This is how education should be performed, it takes more time and resources but the people taught will be able to develop way better than a full class of kids doing the same exercises like the kids last year.
It was sad to watch youtube lose it´s potential for critical thinking, rational inquiry and the scientific sharing of new data. I am glad that we have Bitchute now. TH-cam could have won the war against fake news and misinformation, but lost. I agree with you. These are great lectures!
@@Yatukih_001 - These are great lectures but what the hell are you talking about with Bitchute that shit site is nothing but crazy ass people posting conspiracy and hate filled garbage it has nothing of value let alone sharing anything remotely close to scientific content.
Topology kind of lends itself to a performing art because the transformations we discuss have to happen in time. A demonstration is always necessary in topology
Yep! Clicked on it to have it in my history and watch it tomorrow morning, ended up watching it till the end lol. Now I can't even start part 2. I really need to go to sleep haha
Einstein never nearly understood TIME, E=MC2, F=ma, gravity, or ELECTROMAGNETISM/energy. He was, in fact, a total weasel. c2 represents a dimension ON BALANCE, as E=MC2 IS F=ma in accordance with the following: UNDERSTANDING THE ULTIMATE, BALANCED, TOP DOWN, AND CLEAR MATHEMATICAL UNIFICATION OF ELECTROMAGNETISM/energy AND gravity, AS E=MC2 IS CLEARLY F=ma: The stars AND PLANETS are POINTS in the night sky. E=MC2 IS F=ma, AS this proves the term c4 from Einstein's field equations. SO, ON BALANCE, this proves the fourth dimension. ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy !!! TIME is NECESSARILY possible/potential AND actual IN BALANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. INDEED, TIME dilation ULTIMATELY proves ON BALANCE that E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE. Gravity IS ELECTROMAGNETISM/energy. E=mC2 IS CLEARLY F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy !!! By Frank DiMeglio
@@hajerjm UNDERSTANDING EXACTLY WHAT IS A TWO DIMENSIONAL SURFACE OR SPACE AS invisible AND VISIBLE IN BALANCE, AS E=MC2 IS clearly F=ma (ON BALANCE): The stars AND PLANETS are POINTS in the night sky. Now, very carefully consider what is a galaxy. Get a good look at what is THE EYE, AND notice the black space. E=MC2 AND F=ma IN BALANCE do ALSO FUNDAMENTALLY represent (ON AVERAGE) what is a TWO DIMENSIONAL surface OR SPACE (as what is a BALANCED MIDDLE DISTANCE in/of SPACE), AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=MC2 IS F=ma. The stars AND PLANETS are POINTS in the night sky. Now, consider what is the speed of light (c) ON BALANCE. I have explained why THE PLANETS (including WHAT IS THE EARTH) move away very, very, very slightly in relation to what is THE SUN on balance, as ELECTROMAGNETISM/energy is gravity. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS CLEARLY and NECESSARILY F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity !!! Accordingly, the rotation of WHAT IS THE MOON matches it's revolution. It is CLEARLY proven ON BALANCE. E=MC2 IS CLEARLY F=ma ON BALANCE. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity !!! TIME dilation ULTIMATELY proves (ON BALANCE) that ELECTROMAGNETISM/energy is gravity, AS E=MC2 IS F=ma ON BALANCE !!! Indeed, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=MC2 IS F=ma IN BALANCE; AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity. (BALANCED inertia/INERTIAL RESISTANCE is fundamental.) Objects AND MEN fall at the SAME RATE (neglecting air resistance, of course), AS E=MC2 IS F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Gravity is ELECTROMAGNETISM/energy ON BALANCE. The sky is BLUE, AND what is the Earth is ALSO BLUE. Carefully consider what is a galaxy !!! Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. “Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, as ELECTROMAGNETISM/energy is gravity (ON BALANCE); as E=MC2 is CLEARLY and NECESSARILY proven to be F=ma ON BALANCE. Inertia/INERTIAL RESISTANCE is proportional to (or BALANCED with/as) GRAVITATIONAL force/ENERGY, as this balances gravity AND inertia; as ELECTROMAGNETISM/energy is gravity; as E=MC2 is CLEARLY and necessarily proven to be F=ma ON BALANCE !!! So, “dark” matter/ENERGY is plainly unnecessary; and it is idiotic. I have mathematically unified physics, as I have explained the term c4 from Einstein's field equations along WITH the fourth dimension, as ELECTROMAGNETISM/energy is CLEARLY AND necessarily proven to be gravity ON BALANCE. E=MC2 is CLEARLY proven to be F=ma IN BALANCE. By Frank DiMeglio
Random youtube recommendation, but stayed for the whole lecture, And i am not even a maths student :) Professor Tokieda is a real gem, we are fortunate to have his wisdom shared for free online.
