Pimping ain’t easy, but you make it look easy! However, how do we know that the Bees are quantifying whole numbers? They may just be approximating the color difference, rather than the discrete items.
I think your comment is quite interesting and I would also like an answer to that. But even a approximation based on colour difference would still amount to the concept of Zero as this could be expressed as levels of distortion of the background, the higher the shape and with that the colour count the more distorted the background is, so a pure background would amount to no distortion and with that Zero. I really hope I could convey my thought process here.
I'm not too convinced about the calculus example... The symbol "limit at 0" does not really contain the idea of 0, it has more to do with very small numbers. This is much like the "limit at infinity" which doesn't require to define a mathematical object "infinity" to be defined. This is merely a notation for a real function behaviour. Still, 0 is the best number out there and definitely the most used one in mathematical research, along with its friend 1
dx=√0 or dx²=0. You are just uncomfortable with this because you are used to derivatives explained in terms of limits. But differential calculus can be done by extending the real number R×R with a+bε in which ε²=0
@@kazedcat I'm not sure how that relates to my remark at all. I'm not saying calculus isn't linked to 0, I'm just saying that I'm not convinced by the choice of limits to explain the role of 0 in maths. Infinitesimals are a way to approach 0 without really using it in this sense they almost "avoid" the notion of 0 and therefore would not be my choice if I had to talk about the importance of 0 in maths. I'm pretty sure you could come up with great explanations, but the one in the video did not do it for me
Zero is the most interesting subject in mathematics. I guess when you play a game of Chess or Go, first of all the board starts off "empty" = 0, then depending on the game, black or white plays the 1st piece but it's dependent on an empty board with nothing or zero pieces on it to begin with: Much like our universe it would seem?
It would have been nice to include a little history about how zero was not considered a number by the ancient Greeks and others. Also, you touched on the pedagogical aspect with little kids, but there's a whole lot more there. I once asked my granddaughter (then 5 years old) which weighed more: zero rocks or zero feathers. Of course she said rocks. I don't think I was entirely successful in explaining why they weighed the same (nothing).
Hey can you do a video on Identity elements across mathematical operations. And then couple that with exploiting symmetry. Remember in school whenyou. Were taught that you can add "0" or multiplying by "1 to simplify an expression, but that was a trick? Well I believe learning about identity elements early build you an intuition on how to solve more complex operations. So, please consider doing a video on this. What you just did is kinda similar but not quite.
@@DrSeanGroathouse awesome. looking forward to it. i dunno how far you could take it, but one of the most complex to me were fouriere and laplace. i'm sure there is even more
Honestly the section on algebra is very incomplete, if you want to discuss the importance of identity the most natural factoid to turn to is the embedding of the category of semigroups into the category of monoids.
The bee experiment was not very convincing. The same behaviour would emerge if the bees followed the rule "fly away from blobs", without any understanding of numbers.
Definitely there are limitations to the study. My understanding is they modeled this experiment after others done with small children and other animals, and the bees do pretty well compared to the other groups. If the bees are shown 4 blobs, and 6 blobs, they will pretty consistently land on the 4 blobs, so the researchers believe they've trained them to go to "less" blobs rather than avoiding all blobs. They'll land on the sheet of 4 in this comparison, but in a comparison of 4 blobs and 1 blob, they'll pick the sheet with 1. But I definitely understand your point, that it's hard or impossible to really know what processing explains their behavior.
6:11 *The box* 😢 ‘I don’t count, do I? I’m nothing to you’. (It must be a female box. It would make sense, given that they have to wait for the 1 to fertilise them with and into existence. Religion was right (not)). 😂 Listen. How many 1s are there in an empty box? Let’s say 1 is a point (though one point is at least 2 = ‘one’+’point’). How big or small must a box be to contain the zero? A box is made up of 4 (sides that contain how many points?) to contain 0. Zero what? And what happens at the corners of the box? Does the 0 sneak in and out of the box through those points or does it play hide and seek remaining there and generating all the points that constitute the actual box? Is the 0 simultaneously in the four corners (localisation?) and why do you put it there (has it done something wrong? Maybe it was zero that killed the cat 🙀). Does the mischievous 0 stay on the outer surface of the box and projects its shadow (or does it generate it) as a box? I’d say we better not disrespect 0 because he is 1 that should not be messed with.
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Video suggestion: Gödel's incompleteness theorems in 5 levels.
Thanks for the suggestion! I added it to my list
That's so cool! I'm literally studying it for my test in the next few weeks!
Pimping ain’t easy, but you make it look easy! However, how do we know that the Bees are quantifying whole numbers? They may just be approximating the color difference, rather than the discrete items.
I think your comment is quite interesting and I would also like an answer to that. But even a approximation based on colour difference would still amount to the concept of Zero as this could be expressed as levels of distortion of the background, the higher the shape and with that the colour count the more distorted the background is, so a pure background would amount to no distortion and with that Zero.
