you get this close, its already over for you. Besides radiation, you would need excessive accelation to get away from there squishing you instantly. The closest safe flyby you can get is above 1.5 times that radius.

Another interesting and informative video from Sabine!

@hyperduality2838

3 жыл бұрын

The big bang singularity is a Janus point (two faces) = Duality! Points, singularities represent limits or boundaries -- Immanuel Kant. Poles (infinities) are dual to zeroes -- Optimized control theory. The positive curvature singularity is dual to the negative curvature singularity -- General relativity, Einstein. Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Elliptic or spherical geometry is dual to hyperbolic geometry (dark energy). Curvature or gravitation is therefore dual. Potential energy is dual to kinetic energy -- gravitational energy is therefore dual. Apples fall to the ground because they are conserving duality. Concepts are dual to percepts -- the mind duality of Immanuel Kant. The intellectual mind/soul (concepts) is dual to the sensory mind/soul (percepts) -- The mind duality of Thomas Aquinas. Mind is dual to matter -- Descartes. Bosons are dual to fermions -- Matter duality. Active matter (life) is dual to passive matter (atoms, forces) -- matter duality. Mind duality is dual to matter duality Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. "Always two there are" -- Yoda. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality). Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Duality creates reality.

I loved this video. Happy holidays.

Sabine, a light in the dark.

@v2ike6udik

3 жыл бұрын

Perturbation in the aether.

@ListenToMcMuck

3 жыл бұрын

> Not unlike Galadriel (8)

@simesaid

3 жыл бұрын

@@v2ike6udik she's bloomin' luminiferous!

The technological singularity would probably be better described as a technological event horizon. Love your work Sabine. Thanks from Australia.

@SabineHossenfelder

3 жыл бұрын

Isn't every moment a horizon in the sense that you can't return to an earlier time?

@fieldo85

3 жыл бұрын

@@SabineHossenfelder True, but I meant in a technological sense, our ability to stop it progressing crosses a horizon and no matter how much fuel we burn, there is no escaping the inevitable slide towards the singularity where we will cease to exist. Doesn't matter, semantics really.. thanks for the reply :)

@drrtfm

3 жыл бұрын

@@fieldo85 That is true for any non-trivial technological innovation. Just think of agriculture: can you go back for there? The horse stirrup? The clock? ....

@fieldo85

3 жыл бұрын

@@drrtfm Not really. We could still return to surviving without agriculture (with a reduced population), as humans did for 200k years. We go without horse stirrups now and we don't actually need clocks for survival either, as our past shows.

@drrtfm

3 жыл бұрын

@@fieldo85 "We could still return to surviving without agriculture (with a reduced population)," Ummm, no, we couldn't because you see (a) people don't know how to do that any more; and (b) that mass population that you need to eliminate tends not to go quietly. In point of fact, the idea that "we cannot go back" is precisely the fact that to go back _requires_ mass death. We go without horse stirrups because we have invented yet further technology. The point is: it couldn't be put back and hidden away, and it changed the face of Europe for a millennium. As for clocks, stop showing up for meetings and see just how far that gets you. Fail to pay your mortgage on time and see how far that gets you. Heck, you are currently using a device that depends on extremely precise clocks.

Brilliant video. Thank you.

I would love to see a video about the twins paradox. I know there are a lot of those out there, but many do not sound satisfactory, and your view is always interesting to see

@eljcd

3 жыл бұрын

Hello, maybe you mean this: kzread.info/dash/bejne/X2aXkrJrc6i7aaQ.html

4:40 sad Hawking noises

@pushkargautam6826

3 жыл бұрын

😂

When Sabine speaks minds are Relatively blown.

@feynstein1004

3 жыл бұрын

So take a seat, Steve. Oop, I see you brought your own.

@canyadigit6274

3 жыл бұрын

@@feynstein1004 what’s with your voice? I can’t tell

@joaoamaro1259

3 жыл бұрын

@@canyadigit6274 You sound like Wall-E

@vickas54

3 жыл бұрын

@@joaoamaro1259 havin s** with a speak-n-spell

That was wonderful. Thank you.

Brilliant as usual. Sabine, what mathematics would be without infinities?