Thanks to Professor and African Institute of Mathematical Science. Long live sir... I will try to understand and will teach to my students. Thanks a lot
I love this guys numberphile bits on youtube, have done so for years. And today the almighty yt algorithm decides to drop a whole lecture plaxlist bd him on one of my favorite subjects in my lap. brilliant!
Amazing teacher. I wish i could attend Dr. Tadashi Tokieda lectures live. Those students are really very lucky. Thank you for uploading this excellent lectures.
i wish my teacher back then was as dedicated. im intrigued although i was always rather bad at maths; now lets see if youtube manages to do what school failed - getting me into math. Scott Flansburg managed to spark my interest, teachers like Dr Tadashi give me hope to keep it up
Interactive Class, Professor is energetic as well as method used for set induction to explain topology is better than most of the lecturers that I have seen on you Tube.
The answer to the questions at the end of the video: If n is even, with the cut a distance d away, you will get two entangled strips of equal length (the original length), each with n twists. And the width of one strip is d, while that of the other strip is 1-d. The degree of entanglement increases with n. One of the strips crosses the centre of the other strip n times. If n is odd, with the cut a distance d away, you will get two entangled strips of unequal length. The shorter strip is of the same length as the original one, while the longer strip has twice the length. The twist and width of the shorter strip is n and d, while those of the longer strip is 2n+2 and 1-2d. The degree of entanglement increases with n. One of the strips crosses the centre of the other strip n times. I have verified my answer with a Mobius strip with 4 twists and another one with 5 twists.
wow! true teachers still exist!! such an amazing lesson. I was about to skipt the video thinking it's same old boring lectures but was captivated! I am looking for all means to take topology at my school now knowing that I can use this playlist to learn and do well! Way to go prof Tokieda and AIMS!!!
I"m not sure how this helps me, but I sure feel a lot smarter, I actually feel the urge to keep strips and scissors on me at all times to show other people my knew knowledge of twists XD
When it comes to untying the knot through cuts, that is another mathematical problem that does not feet with in the confines of topology. In topology, we deal with continuous deformation of smooth surfaces from twisted surfaces (knots) to untwisted surface(untied knots) with out discontinuities(cuts)
Awesome!! My answer to the question at the end of the video.. Q: What happens if you cut a mobius strip that is twisted 'n' times? my A: If n is an odd number (1,3,5 etc.,.), we will end up with a single strip that is connected with 4 times of n (4xn) twists If n is an even number, then we will end up with two mobius strips that are inter-linked like chain, each having n number of twists.
I'm 15 minutes and ten seconds in and I personally believe the reason the one loop is disconnected from the bigger one, is because while cutting alongside the thirds, they esentially mirrored each other when looping back around, along the "spine" of the Mobius Strip. I feel like one must imagine any action done contiunously along the spine of a mobius strip, to eventually be mirrored on the other side. I feel like because you twist 180 degrees, that causes a mirroring that allows what would previously be disconnect, to remain one.
