My math professor was an engineer and mathematician and alluded to the power of this that you're talking about. He even had the picture of Vladimir Arnold on his desk because he respected his results so much.
@Gennady Arshad Notowidigdo Just a question. Do you know any other more rigorous courses online about the subject or is this most likely going to be the most rigorous one. Let me know if there is a better course on the subject, then I will follow that one. If not, I'm very happy with this one.
@@johnstroughair2816 This video series starts with infinite processes, wich Norman Wildberger doesn't believe in. In that sense, this course will be more rigorous since, finite processes are more rigorous, in my opinion. th-cam.com/video/eBq_DeJHfiU/w-d-xo.html&ab_channel=JonathanEvans
Professor Wildberger, I'm not a mathematician, I am a retired machinist and have always been interested in the beauty of the Platonic solids, so much so that I have made a precise set of them out of brass with others nested inside, like Russian dolls. perhaps if you are so inclined you may care to look at them on TH-cam. With your permission I would leave link. Keep up the great work, although most of it is over my head...I'm only self taught up to calculus, level 3, and getting on a bit...73.
I have been digging into the Wolfram Physics Project which has led me to diving deeper on graphs and category theory. A few days ago, I said to myself, "I wish Dr Wildberger would cover this subject." And here we are :)
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. Points are dual to lines -- the principle of duality in geometry! Symmetry is dual to conservation -- the duality of Noether's theorem. Symmetry is dual to anti-symmetry. Spin statistics theorem:- Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- wave/particle or quantum duality. Bosons are dual to Fermions. Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic. The proton (thesis) is dual to the electron (anti-thesis) synthesizes the photon or pure energy -- atomic duality. Pure energy or photons of light are a bi-product of conserving duality! Injective is dual to surjective creates bijective (isomorphism). Being is dual to non-being creates becoming -- Plato. "Reflections preserve perpendicularity (duality) in hyperbolic geometry" -- Professor Norman Wildberger, universal hyperbolic geometry. You are the same person now but different compared to a few hours ago. The passage of time means that you are a different person (time duality) but still the same. Same is dual to different. Personal identity or the self is a dual construct. Absolute time (Galileo) is dual to relative time (Einstein) -- time duality. "Always two there are" -- Yoda.
@@phiarchitect Not necessarily, not in the context that I am stating here. You can join the two dual points to form a circle -- topology. Homology is dual to co-homology. Boundaries, limits -- homology. There is a pattern of duality hardwired into physics & mathematics:- Mind (the internal soul, syntropy) is dual to matter (the external soul, entropy) -- Descartes. Convergence (syntropy) is dual to divergence (entropy). Syntropy (prediction, projection) is dual to increasing entropy -- the 4th law of thermodynamics! Teleological physics (syntropy) is dual to non-teleological physics (entropy). Randomness (entropy, uncertainty) is dual to order (syntropy, certainty) -- the Heisenberg certainty/uncertainty principle. Energy is dual to mass -- Einstein. Dark energy is dual to dual matter. When you have a good grasp of duality you can create new laws of physics! Y = X. Y is equal to X. Y is the same, similar, equivalent or dual to X. Same is dual to different. Y is dual to X. All mathematical equations are dualities! Integration (syntropy, convergence) is dual to differentiation (entropy, divergence).
@@hyperduality2838 I am intrigued by all of what you are saying. But let's just consider a point and a line as a dual (as NJW defines in hyperbolic geometry). From the relationship of a line and a circle, one can derive the dual point. And from a point and a circle, one can derive the dual line. The circle is the context for the duality. But is it possible to determine the circle, if you have just the point and the line?
24:00 the most extreme state at the bottom looks like discrete solution of the Laplace's equation. Interesting is also that mutating system never reaches synchronization, there is no fixed point during evolution, only a set of antisymmetric couples. It then appears as oscillating system.
