42:29 I have been watching videos about Geometric Algebra as present by Hermann Grassmann in 1844 and further explored by William Kingdom Clifford in 1878, as well as being advocated for in modern day by David Hestenes. Hestenes also talks about the effect of being able to see thing from a different perspective to have a greater understanding of the sciences with the idea of bivectors, pseudo vectors, and corresponding three dimensional aspects. It does remind me of the point you were making about how 19th century Mathematicians were limiting their think by a focus on Euclid. And certainly the review of the complex unit i, reminds me of the j and k of quaternions and the vectors of Heavyside as well as the bivectors of Clifford.
The concepts of 'ana' and 'kata' as geometric directions in a higher dimension (4th) are right in line with this. The presentation of names for these post- or overtrine dimensions' directions were introduced to me in junior high school when I read: The 4th Dimension: Towards a Geometry of Higher Reality, by Rudy Rucker. I only recently found out that the MAA (Mathematical Association of America) added this to their Recommended Reading list.
Thanks! Line through north pole and a point on the sphere gives a point on the plane. Line through south pole and the same point on the sphere gives another point on the plane. Those points on the plane satisfy the circle inversion in 2d. Thanks for all your videos.they inspired me in many ways!!
Thank you Norman such a great overview of the evolutionary development of the technical and philosophical awareness that was taking place most enlightening. Loved it!
The reason algebra took over was three fold. (In the early to middle 1800's) 1. Discovery of electricity. 2. Partial Differentials are easier in equations. Rather than geometric fields. 3. James Clerk Maxwell.
Inversion is reflection with respect to a circle. The composition of such reflection generate the whole conformal group. For example, two Inversions with respect to circle with the same center produce a dilatation.
At 21:00, you demonstrate the math model used in Von Neumann computation. The stack of grids for gradient descent is virtual. If you know that now, time resolves in the search and the output is always the same, the search path is now non-deterministic, then the current stupidity of the world is illuminated. The Stinkularity.
In the mid 19th century Bernard Riemann, a student and associate of Gauss, who had much earlier reproduced an alternate geometry in an unpublished non-Euclidean hyperbolic form, had privy to all Gauss’s work. Riemann, in his presentation to seek paid professorship, he extended Gauss’s 2 dimensional hyperbolic geometry, to include a 2 dimensional spherical (elliptic) geometry.
Just tried to 'image the tangents' to the small green circle on the sphere, at 14', but then I got totally lost. Maybe not meant to be tangents to the circle/sphere, but what then? Hope to see it later...
Faraday was experiment all the time. Could have gone geometric . As Wildberger says, keep it on the page. That is the whole point of the algebraic calculus . Yet geometry is more fluid than algebra. The side of a circle from the origin is so great that it is a line at the micro. Infinity at the macro.
I'm a long time from my university math classes, but maybe 1/0 is undefined (in part) because it diverges to two different infinities (+ve and -ve) depending on which side of zero 1/x approaches it from? Where maybe the projective infinity is unique in some sense?
Yeah I think that may be the key way to make a case that there can't reasonably be two different infinities on the number line, except in the same scenarios where we might talk about "0+" and "0-", like if we're talking about x in f(x) = 1/x
Stephen Wolfram makes very important note that computable reducibility has two basic relations: 1) additivity (cf standard school arithmetic) and 2) nesting (mereology). Sociology has been rejecting mereology, because of perceived conflict with set theory, which is based on the additive relation in the form of point reductionism - the absurd idea that a line etc. consist of actual infinity of infinitesimal points. Projective geometry is intuitively mereological with complex nesting relations and continuous process of measuring, which are holistic - not additive sum of any parts. The profound mathematical method of 'LOOKING FROM HIGHER DIMENSION' is holistic mereology.
