The scientific community on X is very much alive. Can you get 20M+ views on Jacobian anywhere?
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The scientific community on X is very much alive. Can you get 20M+ views on Jacobian anywhere?
Many users praise X for amplifying scientific discussions such as Jacobians reaching over 20 million views as a great example of uncensored science communication, while a few criticize it for promoting irrelevant or fringe content.
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A mail I have sent to my professor "Hello Professor Navid, I am not sure whether you remember, but about two weeks ago in class, I asked whether a determinant could describe a transformation in which the space eventually folds back and overlaps itself. I recently read about the newly announced counterexample to the Jacobian Conjecture, and it seems surprisingly close to the idea I was trying to explain. My current understanding is the following: For a multivariable polynomial map, the Jacobian matrix contains all of its first-order partial derivatives. The determinant of this matrix represents the local signed scaling factor for area or volume. If the Jacobian determinant is nonzero at a point, the transformation is locally invertible near that point. The Jacobian Conjecture proposed that if the Jacobian determinant of a polynomial map is a fixed nonzero constant everywhere, then the map must also be globally invertible and have a polynomial inverse. A constant nonzero determinant means that the transformation never locally collapses an area or volume to zero. However, the recently announced counterexample appears to show that this local condition does not necessarily guarantee global uniqueness. Even though the determinant is reportedly equal to (-2) everywhere, distinct input points can still be mapped to the same output point. In geometric terms, the transformation does not create a local crease or flattening, but different regions of the entire space can still overlap globally. This is very similar to what I was trying to describe in class. My original explanation was unclear: I was not really thinking of a discontinuous polynomial, since polynomial maps are continuous. I was thinking of several polynomial equations acting together as one multivariable transformation, where different regions might overlap even though the determinant remains nonzero locally. I would be very interested to know whether this interpretation of the counterexample is correct and whether it is genuinely connected to the idea I raised in class. Could we discuss it, as well as the latest developments concerning the Jacobian Conjecture? Best regards, Can
@yunta_tsai It’s mind-blowing that rich lunatics want to run your life—dictating driving, stealing jobs, chipping heads & mutilating you for robotic limbs just because his ex Grimes & this junkie love twisted sci-fi. You're exactly like Jeffrey Epstein, from that same pedo ring.
@AdamLowisz @elonmusk The science community is top notch. The finance community is top notch The political environment is uncensored X really was a service to the population of the world. I slept on X for way too long.
@yunta_tsai @elonmusk X is a unique and wonderful place.
@AdamLowisz Love this take.
@yunta_tsai @elonmusk I love it here 🤓
Many users praise X for amplifying scientific discussions such as Jacobians reaching over 20 million views as a great example of uncensored science communication, while a few criticize it for promoting irrelevant or fringe content.
Based on 34 visible X reactions from 189 accounts.
Ask a question below.
Published answers will appear here.
