So far i've watched 3-4 videos on homology/cohomology and they all had creepy music playing in the back and just an eerie vibe. From now on it will forever be creepy math for me
Thanks for watching! As of this video, I've just finished my first year of college, and by no means am a master on the subject- in fact I'm hoping to learn by making these sorts of instructional videos. I'm sure that there are inaccuracies, so I'd really appreciate it if you could let me know in the comments. I'll pin them and make sure they are addressed, so myself and others don't make the same mistake. Feel free to ask questions too!
I think you need to explain more why the integral is not zero in the second case and is zero in the third case. And why is desirable that the fundamental theorem of calculus holds in an arbitrary space? In the second case it doesn't hold but you can still calculate the integral, so what would be the advantage of the Fundamental theorem?
For the (y, 0) vector field (3:14) it was unclear exactly what was being integrated and with respect to what? I assume we are integrating "y" with respect to theta along the circle? OK, later (7:19) I noticed that you are integrating y dx + 0 dy which is the line integral of the tangential component of the vector field with respect to the arc length in the language of vector calculus. I don't know if it is the same thing in the language of differential forms---I am still confused about whether "dx" in differential forms refers to an infinitesimal or a basis of a co-vector. Thanks.
Vectors are dual to co-vectors. Homology is dual to cohomology. Electro is dual to magnetic -- Maxwell's equations. Positive is dual to negative -- electric charge. North poles are dual to south poles -- magnetic fields. Electro-magnetic energy or light, photons are inherently dual -- wave/particle or quantum duality. Particles are dual to anti-particles, spin up is dual to spin down -- Dirac equation. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality). Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. Space is dual to time -- Einstein. Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Curvature or gravitational energy is therefore dual. Potential energy is dual to kinetic energy. Apples fall to the ground because they are conserving duality. Action is dual to reaction -- Sir Isaac Newton. "Always two there are" -- Yoda.
@@Sidionian Homology:- reducing the number of dimensions or states is a convergent or syntropic process. Co-homology:-increasing the number of dimensions or states is a divergent or entropic process. Syntropy (convergent, homology) is dual to entropy (divergent, co-homology) -- the 4th law of thermodynamics! Teleological physics (syntropy) is dual to non teleological physics (entropy). The 4th law of thermodynamics is hardwired into mathematics and mathematical thinking. The word co means mutual and implies duality. Sine is dual to cosine (mutual sine). Perpendicularity, orthogonality = duality. The inner product is dual to the cross product -- Maxwell's equations for EM waves. Electro is dual to magnetic -- EM waves or photons are dual, pure energy = duality. Null vectors (lines, space/time) are dual to null points (twistor space, spinors) -- Roger Penrose. Points are dual to lines -- the principle of duality in geometry. Null points (space/time) are dual to null lines (twistor space) -- Roger Penrose. Twistor space is an equivalent or dual description of space/time. Space is dual to time -- Einstein. The integers or real numbers are self dual:- ruclips.net/video/AxPwhJTHxSg/видео.html Duality creates reality. If I am a clown, then what does that make you? There are new laws of physics and everything in physics is made from duality (energy). Waves are dual to particles -- quantum duality or pure energy is duality, duality is energy.
@@Sidionian Mathematics and the force of gravity are empirical proof that duality is real. Classical reality is dual to quantum reality synthesizes true reality -- Roger Penrose. Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic. Roger Penrose is using the Hegelian dialectic here -- metaphysics. "Philosophy is dead!" -- Stephen Hawking. Roger Penrose is not allowed to use metaphysics according to Stephen Hawking. Antinomy (duality) is two truths that contradict each other -- Immanuel Kant. Absolute truth is dual to relative truth -- Hume's fork.
Happy to! Though I have to apologize in advance for the *extremely* messy code- I wasn't planning on someone asking to see it. github.com/treemcgee42/animations/blob/master/derahm2.py
![FNAF vs TF2 - Episode 2 [SFM]](http://i.ytimg.com/vi/z5b3V2-VLb0/mqdefault.jpg)
So far i've watched 3-4 videos on homology/cohomology and they all had creepy music playing in the back and just an eerie vibe. From now on it will forever be creepy math for me
Thanks for watching! As of this video, I've just finished my first year of college, and by no means am a master on the subject- in fact I'm hoping to learn by making these sorts of instructional videos. I'm sure that there are inaccuracies, so I'd really appreciate it if you could let me know in the comments. I'll pin them and make sure they are addressed, so myself and others don't make the same mistake. Feel free to ask questions too!
I think you need to explain more why the integral is not zero in the second case and is zero in the third case. And why is desirable that the fundamental theorem of calculus holds in an arbitrary space? In the second case it doesn't hold but you can still calculate the integral, so what would be the advantage of the Fundamental theorem?