Hi Norman! I watched the video. It looks a very interesting subject since it seems that has connections with physics!I have some questions related with the graphs but these maybe clarified in the future videos.....:)
Points are dual to lines -- the principle of duality in geometry! Symmetry is dual to conservation -- the duality of Noether's theorem. Symmetry is dual to anti-symmetry. Spin statistics theorem:- Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- wave/particle or quantum duality. Bosons are dual to Fermions. Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic. The proton (thesis) is dual to the electron (anti-thesis) synthesizes the photon or pure energy -- atomic duality. Pure energy or photons of light are a bi-product of conserving duality! Injective is dual to surjective creates bijective (isomorphism). Being is dual to non-being creates becoming -- Plato. "Reflections preserve perpendicularity (duality) in hyperbolic geometry" -- Professor Norman Wildberger, universal hyperbolic geometry. You are the same person now but different compared to a few hours ago. The passage of time means that you are a different person (time duality) but still the same. Same is dual to different. Personal identity or the self is a dual construct. Absolute time (Galileo) is dual to relative time (Einstein) -- time duality. "Always two there are" -- Yoda.
Points are dual to lines -- the principle of duality in geometry! Symmetry is dual to conservation -- the duality of Noether's theorem. Symmetry is dual to anti-symmetry. Spin statistics theorem:- Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- wave/particle or quantum duality. Bosons are dual to Fermions. Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic. The proton (thesis) is dual to the electron (anti-thesis) synthesizes the photon or pure energy -- atomic duality. Pure energy or photons of light are a bi-product of conserving duality! Injective is dual to surjective creates bijective (isomorphism). Being is dual to non-being creates becoming -- Plato. "Reflections preserve perpendicularity (duality) in hyperbolic geometry" -- Professor Norman Wildberger, universal hyperbolic geometry. You are the same person now but different compared to a few hours ago. The passage of time means that you are a different person (time duality) but still the same. Same is dual to different. Personal identity or the self is a dual construct. Absolute time (Galileo) is dual to relative time (Einstein) -- time duality. "Always two there are" -- Yoda.
Thanks from Algeria❤❤❤. I want to tell that i watch your course about homotopy and covering space now, i'm phd student, do you have an email to communicate with you
Norman tends to be very busy. I'm in contact with him through patreon. So if you donate a little bit every month you get to see the videos earlier and more videos. Then you can comment on the videos on patreon and maybe help out as a volunteer if you feel like it. So lot's of opportunities there.
Developing an algebra to describe tiling/packing puzzles like tetrominoes, pentominoes and the Soma cube using a graph mutation process seems like a doable thing. A graph mutation that shows four tetromino "Tee"s can tile a square would be a very nice start. (for me to do...not you) Tilings of rectangles with T-tetrominoes www.math.ucla.edu/~pak/papers/ttet11.pdf Thank you so much for the inspiration and direction.
Is this what this GO game is about ? Math is more at position juxtaposed to other position? Or is that a logic test? I would like to learn actual math. Perhaps I can't . Though the algebraic calculus is at least a degree better than the classical calc. By one degree better, at least.
I think I do not know what it means to describe the set of roots of a graph. I have taken the problem example. I wrote a computer program to start with each possible singleton 1000 0100 0010 0001 To do this I setup a matrix to describe this graph - it is -1 0 1 1 0 -1 1 0 1 1 -1 1 1 0 1 -1 This way I can take the singleton and 'multiply it' by this matrix and get the mutation The -1 gives the required subtraction and the 1 are where the nodes must be added So that makes the programming easy. Then I ran it for a depth of 50 on each singleton - stopping any search if I found a result I already had Starting with 1000 by these 19 mutations on nodes 0,2,0,1,0,3,0,1,0,2,0,1,0,3,1,0,2,0,2,3 I get the singleton 0001 Starting with 0100 by these 6 mutations on nodes 0,1,2,0,1,0,2 I get the singleton 0,0,1,0 Starting with 0010 by these 9 mutations on nodes 0,1,0,1,2,0,1,0,2,1 I get the singleton 0,1,0,0 (I know should just be the reverse of the previous line but that is not the issue that concerns me) Starting with 0001 by these 39 mutations on nodes 0,2,0,1,0,3,0,1,0,2,0,1,0,2,0,1,2,0,1,0,2,0,1,0,3,0,1,3,0,1,2,0,1,0,3,1,2,0,1,2 I return to the singleton 0001 But my query is, what does it mean to 'describe the set of roots'? How is one meant to present them? If one starts with a singleton and by a series of mutations ends up with another singleton does that mean one has described the 'set of roots'? Is there then a problem to see how the number of mutations from one singleton to another can be minimised or maximised? Or is one trying to maximise the sum of the node elements from each singleton? In what way should I alter the program to present 'the set of roots'? Thanks for your help.