Conservation of Spatial Curvature: Both Matter and Energy described as "Quanta" of Spatial Curvature. (A string is revealed to be a twisted cord when viewed up close.) Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree. String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension? What did some of the old clockmakers use to store the energy to power the clock? Was it a string or was it a spring? What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine. Quantum Entangled Twisted Tubules: “We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr (lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957-8, in Scientific American vol. 199, no. 3, 1958) The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with some aspects of the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”, and the work of Dr. Lisa Randall on the possibility of one extra spatial dimension? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics? When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if Quark/Gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks where the tubes are entangled? (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry. Modern physicists say the Strong Force is mediated by a constant exchange of Gluons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other. Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change. ===================== Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons? Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension? Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons . Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase. Gamma photons are produced when a tube unwinds producing electromagnetic waves. ( Mass=1/Length ) The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge. Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms. In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137. 1= Hypertubule diameter at 4D interface 137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted. The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.) How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter? Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles? I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. This topological Soliton model grew out of that simple idea. I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles. .===
Wonderful teaching skills indeed. Sir is their recommended study material along these lectures? If yes then do tell me. Also please make video lectures on differential geometry in the same way. Its just amazing to get geometrical ideas with an ideal teacher. Thanks
This doesn't even feel like a lecture and more like a magician performance. Incredibly captivating.
This is how education should be performed, it takes more time and resources but the people taught will be able to develop way better than a full class of kids doing the same exercises like the kids last year.
What resources? As I think the amazing thing is that he uses a piece of paper…chalk board…he could teach anywhere
You would be amazed how few use the piece of paper...@@markkevin7245
This is what youtube's for :)
Thank you, African Institute for Mathematics Sciences
It was sad to watch youtube lose it´s potential for critical thinking, rational inquiry and the scientific sharing of new data. I am glad that we have Bitchute now. TH-cam could have won the war against fake news and misinformation, but lost. I agree with you. These are great lectures!
Look at my African American over there. Look at him. Are you the greatest?
For complete hand written notes follow ROBEL BHATIA MATHEMATICSth-cam.com/channels/_wDGFo02ck_egU6upx6AkQ.html
@@Yatukih_001 - These are great lectures but what the hell are you talking about with Bitchute that shit site is nothing but crazy ass people posting conspiracy and hate filled garbage it has nothing of value let alone sharing anything remotely close to scientific content.
This proves that excellent teaching is also a performance art. Awesome lecture.
Topology kind of lends itself to a performing art because the transformations we discuss have to happen in time. A demonstration is always necessary in topology
Captivating lecturer. Lucky class.
Caught my attention from the first minute!!! Amazing
Very cool
Yep! Clicked on it to have it in my history and watch it tomorrow morning, ended up watching it till the end lol. Now I can't even start part 2. I really need to go to sleep haha
Einstein never nearly understood TIME, E=MC2, F=ma, gravity, or ELECTROMAGNETISM/energy.
He was, in fact, a total weasel.
c2 represents a dimension ON BALANCE, as E=MC2 IS F=ma in accordance with the following:
UNDERSTANDING THE ULTIMATE, BALANCED, TOP DOWN, AND CLEAR MATHEMATICAL UNIFICATION OF ELECTROMAGNETISM/energy AND gravity, AS E=MC2 IS CLEARLY F=ma:
The stars AND PLANETS are POINTS in the night sky. E=MC2 IS F=ma, AS this proves the term c4 from Einstein's field equations. SO, ON BALANCE, this proves the fourth dimension. ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy !!!
TIME is NECESSARILY possible/potential AND actual IN BALANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. INDEED, TIME dilation ULTIMATELY proves ON BALANCE that E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy.
Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE. Gravity IS ELECTROMAGNETISM/energy.
E=mC2 IS CLEARLY F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy !!!