I really hope I could convey my thought process here.
Lets go~ Just what I needed after a long work day. edit: Whoa, the level 5 one is super neat.
Thank you, this retired engineer loves you videos.
Please do videos in dark mode my eyes hurt 🤕
This is a great suggestion. 🎉
I second this
I'm not too convinced about the calculus example... The symbol "limit at 0" does not really contain the idea of 0, it has more to do with very small numbers. This is much like the "limit at infinity" which doesn't require to define a mathematical object "infinity" to be defined. This is merely a notation for a real function behaviour.
Still, 0 is the best number out there and definitely the most used one in mathematical research, along with its friend 1
dx=√0 or dx²=0. You are just uncomfortable with this because you are used to derivatives explained in terms of limits. But differential calculus can be done by extending the real number R×R with a+bε in which ε²=0
@@kazedcat I'm not sure how that relates to my remark at all. I'm not saying calculus isn't linked to 0, I'm just saying that I'm not convinced by the choice of limits to explain the role of 0 in maths. Infinitesimals are a way to approach 0 without really using it in this sense they almost "avoid" the notion of 0 and therefore would not be my choice if I had to talk about the importance of 0 in maths.
I'm pretty sure you could come up with great explanations, but the one in the video did not do it for me
Zero is the most interesting subject in mathematics. I guess when you play a game of Chess or Go, first of all the board starts off "empty" = 0, then depending on the game, black or white plays the 1st piece but it's dependent on an empty board with nothing or zero pieces on it to begin with: Much like our universe it would seem?
It would have been nice to include a little history about how zero was not considered a number by the ancient Greeks and others.
Also, you touched on the pedagogical aspect with little kids, but there's a whole lot more there. I once asked my granddaughter (then 5 years old) which weighed more: zero rocks or zero feathers. Of course she said rocks. I don't think I was entirely successful in explaining why they weighed the same (nothing).
Keep up the good work, as a math enjoyer I love your content
Thanks! I'm glad you liked it
Hey can you do a video on Identity elements across mathematical operations. And then couple that with exploiting symmetry. Remember in school whenyou. Were taught that you can add "0" or multiplying by "1 to simplify an expression, but that was a trick? Well I believe learning about identity elements early build you an intuition on how to solve more complex operations. So, please consider doing a video on this. What you just did is kinda similar but not quite.
Thanks for your suggestion! I think that would be a great video. I added it to my list
@@DrSeanGroathouse awesome. looking forward to it. i dunno how far you could take it, but one of the most complex to me were fouriere and laplace. i'm sure there is even more
Very Interesting! Well done
Glad you liked it!
What would the bees do if you put -1 shapes
Interesting, thank you.
I'm glad you liked it!
My mind's natural understanding of zero is that it's the additive identity.
Honestly the section on algebra is very incomplete, if you want to discuss the importance of identity the most natural factoid to turn to is the embedding of the category of semigroups into the category of monoids.
Nice
Hello Master
There is no 0 in Roman numerals.
{} comment
The bee experiment was not very convincing. The same behaviour would emerge if the bees followed the rule "fly away from blobs", without any understanding of numbers.
Definitely there are limitations to the study. My understanding is they modeled this experiment after others done with small children and other animals, and the bees do pretty well compared to the other groups. If the bees are shown 4 blobs, and 6 blobs, they will pretty consistently land on the 4 blobs, so the researchers believe they've trained them to go to "less" blobs rather than avoiding all blobs. They'll land on the sheet of 4 in this comparison, but in a comparison of 4 blobs and 1 blob, they'll pick the sheet with 1. But I definitely understand your point, that it's hard or impossible to really know what processing explains their behavior.
6:11 *The box* 😢 ‘I don’t count, do I? I’m nothing to you’. (It must be a female box. It would make sense, given that they have to wait for the 1 to fertilise them with and into existence. Religion was right (not)). 😂
Listen. How many 1s are there in an empty box? Let’s say 1 is a point (though one point is at least 2 = ‘one’+’point’). How big or small must a box be to contain the zero?
A box is made up of 4 (sides that contain how many points?) to contain 0. Zero what?
And what happens at the corners of the box? Does the 0 sneak in and out of the box through those points or does it play hide and seek remaining there and generating all the points that constitute the actual box? Is the 0 simultaneously in the four corners (localisation?) and why do you put it there (has it done something wrong? Maybe it was zero that killed the cat 🙀).
Does the mischievous 0 stay on the outer surface of the box and projects its shadow (or does it generate it) as a box?
I’d say we better not disrespect 0 because he is 1 that should not be messed with.
It's an absence of quantity. Saying that it is " less than one" is rather misleading, but won't educated in the Americas