The question to is space-time discrete is long answered, it is, just because physicists keep using the stupid continuum maths for everything, doesn't mean that they don't realize it. Carlo Rovelli talks about this extensively in en.wikipedia.org/wiki/Reality_Is_Not_What_It_Seems Do not let mathematicians and bad philosophers confuse you. Physics experiments long proved that our universe is not deterministic and is essentially quantized, not continuous. Anyone says otherwise is ignorant at best, willfully malevolent at worst. Many people would have to give up their positions if people would stop believing not just the 'big infinites' that extend limitlessly, but also the small infinites, that are required for all the BS continuum we invent to explain our own subjective world.
Those are some words. But anyone who thinks anything is ever "proved" in the natural sciences is also ignorant at best and willfully malevolent at worst; that is not what science does, or can do, so please don't portray it as such.
@@landsgevaer well, sure, I forgot I am talking to mathematicians, I retract the word 'proved' and replace it 'has shown'. Are you happier? Is this really the best you can do? Nitpickingly select a single word to attack, instead of responding to the actual content?
@@ashnur Your content was very confident and sure. I don't think that is warranted since we don't really have *any* solid fundamental theory of the nature of space and time that includes both it "discreteness" and its "curviness". So I think that even "has shown" is too strong. "Suggests" seems appropriate. At best we have some descriptions that fit reality very well (but not exactly) under some fair number of circumstances (but not all) and these suggest spacetime is not as smooth as generally thought. So we may hypothesize that actual spacetime has a discrete-like nature too. How, we don't fully know; not like it can be subdivided into tiny Planck cubelets, likely. It seems more like it may be limited in the amount of information that it contains. Who knows... Being nuanced about how confident and exact you are about theories is a hallmark of science, just as much (and likely more) as the actual content of its best descriptive models are. Insisting on that is not pettiness.
"Mathematics as such is always a measure, not the thing measured" - Wittgenstein. Planck scale does not give concrete metric, real numbers are bogus, Zeno's proof holds. As for philosophy, continuity =/= infinity. Discrete can be coherently derived from continua, but not vice versa.
Most importantly, before I write any more, thank you for taking your time for an actual response. It does matter. tl;dr: the past and the future cannot be part of the present, but our brain paints such a picture, we understand the world using our brain which sees only what's continuous, so language and mathematics inherited this bias and we have to fight it constantly. I did not say we can describe reality "exactly" or "in all circumstances", so I am not sure why you have to go there. My confidence goes so far, that I can say, if someone shows me something that's continuous, I will have to change my mind. Otherwise, it will be really hard. What I did say was that the theory that the world is continuous leads to consequences that were disproven. I hope that's correct phraseology for you? No amount of experimenting can fully prove something, but even one counterexample can disprove something? I believe this is what happened to the continuous worldview. If the world would be continuous we would expect certain facts to be such and such, and we find the exact opposite. Apart from pointing to Rovelli and others who say the exact same thing as me, and probably could give much better arguments why they believe it so, I can also give my very simple reasoning, but I am afraid you will question every bit of information. Anyway, here it goes: reality cannot be continuous, because that would mean that the past and the future are real things (otherwise how could be continuously connected to the present?) and because we also know that reality at least at one level is not deterministic (e.g. the past and the future are not clearly defined based on the present) these two assumptions cannot be both true at the same time. I know that this fact is hard to swallow, I see smart people go so far to believe in such things as the 'multiverse' just to be able to keep believing in the reality of the continuum. On a much less philosophical note, one would expect smart people to notice a trend where physicists assume something is continuous and then have to change everything to quantized to make the equations work. Ultraviolet catastrophe, electron orbitals, Feynman diagrams, P!