By Frank DiMeglio
@@hajerjm UNDERSTANDING EXACTLY WHAT IS A TWO DIMENSIONAL SURFACE OR SPACE AS invisible AND VISIBLE IN BALANCE, AS E=MC2 IS clearly F=ma (ON BALANCE):
The stars AND PLANETS are POINTS in the night sky. Now, very carefully consider what is a galaxy. Get a good look at what is THE EYE, AND notice the black space. E=MC2 AND F=ma IN BALANCE do ALSO FUNDAMENTALLY represent (ON AVERAGE) what is a TWO DIMENSIONAL surface OR SPACE (as what is a BALANCED MIDDLE DISTANCE in/of SPACE), AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=MC2 IS F=ma. The stars AND PLANETS are POINTS in the night sky. Now, consider what is the speed of light (c) ON BALANCE. I have explained why THE PLANETS (including WHAT IS THE EARTH) move away very, very, very slightly in relation to what is THE SUN on balance, as ELECTROMAGNETISM/energy is gravity. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=MC2 IS CLEARLY and NECESSARILY F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity !!! Accordingly, the rotation of WHAT IS THE MOON matches it's revolution. It is CLEARLY proven ON BALANCE. E=MC2 IS CLEARLY F=ma ON BALANCE. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity !!! TIME dilation ULTIMATELY proves (ON BALANCE) that ELECTROMAGNETISM/energy is gravity, AS E=MC2 IS F=ma ON BALANCE !!! Indeed, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=MC2 IS F=ma IN BALANCE; AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity. (BALANCED inertia/INERTIAL RESISTANCE is fundamental.) Objects AND MEN fall at the SAME RATE (neglecting air resistance, of course), AS E=MC2 IS F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Gravity is ELECTROMAGNETISM/energy ON BALANCE. The sky is BLUE, AND what is the Earth is ALSO BLUE. Carefully consider what is a galaxy !!! Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. “Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, as ELECTROMAGNETISM/energy is gravity (ON BALANCE); as E=MC2 is CLEARLY and NECESSARILY proven to be F=ma ON BALANCE. Inertia/INERTIAL RESISTANCE is proportional to (or BALANCED with/as) GRAVITATIONAL force/ENERGY, as this balances gravity AND inertia; as ELECTROMAGNETISM/energy is gravity; as E=MC2 is CLEARLY and necessarily proven to be F=ma ON BALANCE !!! So, “dark” matter/ENERGY is plainly unnecessary; and it is idiotic. I have mathematically unified physics, as I have explained the term c4 from Einstein's field equations along WITH the fourth dimension, as ELECTROMAGNETISM/energy is CLEARLY AND necessarily proven to be gravity ON BALANCE. E=MC2 is CLEARLY proven to be F=ma IN BALANCE.
By Frank DiMeglio
Honestly, encouraging the guessing and allowing wrong answers among those is a relieving mindset to have
I don't think this can be topped. You're a gem Prof. Tadashi.
Dr Tadashi Tokieda is a great mathematician and teacher to inspire anybody who knows some math at least
Random youtube recommendation, but stayed for the whole lecture, And i am not even a maths student :)
Professor Tokieda is a real gem, we are fortunate to have his wisdom shared for free online.
'Always guess in public so that your stakes are higher.' Very clever!
Good ol' Tadashi, What a guy
Thanks to Professor and African Institute of Mathematical Science. Long live sir... I will try to understand and will teach to my students. Thanks a lot
Incredible lecturer. Please make more videos Dr. Tokieda; Mathematics needs more expositors like you!!
you not turkish turkiye best
The teacher is a real artist.......if there is smthng more than awesome then this is it....
I love this guys numberphile bits on youtube, have done so for years. And today the almighty yt algorithm decides to drop a whole lecture plaxlist bd him on one of my favorite subjects in my lap. brilliant!
I envy the students sitting there. Amazing lecture. Brilliant pedagogy!
Most engaging professor I've ever seen I'm jealous of those students they will no doubt learn more then they ever have
Not even 5 minutes in and I am learning so much. His advice on guessing in mathematics is so on point!!!