Although I don't understand everything Sabine says, she makes much more sense and appears much more trustworthy, than any of our current politicians. 🙂

@windwalkerrangerdm

3 жыл бұрын

Sabine for the world leader! I would vote!

@patrickfitzgerald2861

3 жыл бұрын

That's a pretty broad statement. Is Angela Merkel included in that?

@ant7936

3 жыл бұрын

@@patrickfitzgerald2861 Have you seen the choice? One hand would be enough to count them all. 😄

@Cythil

3 жыл бұрын

Well that might be because the education on how the political system works or how economic theory works is pretty poor in schools. Not to mention the related field of philosophy and the subset if or morality that goes along with it. And even then I see that is actually hard to get people to educate themselves on this matters. Being someone that has a politically related mission. It is pretty hard to get people to sign up to just learn the basics. (And that was before Covid-19) It is easy to blame the politicians, but most of us here have elected representatives and should really blame our selves more. That is not to say the system is not broke. In most countries there are issues with how politics are conducted. But is very few who to change that system for the better. And if you live in a democracy then is partly on you do help make that change.

@ant7936

3 жыл бұрын

@@Cythil All true. But I was being slightly facetious. 😉😄

“Singularity is a point beyond which prediction is not possible.” So, I would define children between 2 years and 4 years as singularity. Right now I have the proof of it in the form of my 2 years old grandson! Wishing you a Merry Christmas!💐🧀

@SabineHossenfelder

3 жыл бұрын

Thanks, Merry Christmas to you too! (Is this cheese?)

@jasonjackson3114

3 жыл бұрын

Yep. And teens become quantum particles. They colapse to a fixed state the moment you interact with them.

Elocuente y claridad , sin desperdicio alguno . Bravo !

Sabine, please a video on self-similarity and renormalization relating it to physical reality. You are awesome.

@hyperduality2838

3 жыл бұрын

Self similarity (fractals) or equivalence (homotopy) = duality. The big bang singularity is a Janus point (two faces) = Duality! Points, singularities represent limits or boundaries -- Immanuel Kant. Poles (infinities) are dual to zeroes -- Optimized control theory. The positive curvature singularity is dual to the negative curvature singularity -- General relativity, Einstein. Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Elliptic or spherical geometry is dual to hyperbolic geometry (dark energy). Curvature or gravitation is therefore dual. Potential energy is dual to kinetic energy -- gravitational energy is therefore dual. Apples fall to the ground because they are conserving duality. Concepts are dual to percepts -- the mind duality of Immanuel Kant. The intellectual mind/soul (concepts) is dual to the sensory mind/soul (percepts) -- The mind duality of Thomas Aquinas. Mind is dual to matter -- Descartes. Bosons are dual to fermions -- Matter duality. Active matter (life) is dual to passive matter (atoms, forces) -- matter duality. Mind duality is dual to matter duality Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. "Always two there are" -- Yoda. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality). Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Duality creates reality.

I always drop when I'm doing when prof H drops a video.

There must be a singularity in my brain, a point at which nothing can pass through.

@rushunnhfernandes

3 жыл бұрын

😂

@rushunnhfernandes

3 жыл бұрын

@@johnm.v709 self promotion.. Gtfoh

Interesting! Really I haven't found anything *so clear* and understandable on the tube! Maybe something alike what is a singularity in mathematics; could be what happens in the real world at the atomic level, where two atoms link together to form a molecule, or where inside the nucleus protons and neutrons exchange that tiny space each other.. Oh well... Maybe!

Oh, that cut to black holes! It hurt my soul deeply and scared me for life. I see you (your editor?) have a peculiar sense of humor.

@SabineHossenfelder

3 жыл бұрын

No, I just suck at cutting footage. But do not despair, as of early 2021, I'll be handing over to someone who knows what he's doing.

@null_carrier

3 жыл бұрын

@@SabineHossenfelder I am deeply grateful indeed.

Sabine Hossenfelder SPEAK AND I SHOULD HEAR

I have been single for such a long time, I guess I’m currently a singularity.