=NP just to name a few cases where if the world would be continuous, we would have to deal with very different problems. Furthermore, partly my confidence stems not from what I know from physics, but on what I know from personal experience. Our brain's main feature is to take an unimaginably large amount of information and to produce a 'continuous' experience from it. Basically, almost anything we perceive is through this. It's our brain that presents things as continuous, and creates the illusion of 'present' time that holds everything that's continuous. The fact is, that the A series of time cannot be correct, it yields clearly false assumptions, like the 'universal present'. I hope at least about this we can agree? But our brain creates the experience of the A series of time and our language is 100% built on it. You can observe the problems that stem from this in almost every minute of our daily lives, no need to be a scientist for it. So I just said, wait a minute, if I compensate for this, if I compensate for my biology expecting everything to be static, what is the alternative? And the alternative is that everything is a process, like Whitehead said. "There is becoming of continuity but no continuity of becoming" And lastly, what convinced me before everything else was the immense usefulness of this worldview, how it simplifies a lot of human problems to simple misunderstanding that can be corrected if all participants are willing, instead of arguing over whose worldview is the more 'real'.
@Gennady Arshad Notowidigdo no there is more, but I leave that as an exercise for the viewer. Also I enjoy watching math videos when they film it while taking a 💩 😉
Points are dual to lines -- the principle of duality in geometry! Symmetry is dual to conservation -- the duality of Noether's theorem. Symmetry is dual to anti-symmetry. Spin statistics theorem:- Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- wave/particle or quantum duality. Bosons are dual to Fermions. Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic. The proton (thesis) is dual to the electron (anti-thesis) synthesizes the photon or pure energy -- atomic duality. Pure energy or photons of light are a bi-product of conserving duality! Injective is dual to surjective creates bijective (isomorphism). Being is dual to non-being creates becoming -- Plato. "Reflections preserve perpendicularity (duality) in hyperbolic geometry" -- Professor Norman Wildberger, universal hyperbolic geometry. You are the same person now but different compared to a few hours ago. The passage of time means that you are a different person (time duality) but still the same. Same is dual to different. Personal identity or the self is a dual construct. Absolute time (Galileo) is dual to relative time (Einstein) -- time duality. "Always two there are" -- Yoda.
@Gennady Arshad Notowidigdo Listen, I am very appreciative of what this man is doing and because I trust him, and I know that he is smart and strong. I am asking him more quickly because he is great and I am young so I want to learn from him as much as possible.
My math professor was an engineer and mathematician and alluded to the power of this that you're talking about. He even had the picture of Vladimir Arnold on his desk because he respected his results so much.
Yesss ! I love this stuff ! It is such a thrill that there is going to be a rigorous course on the subject on the internet !
@Gennady Arshad Notowidigdo I guess the rational
algebraic approach of Norman seems rigorous to me in general
@Gennady Arshad Notowidigdo what is the name of that book ?
@Gennady Arshad Notowidigdo Just a question. Do you know any other more rigorous courses online about the subject or is this most likely going to be the most rigorous one. Let me know if there is a better course on the subject, then I will follow that one. If not, I'm very happy with this one.
There is a very standard discussion of Lie Algebras in a TH-cam course by Jonathan Evans.
@@johnstroughair2816 This video series starts with infinite processes, wich Norman Wildberger doesn't believe in. In that sense, this course will be more rigorous since, finite processes are more rigorous, in my opinion. th-cam.com/video/eBq_DeJHfiU/w-d-xo.html&ab_channel=JonathanEvans
Professor Wildberger, I'm not a mathematician, I am a retired machinist and have always been interested in the beauty of the Platonic solids, so much so that I have made a precise set of them out of brass with others nested inside, like Russian dolls. perhaps if you are so inclined you may care to look at them on TH-cam. With your permission I would leave link. Keep up the great work, although most of it is over my head...I'm only self taught up to calculus, level 3, and getting on a bit...73.