One of the best teachers i have ever seen!!!!! thank you sir!!!!
Amazing teacher. I wish i could attend Dr. Tadashi Tokieda lectures live. Those students are really very lucky. Thank you for uploading this excellent lectures.
What an amazing professor!!... really brilliant lecture...in love with his class!!
I’m a junior in high school and I’m in algebra 2 but I found this lecture very interesting
i wish my teacher back then was as dedicated. im intrigued although i was always rather bad at maths; now lets see if youtube manages to do what school failed - getting me into math.
Scott Flansburg managed to spark my interest, teachers like Dr Tadashi give me hope to keep it up
What a wonderful explanation..... a great respect for teacher
Interactive Class, Professor is energetic as well as method used for set induction to explain topology is better than most of the lecturers that I have seen on you Tube.
The answer to the questions at the end of the video:
If n is even, with the cut a distance d away, you will get two entangled strips of equal length (the original length), each with n twists. And the width of one strip is d, while that of the other strip is 1-d. The degree of entanglement increases with n. One of the strips crosses the centre of the other strip n times.
If n is odd, with the cut a distance d away, you will get two entangled strips of unequal length. The shorter strip is of the same length as the original one, while the longer strip has twice the length. The twist and width of the shorter strip is n and d, while those of the longer strip is 2n+2 and 1-2d. The degree of entanglement increases with n. One of the strips crosses the centre of the other strip n times.
I have verified my answer with a Mobius strip with 4 twists and another one with 5 twists.
I know its been 6 years but thanks
Shouldn't the longer strip in the odd case have width d and the shorter strip width 1-2d?
@EastBurningRed, yes you're right.
wow! true teachers still exist!! such an amazing lesson. I was about to skipt the video thinking it's same old boring lectures but was captivated! I am looking for all means to take topology at my school now knowing that I can use this playlist to learn and do well! Way to go prof Tokieda and AIMS!!!
This totally blew my mind, and the teacher is great!
Three cheers for Tadashi Tokieda!! Super like.
A thousand likes to this guy. Simply superb.
I'm clapping after watching this. This was more than maths, a miracle!! Bless teachers like him!
I haven't seen this in my life.. Outstanding... Unbelievable... 😊
Mathematics is a formalization of intuition. This lecture illustrates this concept brilliantly. Quite inspiring.
Brilliant ... I didnt know that one can get that much out of a Moebius strip.
This teacher is fantastic, I would love to attend this college
thanks for sharing, that man is really a great teacher
What an amazing Professor! I already watch this since 7 years ago and still amazed by his lecture. What a great teacher!
I love this method of teaching. Awesome Teacher.
26:39-27:13 this part was so amazing. Sir u have amazing humor.
Great teacher I ever seen mathematics.
I love this man! I need a lecturer like him.
Thanku Dr Tadashi Tokieda sir, topology and geometry can't be much simple than this.
Such a gem Dr. Tadashi Tokieda!!! Thank you so much!!!!
Mind blown. The universe is truly mysterious.
Great lecture
*_Respected teacher is pulling my leg._* I like this guy. Thanks! Rikki Tikki.
I wish i could attend Dr. Tadashi 's lectures live.
no go to turkiye #1 🇹🇷
,
how many time can a mobius strip surprise me
So true.
Möbius
I guess I need to go to the mobius strip club...
how can topology be so enjoyingly learnt, too good, too good..
Incredibly clear and engaging lecture. Thanks for sharing!
This was more enjoyable than I expected!
This amazing lecture helped me a lot in my research area: Gravitation and Cosmology. Huge Respect from India.
Great speaker
He is really passionate teacher
Simply Marvelous!! Excellent teacher!
Great teacher .. Thank you teacher for your efforts to make the class so interesting ... From India ....
I'm mind blown! This is amazing!
