Also: the cocaine example was both unexpected and incredibly good! The idea of swiping the material with a straight line is the clearest illustration of the concept. Congrats!
@JenkoRun
Күн бұрын
This @ExistenceUniversity guy must feel personally attacked by your content, lol.
@Inductica
Күн бұрын
Haha, I know. I can't tell if he's my biggest fan, or biggest hater, or both.
@ExistenceUniversity
Күн бұрын
@@Inductica If you think someone is a hater, make the honest changes to your channel that they suggest. If they still hate, they are a hater. If they are happy you became better, they are a fan. There you go, I have purified your comments. Good luck with life.
@TheFramto
Күн бұрын
I really love the inductive proofs (this video is good, too), but I'm not sure why you think that a story is necessary. For me, an understanding of the abstractions of ideas and how they relate to each other is a kind of story, as well, but is actually easier to apply to real world contexts since I can notice the relation to mathematical ideas just from the patterns in the scenario that I am considering. I can take certain abstract perspectives in any situation and come up with mathematical ideas that describe those situations because I think of the math in their general, abstract forms. I understand that this doesn't work for everyone (though it might be able to given the right support), but it seems like you think that the abstract view is never good enough. I may be misunderstanding, though. From some perspective, I agree that a story is necessary, but the story can be abstract. A real understanding of this abstract story may require a deep understanding of all mathematics used in the story in the abstract, as well, bun I'm not sure of that since a lot of this understanding comes from finding any pattern or relationship that you can between the ideas without understanding them fully. I think that ideas can be understood simply in relation to each other, and those understandings can be made valuable by understanding their relation to the real world. I also think that the understandings and relationships necessary to make them useful can take a variety of forms, even for the same mathematical ideas. However, I do not think that those understandings need to be built from real world scenarios once the basis has been built up. Simply, I think that the inductive proofs are really important for early mathematical ideas, but later ideas can be understood in reference to those rather than new, real-world scenarios. Does relating more advanced ideas in mathematics to a real world scenarios not limit understanding in that ideas relation to other mathematics? I don't know that the real-world scenarios in this video actually help to relate the ideas to the real world more so than the abstract mathematical ideas which have themselves already been related to the real world; although, of course, they would be very valuable to some, especially those who were originally taught this mathematics poorly.
@Inductica
Күн бұрын
@@TheFramto a very good question. It is true that an abstract proof is fine as long as you understand each of the abstractions inductively. For example, you could tell the stories in this video using an abstract “border of integration “ instead of the example of a line of tractors or a razor blade. Now, for an inductive proof, the concept must be motivated by some real life problem (like harvesting corn), but once that is done, pure deduction from existing abstractions is acceptable to furnish a solution so long as those abstractions have been induced from reality in the way I have in my induction videos. I must also emphasize that this video is not an inductive proof, since I have not tied it back to previously induced ideas, nor did I motivate it in inductive form.
@Inductica
Күн бұрын
@@TheFramto so mathematical ideas cannot just be related to one another, they must constantly be given reference to observations throughout the inductive progression. However, individual reasoning steps within that narrative can be pure deductions. Does that address your points? If not, follow up: your are making an important point I want to answer.
@TheFramto
Күн бұрын
@@Inductica I am still working through my ideas at the moment and I love the discourse that is able to happen here. I know how valuable this way of thinking can be, but I still have a question: Where does the "must" comes from in "they must constantly be given reference to observations".
@juanmanuelmunozhernandez7032
23 минут бұрын
You know me, I'm a guy naturally curious for fringe cases, so here's a little line of induction from the video: WIP
@BlackbodyEconomics
Күн бұрын
Hah - dude, math and drugs ... as counter-intuitive as most people may find this - have gone hand-in-hand since the Sumerians. Very pertinent examples :P
@Inductica
Күн бұрын
Hahah, I didn’t know that.
@BlackbodyEconomics
15 сағат бұрын
@@Inductica It's kind of crazy - but I think it's just woven into the type of mind that is science and discovery driven; that has a deep curiosity to experience and learn new things. Pythagoras learned to use substances to "purify the mind" from Zaractus. Heck, almost any thinker from the middle east was at least a cannabis user - and often opium users. Even today, some of the most prolific mathematicians were either very liberal with the range of substances they used, or deeply addicted to one thing or another. Carl Sagan, Feynman, Turing, Erdos (hardcore amphetamine user), Newton was all over the place with his psychoactive dabbling (including cocaine) ... the list goes on. There are probably way more who kept it private that we just don't know about.
@CausalDiscoveries
Күн бұрын
lol calculus… cocaine user math to optimize your high.
@Inductica
Күн бұрын
And they said math is just disconnected abstractions! 😂
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