There at the end of this series th-cam.com/video/EvP8VtyhzXs/w-d-xo.html&ab_channel=InsightsintoMathematics
I have been digging into the Wolfram Physics Project which has led me to diving deeper on graphs and category theory. A few days ago, I said to myself, "I wish Dr Wildberger would cover this subject." And here we are :)
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.
Points are dual to lines -- the principle of duality in geometry!
Symmetry is dual to conservation -- the duality of Noether's theorem.
Symmetry is dual to anti-symmetry.
Spin statistics theorem:- Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- wave/particle or quantum duality.
Bosons are dual to Fermions.
Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
The proton (thesis) is dual to the electron (anti-thesis) synthesizes the photon or pure energy -- atomic duality.
Pure energy or photons of light are a bi-product of conserving duality!
Injective is dual to surjective creates bijective (isomorphism).
Being is dual to non-being creates becoming -- Plato.
"Reflections preserve perpendicularity (duality) in hyperbolic geometry" -- Professor Norman Wildberger, universal hyperbolic geometry.
You are the same person now but different compared to a few hours ago. The passage of time means that you are a different person (time duality) but still the same. Same is dual to different. Personal identity or the self is a dual construct.
Absolute time (Galileo) is dual to relative time (Einstein) -- time duality.
"Always two there are" -- Yoda.
@@hyperduality2838 this is a fascinating list! Thanks.
@@hyperduality2838 >Points are dual to lines
the duality of points and lines requires the presence of a circle, correct?
@@phiarchitect Not necessarily, not in the context that I am stating here. You can join the two dual points to form a circle -- topology.
Homology is dual to co-homology.
Boundaries, limits -- homology.
There is a pattern of duality hardwired into physics & mathematics:-
Mind (the internal soul, syntropy) is dual to matter (the external soul, entropy) -- Descartes.
Convergence (syntropy) is dual to divergence (entropy).
Syntropy (prediction, projection) is dual to increasing entropy -- the 4th law of thermodynamics!
Teleological physics (syntropy) is dual to non-teleological physics (entropy).
Randomness (entropy, uncertainty) is dual to order (syntropy, certainty) -- the Heisenberg certainty/uncertainty principle.
Energy is dual to mass -- Einstein.
Dark energy is dual to dual matter.
When you have a good grasp of duality you can create new laws of physics!
Y = X.
Y is equal to X. Y is the same, similar, equivalent or dual to X. Same is dual to different. Y is dual to X.
All mathematical equations are dualities!
Integration (syntropy, convergence) is dual to differentiation (entropy, divergence).
@@hyperduality2838 I am intrigued by all of what you are saying. But let's just consider a point and a line as a dual (as NJW defines in hyperbolic geometry). From the relationship of a line and a circle, one can derive the dual point. And from a point and a circle, one can derive the dual line. The circle is the context for the duality. But is it possible to determine the circle, if you have just the point and the line?
Wow very magic and intriguing - marvellous! :)
The way you talk about it is so interesting to listen!
You make it so simple, easy to understand!
24:00 the most extreme state at the bottom looks like discrete solution of the Laplace's equation. Interesting is also that mutating system never reaches synchronization, there is no fixed point during evolution, only a set of antisymmetric couples. It then appears as oscillating system.
been waiting on a video like this seem like 2015!!!
Interesting mix of the concrete and abstract.
Hi Norman! I watched the video. It looks a very interesting subject since it seems that has connections with physics!I have some questions related with the graphs but these maybe clarified in the future videos.....:)
Points are dual to lines -- the principle of duality in geometry!
Symmetry is dual to conservation -- the duality of Noether's theorem.
Symmetry is dual to anti-symmetry.