I"m not sure how this helps me, but I sure feel a lot smarter, I actually feel the urge to keep strips and scissors on me at all times to show other people my knew knowledge of twists XD
When it comes to untying the knot through cuts, that is another mathematical problem that does not feet with in the confines of topology. In topology, we deal with continuous deformation of smooth surfaces from twisted surfaces (knots) to untwisted surface(untied knots) with out discontinuities(cuts)
One of the best introductory lecutres I have seen covering the topic material, brilliant work Dr. Tokieda!
He's brilliant!
At 12:50 the student was right, the strips were going to get chained, not "entangled".
Absolutely fabulous way to teach.. Love it.
I'm not even studying geometry and yet I watched the movie video.
Awesome Lecture.
Wish this guy was my math teacher. He's great.
I wish I had teachers like you during my School Years!
Best teacher i have ever met online😄
This is absolutely amazing!! The topic, and the teacher as well!
Awesome!! My answer to the question at the end of the video..
Q: What happens if you cut a mobius strip that is twisted 'n' times?
my A: If n is an odd number (1,3,5 etc.,.), we will end up with a single strip that is connected with 4 times of n (4xn) twists
If n is an even number, then we will end up with two mobius strips that are inter-linked like chain, each having n number of twists.
The best course ever
What a class!!! Totally amazed!!
Oh my god, this is just amazing
Brilliant way of explaining things ;
Woow! I wanna attend this professor class! I usually enjoy when professors give breaks but i felt sad here to go for a break:(
I'm 15 minutes and ten seconds in and I personally believe the reason the one loop is disconnected from the bigger one, is because while cutting alongside the thirds, they esentially mirrored each other when looping back around, along the "spine" of the Mobius Strip.
I feel like one must imagine any action done contiunously along the spine of a mobius strip, to eventually be mirrored on the other side.
I feel like because you twist 180 degrees, that causes a mirroring that allows what would previously be disconnect, to remain one.
Absolutely mesmerizing!
oh, thank you, it's a very interesting and intuitive lecture🌞
Conservation of Spatial Curvature:
Both Matter and Energy described as "Quanta" of Spatial Curvature. (A string is revealed to be a twisted cord when viewed up close.)
Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree.
String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension? What did some of the old clockmakers use to store the energy to power the clock? Was it a string or was it a spring?
What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine.
Quantum Entangled Twisted Tubules:
“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr
(lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957-8, in Scientific American vol. 199, no. 3, 1958)
The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with some aspects of the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”, and the work of Dr. Lisa Randall on the possibility of one extra spatial dimension? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics?
When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if Quark/Gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks where the tubes are entangled? (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry.
Modern physicists say the Strong Force is mediated by a constant exchange of Gluons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other.
Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change.
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Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons?
Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension?
Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons
. Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase.
Gamma photons are produced when a tube unwinds producing electromagnetic waves. ( Mass=1/Length )
The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge.
Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms.
In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.
1= Hypertubule diameter at 4D interface
137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.
The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)
How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter?
Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles?
I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. This topological Soliton model grew out of that simple idea. I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles.
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Great teacher...
I really enjoy this lesson 👍❤❤❤🎉🎉🎉
Amazing class, like others have said.
Tokieda is a legend!
This is just amazing!
Wonderful teaching skills indeed. Sir is their recommended study material along these lectures? If yes then do tell me. Also please make video lectures on differential geometry in the same way. Its just amazing to get geometrical ideas with an ideal teacher. Thanks
wow this is so brilliant!
Extraordinary class.
he made it very intuitive!!
Thumbs up from numberphile!!
Topology is truly great ^^
Fantastic lecture.
Excellent teacher
This is very amazing
Thank You Professor.
wow excellent
This is awesome !
Very nice. Fantastic Dr Tadashi
Fantastic teaching
Can you say which book to follow?
excellent teaching
Loved it .Awesome teacher
awesome interpretation
wonderful lesson!!!
Great lecture