Re: Sociologists' degree of experience with math. As far as I can tell -- I studied mainly computer science, but also took several courses in pretty much all the sciences, including two courses (one 1st- and one 2nd-year) in Sociology) -- I'm pretty sure that every Sociology degree requires at least 1st-year (and probably also at least 2nd-year) Statistics. The same goes for Psychology I think (I also took one 1st-year Psychology course), but the need for Statistics is especially true for Sociology. The very nature of the study of Sociology requires collecting information from large groups of people, and then doing at least some form of processing on that information in order to generate any sort of publishable results. While not a 'hard science' like Physics, it is indeed an actual science, in the sense that they adhere to the scientific method. Indeed, the 2nd-year Sociology course I took was heavily focused on 'how to perform sociological research', and we were required to develop and conduct a survey, collecting the results, and writing it up. So, while they may not have extensive experience with Calculus, Geometry, or Algebra (e.g. Linear Algebra), I would wager that most working Sociologists would not be as prone to math-phobia as the general public, IMHO. Just some feedback. Again, not a sociologist myself, but I did get a glimpse into general Sociology at university a bit. It's more of a 'crunching the numbers' field (at least in terms of doing statistics on data) than probably most people realize.
It seems like the youtube bot has gotten into the habit of removing my comments. Maybe it is because they contain links or it is because I wrote something critical about a piece of modern music with atonalities so that people flagged my comment and this changed youtube's priors about me. I don't like this platform any longer. It is not a good place to write one's thoughts, not even as a quick back-and-forth technical and mildly creative discussion related to the content of a video. Rules are enforced arbitrarily at random with no explanation.
42:29 I have been watching videos about Geometric Algebra as present by Hermann Grassmann in 1844 and further explored by William Kingdom Clifford in 1878, as well as being advocated for in modern day by David Hestenes. Hestenes also talks about the effect of being able to see thing from a different perspective to have a greater understanding of the sciences with the idea of bivectors, pseudo vectors, and corresponding three dimensional aspects. It does remind me of the point you were making about how 19th century Mathematicians were limiting their think by a focus on Euclid. And certainly the review of the complex unit i, reminds me of the j and k of quaternions and the vectors of Heavyside as well as the bivectors of Clifford.
The concepts of 'ana' and 'kata' as geometric directions in a higher dimension (4th) are right in line with this. The presentation of names for these post- or overtrine dimensions' directions were introduced to me in junior high school when I read:
The 4th Dimension: Towards a Geometry of Higher Reality, by Rudy Rucker.
I only recently found out that the MAA (Mathematical Association of America) added this to their Recommended Reading list.
This series, and playlist - A Brief History of Geometry, by M J Wildeberger - is my all-time favorite educational playlist on TH-cam. Ever.
Thanks! Line through north pole and a point on the sphere gives a point on the plane. Line through south pole and the same point on the sphere gives another point on the plane. Those points on the plane satisfy the circle inversion in 2d. Thanks for all your videos.they inspired me in many ways!!
Thank you Norman such a great overview of the evolutionary development of the technical and philosophical awareness that was taking place most enlightening. Loved it!
Brilliant Sir, I do believe I understand it all now because of your brilliant insight to an extremely complex set of ideas.
This is a packed video. I look forward your unpacking.
Probably my favorite of his lectures
The reason algebra took over was three fold. (In the early to middle 1800's)
1. Discovery of electricity.
2. Partial Differentials are easier in equations. Rather than geometric fields.
3. James Clerk Maxwell.
Agree. The projections were used in electrostatics to calculate field lines (curves).
Inversion is reflection with respect to a circle. The composition of such reflection generate the whole conformal group. For example, two Inversions with respect to circle with the same center produce a dilatation.
we love u professor. keep heathy and happy. xixi
At 21:00, you demonstrate the math model used in Von Neumann computation. The stack of grids for gradient descent is virtual. If you know that now, time resolves in the search and the output is always the same, the search path is now non-deterministic, then the current stupidity of the world is illuminated. The Stinkularity.
I looked into stenographic projection. Thankyou. It is interesting.
Very interesting!
In the mid 19th century Bernard Riemann, a student and associate of Gauss, who had much earlier reproduced an alternate geometry in an unpublished non-Euclidean hyperbolic form, had privy to all Gauss’s work. Riemann, in his presentation to seek paid professorship, he extended Gauss’s 2 dimensional hyperbolic geometry, to include a 2 dimensional spherical (elliptic) geometry.