Spin statistics theorem:- Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- wave/particle or quantum duality.
Bosons are dual to Fermions.
Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
The proton (thesis) is dual to the electron (anti-thesis) synthesizes the photon or pure energy -- atomic duality.
Pure energy or photons of light are a bi-product of conserving duality!
Injective is dual to surjective creates bijective (isomorphism).
Being is dual to non-being creates becoming -- Plato.
"Reflections preserve perpendicularity (duality) in hyperbolic geometry" -- Professor Norman Wildberger, universal hyperbolic geometry.
You are the same person now but different compared to a few hours ago. The passage of time means that you are a different person (time duality) but still the same. Same is dual to different. Personal identity or the self is a dual construct.
Absolute time (Galileo) is dual to relative time (Einstein) -- time duality.
"Always two there are" -- Yoda.
Can't wait to start this course, looks so intersesting. Some dates already? looking forward to liftoff
Could you talk about the so-called graph Lie algebra and its relation with your work?
I'm looking forward this lecture!!
Points are dual to lines -- the principle of duality in geometry!
Symmetry is dual to conservation -- the duality of Noether's theorem.
Symmetry is dual to anti-symmetry.
Spin statistics theorem:- Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- wave/particle or quantum duality.
Bosons are dual to Fermions.
Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
The proton (thesis) is dual to the electron (anti-thesis) synthesizes the photon or pure energy -- atomic duality.
Pure energy or photons of light are a bi-product of conserving duality!
Injective is dual to surjective creates bijective (isomorphism).
Being is dual to non-being creates becoming -- Plato.
"Reflections preserve perpendicularity (duality) in hyperbolic geometry" -- Professor Norman Wildberger, universal hyperbolic geometry.
You are the same person now but different compared to a few hours ago. The passage of time means that you are a different person (time duality) but still the same. Same is dual to different. Personal identity or the self is a dual construct.
Absolute time (Galileo) is dual to relative time (Einstein) -- time duality.
"Always two there are" -- Yoda.
My goodness how interesting.
Is here a version of Hilbert space that is a root system?
really cool
BTW how do you sign up for these courses? I didn’t see a link anywhere.
I am using an iPad and I don’t see that tab.
Can't wait :)
Thanks from Algeria❤❤❤. I want to tell that i watch your course about homotopy and covering space now, i'm phd student, do you have an email to communicate with you
Norman tends to be very busy. I'm in contact with him through patreon. So if you donate a little bit every month you get to see the videos earlier and more videos. Then you can comment on the videos on patreon and maybe help out as a volunteer if you feel like it. So lot's of opportunities there.
@@ChrisDjangoConcerts Okay Thank you very much bro!!!
Developing an algebra to describe tiling/packing puzzles like tetrominoes, pentominoes and the Soma cube using a graph mutation process seems like a doable thing.
A graph mutation that shows four tetromino "Tee"s can tile a square would be a very nice start. (for me to do...not you)
Tilings of rectangles with T-tetrominoes www.math.ucla.edu/~pak/papers/ttet11.pdf
Thank you so much for the inspiration and direction.
fascinating
Could you add subscripts? It would help me.
Why are we calling this perturbation a 'mutation', would it not be better described as a vibration?
Is this what this GO game is about ? Math is more at position juxtaposed to other position?
Or is that a logic test? I would like to learn actual math. Perhaps I can't . Though the algebraic calculus is at least a degree better than the classical calc. By one degree better, at least.
I think I do not know what it means to describe the set of roots of a graph.
I have taken the problem example.
I wrote a computer program to start with each possible singleton 1000 0100 0010 0001
To do this I setup a matrix to describe this graph - it is
-1 0 1 1
0 -1 1 0
1 1 -1 1
1 0 1 -1
This way I can take the singleton and 'multiply it' by this matrix and get the mutation
The -1 gives the required subtraction and the 1 are where the nodes must be added
So that makes the programming easy.
