What the hell is a tensor, anyway?
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- Опубліковано 18 вер 2024
- For more details on this subject, you can download the first chapter of my book here: www.researchga...
This is a supplementary video to the general relativity series dealing with tensors and their covariant derivatives.
Video on the covariant derivative:
• Riemann geometry -- co...
The other video on covariant differentiation:
• A quick note on the co...
Music by Galt MacDermot -- Coffee Cold
For more details on this subject, you can download the first chapter of my book here: www.researchgate.net/publication/342330200_General_theory_of_relativity_for_undergraduates
"thank you for calling the general relativity helpdesk....." brilliant introduction
wow, dont understand everything but this playlist is sooo satisfying, youre awesome!
Thanks. Cheers.
First of all I wish to congratulate you for this video, but I must admit that while I tried to think of what I did 60 years ago and interpret it in the manner which you explain, I find that I lag behind and I need more time to accustom myself to the last part of the "language symbols" expressing these operations.
At my old age, I am experimenting with giving lectures to children in summer schools were all my lectures involve practical movements with wooden toys which include diverse functions commencing with the function being contained in static shapes to dynamic models which include the operations of rotating and non rotating vectors in all fields including the combinations of cranks and pistons and torques , and scalar and vector fields and the interpretations of line and surface and volume integrals and contour integration in various vector fields.
The concepts of rotation described by "imaginary numbers" is something I do not agree with as rotation is real and to tell children about imaginary numbers to explain the square root of minus one, is a terrible preparation for children to reach a higher mind operation. There are so many issues in the preparation of a young person's mind that seem to sway people from the real meaning of mathematical operators. While people seem to understand what is a function, when it comes to rate of change and higher rate of changes, many people in the arts and social and entertaining professions seem to be lost as to what is associated with a mathematical symbol, which contains logic and reason in the manner it is selected to project he meaning. When it comes to derivatives and integrals, many people's mind just do not accept the field presented to them.
It seems that most people prefer to remember by rote the meaning associated with language symbols where the symbol shape has not relation to the entity they describe. The human mind seems to reject the logic in the mathematical symbols and accept to remember symbols which identify a vision rather than an invisible silent action.
In systems described by different coordinate systems, I find that many people cannot even appreciate the difference between a position vector and a floating vector, and the change in the coordinate systems when it comes to being applied to Gradients and Divergence and Curls seems that one needs to wait a very long time till the concept which is not described by conventional language symbols is accepted as being meaningful in describing the actual state of the situation. I am beginning to conclude that the symbolic representation of mathematical operations are just like the symbols in music, but much more complex as the function described is not a case of describing one sound note. I always ask myself , how can one make people understand the music being described by mathematical symbols. To many people, there is not music behind mathematical symbols, and the real world is described by language symbols which is decided by tribal culture and the isolation of the tribe with all its tradition. There is not an ounce of logic an any language symbol.
Tensors are the " ultimate" mathematical operations I covered in my engineering course. I had not enough time to cover all that I wanted to, but it seems that may other even rejected the symbolic representation of the combinations involved. In the last ten years I tried to project the meaning of mathematical symbols through " wooden arrangements" including the operation of digital operations using marbles and bits of woods, but when it comes to the introduction of Tensors, I find it difficult to illustrate the change from vectors to tensors, and there are many young people who will not learn unless the action or operation is illustrated in a practical sense as their inspiration does not seem to allow them to imagine the permutations of the basis components let alone any "product" involved. Also the meaning of " a product of multiplication" is not so easy to project to people who do not see an operation in mathematical symbols but only in language symbols. It would be useful to find a way to reap off more human minds to know that there is even better music in mathematical symbols with their associated operations rather than the artificial language symbols which call the same entity by different sounds. Well sometime I do think that is related to identifying the same vector by different coordinate systems. In language translation there is function that people accept, but why is it that people do not accept so easily the translations and operations from one coordinate system to another?
How can one increase the reap from schools so that young people are inspired by what is contained in this video?
Congratulations for such good work, and I hope to return to this when time is available. Thank you for uploading this work.
Thank you for such a detailed comment. I intended this video to be geared towards people who have already some understanding of vectors and vector calculus. But there are other videos on UA-cam that are much more visual and do not use heavy notation etc. One I saw recently was by "Physics Videos by Eugene Khutoryansky" called "Tensors Explained Intuitively: Covariant, Contravariant, Rank." I recommend you take a look. Cheers.
amazing,keep making videos like this
Thanks!
I like the way you explain things. I've read Chapter 1 of your book. How can I obtain your book?
Hi, thank you for your interest. Unfortunately, I have not written the whole book yet. Since the pandemic started I have had too many things to do, so I had to put the book on hold. I will keep you and all my subscribers posted on the progress. Cheers
My poor wee brain had a melt down at 8:37 :( But, I will not give up!
hahaha "Paint Milton's stapler blue"
Well,but how to visualise tensor as geometric object like vector as a rigid rod?
They have the wrong music at the end. "I'm a cowboy" was the tune I believe. Funny movie. Really a classic from the 90s.
Yes, I know. I edited the music just because I thought it was a cool tune.
Handsome boy modelling school was a great choice
gr8 job.
Lovely
Why are they breaking the machine at the end??
In the movie (titled "Office Space"), the printer keeps jamming, so they stole it one day and smashed it.
LOL , Really!
That is a great movie.
I did much the same thing as the protagonist: Spent 15 years in IT/management for telecom companies, and went into construction.
Fuckingg yesss
🧐
Man, there sure are some LONG equations in some of that stuff....