Connection with quantum mechanics in properties of light? Like drawing lights on shadow surface whitch is point of infinity, multiplicity of infinite?
Does the calculation of Pi collide with any of this History so it can be used as a control for the accuracy of Pi? Your Thoughts are appreciated .
The Beauty of the Sinecal Quadrant is that it allows one to do Spherical Trigonometry on a Plane surface.
Thank you
The only three "numbers" one needs is 0, 1, and infinity. As in Log(base infinity) of 1 = 0. Also useful are "time" and 2.
Infinity is not a number, though.
Just tried to 'image the tangents' to the small green circle on the sphere, at 14', but then I got totally lost.
Maybe not meant to be tangents to the circle/sphere, but what then? Hope to see it later...
@Me Too Thanks, I it see now!
Faraday was experiment all the time. Could have gone geometric .
As Wildberger says, keep it on the page. That is the whole point of the algebraic calculus .
Yet geometry is more fluid than algebra. The side of a circle from the origin is so great that it is a line at the micro. Infinity at the macro.
I'm interested in the sociology of accepting an infinity in projective geometry as [1:0], but rejecting an equivalent infinity in algebra as 1/0.
I'm a long time from my university math classes, but maybe 1/0 is undefined (in part) because it diverges to two different infinities (+ve and -ve) depending on which side of zero 1/x approaches it from? Where maybe the projective infinity is unique in some sense?
Yeah I think that may be the key way to make a case that there can't reasonably be two different infinities on the number line, except in the same scenarios where we might talk about "0+" and "0-", like if we're talking about x in f(x) = 1/x
I was busy figuring out the process of protractors
Stephen Wolfram makes very important note that computable reducibility has two basic relations: 1) additivity (cf standard school arithmetic) and 2) nesting (mereology).
Sociology has been rejecting mereology, because of perceived conflict with set theory, which is based on the additive relation in the form of point reductionism - the absurd idea that a line etc. consist of actual infinity of infinitesimal points.
Projective geometry is intuitively mereological with complex nesting relations and continuous process of measuring, which are holistic - not additive sum of any parts. The profound mathematical method of 'LOOKING FROM HIGHER DIMENSION' is holistic mereology.
@@santerisatama5409 good luck. I am so dumbpeoplle think I ama not. They can’t figure it out. Anyway
Re: Sociologists' degree of experience with math. As far as I can tell -- I studied mainly computer science, but also took several courses in pretty much all the sciences, including two courses (one 1st- and one 2nd-year) in Sociology) -- I'm pretty sure that every Sociology degree requires at least 1st-year (and probably also at least 2nd-year) Statistics.
The same goes for Psychology I think (I also took one 1st-year Psychology course), but the need for Statistics is especially true for Sociology. The very nature of the study of Sociology requires collecting information from large groups of people, and then doing at least some form of processing on that information in order to generate any sort of publishable results. While not a 'hard science' like Physics, it is indeed an actual science, in the sense that they adhere to the scientific method. Indeed, the 2nd-year Sociology course I took was heavily focused on 'how to perform sociological research', and we were required to develop and conduct a survey, collecting the results, and writing it up.
So, while they may not have extensive experience with Calculus, Geometry, or Algebra (e.g. Linear Algebra), I would wager that most working Sociologists would not be as prone to math-phobia as the general public, IMHO. Just some feedback. Again, not a sociologist myself, but I did get a glimpse into general Sociology at university a bit. It's more of a 'crunching the numbers' field (at least in terms of doing statistics on data) than probably most people realize.
Thx.
It seems like the youtube bot has gotten into the habit of removing my comments. Maybe it is because they contain links or it is because I wrote something critical about a piece of modern music with atonalities so that people flagged my comment and this changed youtube's priors about me. I don't like this platform any longer. It is not a good place to write one's thoughts, not even as a quick back-and-forth technical and mildly creative discussion related to the content of a video. Rules are enforced arbitrarily at random with no explanation.