Then I ran it for a depth of 50 on each singleton - stopping any search if I found a result I already had
Starting with 1000 by these 19 mutations on nodes 0,2,0,1,0,3,0,1,0,2,0,1,0,3,1,0,2,0,2,3 I get the singleton 0001
Starting with 0100 by these 6 mutations on nodes 0,1,2,0,1,0,2 I get the singleton 0,0,1,0
Starting with 0010 by these 9 mutations on nodes 0,1,0,1,2,0,1,0,2,1 I get the singleton 0,1,0,0
(I know should just be the reverse of the previous line but that is not the issue that concerns me)
Starting with 0001 by these 39 mutations on nodes 0,2,0,1,0,3,0,1,0,2,0,1,0,2,0,1,2,0,1,0,2,0,1,0,3,0,1,3,0,1,2,0,1,0,3,1,2,0,1,2 I return to the singleton 0001
But my query is, what does it mean to 'describe the set of roots'?
How is one meant to present them?
If one starts with a singleton and by a series of mutations ends up with another singleton does that mean one has described the 'set of roots'?
Is there then a problem to see how the number of mutations from one singleton to another can be minimised or maximised?
Or is one trying to maximise the sum of the node elements from each singleton?
In what way should I alter the program to present 'the set of roots'?
Thanks for your help.
Isn’t that best understood by100077201
1002003004. Is also interesting
The question to is space-time discrete is long answered, it is, just because physicists keep using the stupid continuum maths for everything, doesn't mean that they don't realize it. Carlo Rovelli talks about this extensively in en.wikipedia.org/wiki/Reality_Is_Not_What_It_Seems
Do not let mathematicians and bad philosophers confuse you. Physics experiments long proved that our universe is not deterministic and is essentially quantized, not continuous. Anyone says otherwise is ignorant at best, willfully malevolent at worst. Many people would have to give up their positions if people would stop believing not just the 'big infinites' that extend limitlessly, but also the small infinites, that are required for all the BS continuum we invent to explain our own subjective world.
Those are some words. But anyone who thinks anything is ever "proved" in the natural sciences is also ignorant at best and willfully malevolent at worst; that is not what science does, or can do, so please don't portray it as such.
@@landsgevaer well, sure, I forgot I am talking to mathematicians, I retract the word 'proved' and replace it 'has shown'. Are you happier? Is this really the best you can do? Nitpickingly select a single word to attack, instead of responding to the actual content?
@@ashnur Your content was very confident and sure. I don't think that is warranted since we don't really have *any* solid fundamental theory of the nature of space and time that includes both it "discreteness" and its "curviness".
So I think that even "has shown" is too strong. "Suggests" seems appropriate. At best we have some descriptions that fit reality very well (but not exactly) under some fair number of circumstances (but not all) and these suggest spacetime is not as smooth as generally thought. So we may hypothesize that actual spacetime has a discrete-like nature too. How, we don't fully know; not like it can be subdivided into tiny Planck cubelets, likely. It seems more like it may be limited in the amount of information that it contains. Who knows...
Being nuanced about how confident and exact you are about theories is a hallmark of science, just as much (and likely more) as the actual content of its best descriptive models are. Insisting on that is not pettiness.
"Mathematics as such is always a measure, not the thing measured" - Wittgenstein.
Planck scale does not give concrete metric, real numbers are bogus, Zeno's proof holds.
As for philosophy, continuity =/= infinity. Discrete can be coherently derived from continua, but not vice versa.
Most importantly, before I write any more, thank you for taking your time for an actual response. It does matter.
tl;dr: the past and the future cannot be part of the present, but our brain paints such a picture, we understand the world using our brain which sees only what's continuous, so language and mathematics inherited this bias and we have to fight it constantly.
I did not say we can describe reality "exactly" or "in all circumstances", so I am not sure why you have to go there. My confidence goes so far, that I can say, if someone shows me something that's continuous, I will have to change my mind. Otherwise, it will be really hard.