@erikparent8176

3 жыл бұрын

Only on the surface deep within you "interact" with everyone instantaneously! At a fundamental state or level there is no seperation what so ever! You are one with all that is!

@frankman2

3 жыл бұрын

Yes, you are interacting gravitationally with everyone on the planet at this moment.

@MRegah

3 жыл бұрын

As we learned, you are only a "single" singularity if all possible paths would have let there and if there's no escape out of it. So I hope (I'm sure) you aren't.

Hey, Sabine. First off THANK YOU for your wonderful content, I love you videos! Secondly, I was hoping to hear about the singularity of a point particle. Could you please help me understand that one? Thank you. Drew

Thank you Sabine! I had not realized the true nature of an essential singularity before. I'll have to develop this further, but for now I'd like to postulate that the way physical spacetime maps to a spacelike cross section of a mathematical 4D manifold is maximally discontinuous in the sense that you can use all the information available from the past light cone of any point to define its position in its corresponding cross section but you then have no way of extending beyond that point to its neighbors without bringing in information from outside said light cone, the mapping being only well-defined at the point itself and any points contained within its past light cone. A true snapshot of the universe would then be a set of distinct points without an overall topology, 3D or otherwise. And now I have a name to use for the reason and a way to attack the math.

You show me your singularity, and i show you my multiple worlds.

@hyperduality2838

3 жыл бұрын

The big bang singularity is a Janus point (two faces) = Duality! Points, singularities represent limits or boundaries -- Immanuel Kant. Poles (infinities) are dual to zeroes -- Optimized control theory. The positive curvature singularity is dual to the negative curvature singularity -- General relativity, Einstein. Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Elliptic or spherical geometry is dual to hyperbolic geometry (dark energy). Curvature or gravitation is therefore dual. Potential energy is dual to kinetic energy -- gravitational energy is therefore dual. Apples fall to the ground because they are conserving duality. Concepts are dual to percepts -- the mind duality of Immanuel Kant. The intellectual mind/soul (concepts) is dual to the sensory mind/soul (percepts) -- The mind duality of Thomas Aquinas. Mind is dual to matter -- Descartes. Bosons are dual to fermions -- Matter duality. Active matter (life) is dual to passive matter (atoms, forces) -- matter duality. Mind duality is dual to matter duality Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. "Always two there are" -- Yoda. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality). Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Duality creates reality.

@spiritualanarchist8162

3 жыл бұрын

@@hyperduality2838 Indeed ! And let's not forget : 'He who controls the spice, controls the universe -The Kwistach Hadderach , Maud'dib

@hyperduality2838

3 жыл бұрын

@@spiritualanarchist8162 Well said. "The spice extends life and expands consciousness, the spice is vital for space travel." The Janus point -- check out the new book by physicist Julian Barbour, the big bang is a duality. Anti-particles go backwards in time at the big bang -- Richard Feynman. The conservation of duality (energy) will be know as the 5th law of thermodynamics. Energy is duality, duality is energy. "I have foreseen this" -- Lord Sidious

@spiritualanarchist8162

3 жыл бұрын

@@hyperduality2838 'One must overcome duality to reach nirvana '- The Buddha. 'A singularity is the bottom of a black hole'... - Mine 😉

@spiritualanarchist8162

3 жыл бұрын

@@hyperduality2838 P.S: I will check out the Januspoint. You convinced me !

Sabine, you forgot the biggest singularity of them all: the birth of the universe.

@tomashull9805

3 жыл бұрын

Yeah! And the birth of universe out of nothing too... story like that has gotta be true...🤣

@malikuwu49

3 жыл бұрын

@@tomashull9805 who says it is out of nothing? We just don't know, because we do not have information from "before" the big bang. But that doesn't mean it came out of nothing.

@JonnyRobbie

3 жыл бұрын

That really is just a sum of black holes singularities.

@tomashull9805

3 жыл бұрын

@@malikuwu49 Are you familiar with the cosmologist Laurence Krauss and his best selling book A Universe from nothing?

@tomashull9805

3 жыл бұрын

@@JonnyRobbie how do you know?

mind blown, wow, great topic

Energy-mass stress metrics blow spacially at the origin just as the time scale blow at the event horizon in the black holes. Thank you very much Sabine for such inspiring videos.