Are you using Tau creatures?
Dude, this is awsome! Thanks for bringing that up, cohomology gives me nightmares, but this clear the hole thing. Do no stop that amazing job.
super glad i found this channel, please keep them coming! great work :)
Totally!
For the (y, 0) vector field (3:14) it was unclear exactly what was being integrated and with respect to what? I assume we are integrating "y" with respect to theta along the circle? OK, later (7:19) I noticed that you are integrating y dx + 0 dy which is the line integral of the tangential component of the vector field with respect to the arc length in the language of vector calculus. I don't know if it is the same thing in the language of differential forms---I am still confused about whether "dx" in differential forms refers to an infinitesimal or a basis of a co-vector. Thanks.
Excellent! I can sense the great content there will be on this channel in the near future.
Please continue making videos
oh man, watching this I was so looking forward to the rest of the parts! Any chance you'll be doing those videos? Please?!
Excellent cursory introductory look at a complex subject. It's all starting to take shape in my mind.
Nice job!
This is absolutely beautiful!
Hi! Seems like a small channel at the moment but great content here :D
2:02 3B1B character?
loved it!
why only one video :)) loved the explanation
Feels like a sad story
Surface(cos(u/2)cos(v),cos(u/2)sin(v),sin(u)/2),u,0,2pi,v,0,2pi
good work man!
Vectors are dual to co-vectors.
Homology is dual to cohomology.
Electro is dual to magnetic -- Maxwell's equations.
Positive is dual to negative -- electric charge.
North poles are dual to south poles -- magnetic fields.
Electro-magnetic energy or light, photons are inherently dual -- wave/particle or quantum duality.
Particles are dual to anti-particles, spin up is dual to spin down -- Dirac equation.
Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality).
Energy is dual to mass -- Einstein.
Dark energy is dual to dark matter.
Space is dual to time -- Einstein.
Positive curvature is dual to negative curvature -- Gauss, Riemann geometry.
Curvature or gravitational energy is therefore dual.
Potential energy is dual to kinetic energy.
Apples fall to the ground because they are conserving duality.
Action is dual to reaction -- Sir Isaac Newton.
"Always two there are" -- Yoda.
You're a funny little clown aren't you
@@Sidionian Homology:- reducing the number of dimensions or states is a convergent or syntropic process.
Co-homology:-increasing the number of dimensions or states is a divergent or entropic process.
Syntropy (convergent, homology) is dual to entropy (divergent, co-homology) -- the 4th law of thermodynamics!
Teleological physics (syntropy) is dual to non teleological physics (entropy).
The 4th law of thermodynamics is hardwired into mathematics and mathematical thinking.
The word co means mutual and implies duality.
Sine is dual to cosine (mutual sine).
Perpendicularity, orthogonality = duality.
The inner product is dual to the cross product -- Maxwell's equations for EM waves.
Electro is dual to magnetic -- EM waves or photons are dual, pure energy = duality.
Null vectors (lines, space/time) are dual to null points (twistor space, spinors) -- Roger Penrose.
Points are dual to lines -- the principle of duality in geometry.
Null points (space/time) are dual to null lines (twistor space) -- Roger Penrose.
Twistor space is an equivalent or dual description of space/time.
Space is dual to time -- Einstein.
The integers or real numbers are self dual:-
ruclips.net/video/AxPwhJTHxSg/видео.html
Duality creates reality.
If I am a clown, then what does that make you?
There are new laws of physics and everything in physics is made from duality (energy).
Waves are dual to particles -- quantum duality or pure energy is duality, duality is energy.
@@Sidionian Mathematics and the force of gravity are empirical proof that duality is real.
Classical reality is dual to quantum reality synthesizes true reality -- Roger Penrose.
Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
Roger Penrose is using the Hegelian dialectic here -- metaphysics.
"Philosophy is dead!" -- Stephen Hawking.
Roger Penrose is not allowed to use metaphysics according to Stephen Hawking.
Antinomy (duality) is two truths that contradict each other -- Immanuel Kant.
Absolute truth is dual to relative truth -- Hume's fork.
Amazing!
Love your vid
+loved your voice
Spetacular!
Nice!
Hole at infinity?
please , make enphasis on intuitive explanation of what is cohomology and concrete with clear calculus,simple ones
can you share your source code?
Happy to! Though I have to apologize in advance for the *extremely* messy code- I wasn't planning on someone asking to see it.
github.com/treemcgee42/animations/blob/master/derahm2.py
Your voice ♡♡♡♡♡
👩🏻💻👨🏾💻
Too much music, too little information.
Why are you doing everything to put one to sleep?! Is this some weird ASMR math channel?! Also, why steal from other creators?