What I did say was that the theory that the world is continuous leads to consequences that were disproven. I hope that's correct phraseology for you? No amount of experimenting can fully prove something, but even one counterexample can disprove something? I believe this is what happened to the continuous worldview. If the world would be continuous we would expect certain facts to be such and such, and we find the exact opposite.
Apart from pointing to Rovelli and others who say the exact same thing as me, and probably could give much better arguments why they believe it so, I can also give my very simple reasoning, but I am afraid you will question every bit of information. Anyway, here it goes: reality cannot be continuous, because that would mean that the past and the future are real things (otherwise how could be continuously connected to the present?) and because we also know that reality at least at one level is not deterministic (e.g. the past and the future are not clearly defined based on the present) these two assumptions cannot be both true at the same time.
I know that this fact is hard to swallow, I see smart people go so far to believe in such things as the 'multiverse' just to be able to keep believing in the reality of the continuum.
On a much less philosophical note, one would expect smart people to notice a trend where physicists assume something is continuous and then have to change everything to quantized to make the equations work. Ultraviolet catastrophe, electron orbitals, Feynman diagrams, P!=NP just to name a few cases where if the world would be continuous, we would have to deal with very different problems.
Furthermore, partly my confidence stems not from what I know from physics, but on what I know from personal experience. Our brain's main feature is to take an unimaginably large amount of information and to produce a 'continuous' experience from it. Basically, almost anything we perceive is through this. It's our brain that presents things as continuous, and creates the illusion of 'present' time that holds everything that's continuous.
The fact is, that the A series of time cannot be correct, it yields clearly false assumptions, like the 'universal present'. I hope at least about this we can agree?
But our brain creates the experience of the A series of time and our language is 100% built on it. You can observe the problems that stem from this in almost every minute of our daily lives, no need to be a scientist for it. So I just said, wait a minute, if I compensate for this, if I compensate for my biology expecting everything to be static, what is the alternative? And the alternative is that everything is a process, like Whitehead said. "There is becoming of continuity but no continuity of becoming"
And lastly, what convinced me before everything else was the immense usefulness of this worldview, how it simplifies a lot of human problems to simple misunderstanding that can be corrected if all participants are willing, instead of arguing over whose worldview is the more 'real'.
@23:14 Is it a fact or Conjecture? In mathematics definitions matter, just in case you didn't know......"research level" 😂
@Gennady Arshad Notowidigdo no there is more, but I leave that as an exercise for the viewer. Also I enjoy watching math videos when they film it while taking a 💩 😉
Points are dual to lines -- the principle of duality in geometry!
Symmetry is dual to conservation -- the duality of Noether's theorem.
Symmetry is dual to anti-symmetry.
Spin statistics theorem:- Symmetric wave functions (Bosons, waves) are dual to anti-symmetric wave functions (Fermions, particles) -- wave/particle or quantum duality.
Bosons are dual to Fermions.
Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
The proton (thesis) is dual to the electron (anti-thesis) synthesizes the photon or pure energy -- atomic duality.
Pure energy or photons of light are a bi-product of conserving duality!
Injective is dual to surjective creates bijective (isomorphism).
Being is dual to non-being creates becoming -- Plato.
"Reflections preserve perpendicularity (duality) in hyperbolic geometry" -- Professor Norman Wildberger, universal hyperbolic geometry.
You are the same person now but different compared to a few hours ago. The passage of time means that you are a different person (time duality) but still the same. Same is dual to different. Personal identity or the self is a dual construct.
Absolute time (Galileo) is dual to relative time (Einstein) -- time duality.
"Always two there are" -- Yoda.
You need to be fast
change the playback speed 🤷♂️
@Gennady Arshad Notowidigdo upload more video
@Gennady Arshad Notowidigdo Yes, I don't really care about the types of videos I'm talking about algebraic calculus
@Gennady Arshad Notowidigdo Listen, I am very appreciative of what this man is doing and because I trust him, and I know that he is smart and strong. I am asking him more quickly because he is great and I am young so I want to learn from him as much as possible.
@Gennady Arshad Notowidigdo ya one day I hope that I can help
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