@onderozenc4470

3 жыл бұрын

@@bahadrartay4666 such as vacuum decays at Planch temp., trans-dimensional diffusions to the primordial conditions ?

@onderozenc4470

3 жыл бұрын

@@bahadrartay4666 inspiration, aspiration and perspiration pave the way to the reality.. It took Prof. Kip Thorn 40 years to prove the gravitational waves...

@onderozenc4470

3 жыл бұрын

Write in your name. What do you think you are to ask about my inspirations that I have already made written - clear .

Pretty sure my mind is collapsing into a singularity now

I really wish physicists wouldn't pretend/believe that the math = reality.

@mickmiah7605

3 жыл бұрын

Hi Sci Fry, I don't think they do friend which is why Sabine was at pains to point out the difference between Mathematics and Physics- her water drip being a great example. Or were you meaning more generally? I would be interested to know whether you think there is another logical system that could be used to represent nature rendering it predictable, within limits ofc:), and comprehensible. Do you think numbers are a "natural" part of the universe or simply a subjective human construct due to our evolutionary development or a bit of both? Do you think we have reached the end of Physics being able to use Maths to describe aspects of our universe? I would be very interested to hear your opinion:) As a post-grad Social Science student, who thinks Cultural Studies etc belong in music magazines not Universities, my maths stops at Stats but if you suggest human experience is better represented in Poetry I couldn't agree with you more but that is because I am a bit dim and in awe of Donna Stonecipher and her poem "Model CIty" which I heartily recommend to you. Regards, M TAX THE RICH

Very cool video, and Happy Holidays.

I love your videos Sabine! As someone who dropped out of physics and maths at university I find your videos so useful for my own studies. I was wondering if you've ever come across Rhythmodynamics by Yuri Ivanov. It is a compelling model for the quantum processes associated with gravity, right up your alley, as you interested in quantum gravity and axiomatic problems in physics. If you have seen it, maybe you can discuss the pros and cons of this model. Cheers and danke! for your work!

She gives me a Singularity

In mathematics, the theory of residues of complex functions is anything but dull, at least from a mathematical point of view.

im barely literate in algebra and graduated 20 years ago so i escaped any kind of advanced maths but im singularly intrigued by sabine and her explanations of things which are all around us yet invisible. she kind of reminds me of feinman with that. such a great teacher. maybe id have done better if i had her back then.

In my experience (Physics professor), many if not most physicists consider their models more real than "reality" (nature). This is because of the incredible accuracy of physics models.

"if you reach the singularity, that's just the end there is no more space or time beyond this, just ... nothing" this statement really sums up my observation that ever deeper gravity wells taking a simple hydrogen atom through the periodic table of elements (until we get to the fabeled black hole) are the great matter recyclers. What do you have at a singularity? Pure potential. It's like a universe ready to go big bang. It's matter's return to a pure energy state by having all the space time squeezed out of it.

interesting and insightful. 💡 Muito obrigado 🤝

Thanks Sabine.

Great work again! Got me thinking! Maybe mathematics does not explain nature but it models and explains, within error bounds, aspects of observed nature. The idea being that nature is not defined by mathematics or mathematical models. But some aspects of observed events can be explained within error bounds by math

Really interesting thanks.

This one sailed about 3 feet over my head

Sabine could you do video's on how to vary time--Thank you ! 🎄🎁

Thank you Sabine, in a very real way you've shown me the viability of the idea that below the event horizon may in fact exist a dense form of neutronium consisting of higher quark count barrions. I.E. Pentaquarks, Septaquarks, Nanaquarks, etc. Which if you follow this idea to its logical conclusion would seem to indicate that the event we call the big bang may have been the point at which such material was no longer able to withstand the crush of gravity. And in that instant imploded down to the size of a single plank only to rebound as spacetime would no longer have the presence of mass which caused it compress to the point of a black hole. And in this rebounding, if we think of it as the elasticity of spacetime snapping back as would a bungee cord that's been stretched to its limit. Then perhaps we can thus define dark energy, etc as a consequence of the big bang event.