The beauty of math is not to use as many words as possible but as little as possible. You are literally taking something that is supposed to create clarity and use it remove clarity. What you mean is simply:
I used to feel that using (x + y) - y during a proof was just some sort of cheap trick, that for example would never appear in The Book. But this is making me realize that since the -y part tends to stick around, what you're really doing is just revealing this inevitable residual.
Also makes me wonder how you can derive quadratic formula without completing the square.
totally, this residual is exactly what the principle here illustrates. it's necessary to make the rest of the derivation possible
the derivation of the quadratic formula intrinsically relies on the process of completing the square. you could manipulate the equation differently in the initial steps but they will all arrive at a point equivalent to the completed square
So if the arab was going to leave 1/2 to the first son, 1/3 to the second son, and 1/9 to the third son, what was he planning on doing with the remaining 1/18?
Not everybody can be happy, because that 1/18 of a camel should go to someone, but nobody received it!
He is presenting this as if he's teaching you a trick when he's fooling you to believe these numbers add up to 1 when they don't. Classic midwit trying to look smart
I think you might be the midwit here, nobody is pretending anything equals 1
the father in the story didn't say "I want my sons to have X number of Camels" he said "I want them to have some fractional representation of my Camel squad" knowing full well that camels can't be (easily) distributed in pieces and the amount might change by the time of his death
the neighbor comes in and says "I'll help you make your specific distributions work given the current amount of camels" specifically because `1/2 + 1/3 + 1/9 != 1` and the remainder goes back to the person who lent the camel, in the same way it doesn't stay with the values in math when we "lend" values to variables
none of this is done to change the equality, but to make math within that equality easier to compare
The numbers chosen create an illusion that something more impressive is going on.
Here’s a simpler version: the father says, “I want each of my two sons to get 1/3 of my camels when I die.” Upon death, the father only has 2 camels, so the sons just instead take 1/2 of the total, 1 camel each.
“This is a quintessential question. Without this, you don’t have backpropagation, gradient descent, and thus neural networks. (At least until someone invents a clever alternative. But that’ll take a while.)”
I’m not sure whether “NoProp” uses the camel principle in its derivation, but it is a method for training ANNs without back prop or gradient descent. See…
I can see how the camel principal works using the first illustration.
Unfortunately, mathematics to me is like a woman's mind – I love it, I'm fascinated by it, I drown in its unfathomableness-
How on earth I managed to found a successful machinery design and manufacturing company without being able to understand a quadratic equation is a source of wonderment to me.
I guess I didn't know what impostor syndrome was x
The beauty of math is not to use as many words as possible but as little as possible. You are literally taking something that is supposed to create clarity and use it remove clarity. What you mean is simply:
1/2 + 1/3 + 1/9 = 0.9444 != 1
Indeed the camel story is picturesque but seems misleading to me
I used to feel that using (x + y) - y during a proof was just some sort of cheap trick, that for example would never appear in The Book. But this is making me realize that since the -y part tends to stick around, what you're really doing is just revealing this inevitable residual.
Also makes me wonder how you can derive quadratic formula without completing the square.
totally, this residual is exactly what the principle here illustrates. it's necessary to make the rest of the derivation possible
the derivation of the quadratic formula intrinsically relies on the process of completing the square. you could manipulate the equation differently in the initial steps but they will all arrive at a point equivalent to the completed square
So if the arab was going to leave 1/2 to the first son, 1/3 to the second son, and 1/9 to the third son, what was he planning on doing with the remaining 1/18?
Not everybody can be happy, because that 1/18 of a camel should go to someone, but nobody received it!
He is presenting this as if he's teaching you a trick when he's fooling you to believe these numbers add up to 1 when they don't. Classic midwit trying to look smart
I think you might be the midwit here, nobody is pretending anything equals 1
the father in the story didn't say "I want my sons to have X number of Camels" he said "I want them to have some fractional representation of my Camel squad" knowing full well that camels can't be (easily) distributed in pieces and the amount might change by the time of his death
the neighbor comes in and says "I'll help you make your specific distributions work given the current amount of camels" specifically because `1/2 + 1/3 + 1/9 != 1` and the remainder goes back to the person who lent the camel, in the same way it doesn't stay with the values in math when we "lend" values to variables
none of this is done to change the equality, but to make math within that equality easier to compare
SorenJ said it perfect
https://thepalindrome.org/p/the-camel-principle/comment/117413182
It's dumb
everyone gets hung up on "where does the 1/18 go?"
the 1/18th shouldn't go to someone, it doesn't need to go anywhere because the will didn't specify it go anywhere
the father in this story doesn't say "all of the camels should go to my sons" it says "each of my sons gets this specific fraction of my camels"
The numbers chosen create an illusion that something more impressive is going on.
Here’s a simpler version: the father says, “I want each of my two sons to get 1/3 of my camels when I die.” Upon death, the father only has 2 camels, so the sons just instead take 1/2 of the total, 1 camel each.
The post in OP is just that with extra steps.
The wise man was Hazrat Ali Ibn e Abu Tablib (a.s), the Successor of Hazrat Muhammad (P.B.U.H).
have you ever written a deep-dive article on backpropagation? I will like to read.
Check this: https://mlfz.readthedocs.io/en/latest/mlfz.html
“This is a quintessential question. Without this, you don’t have backpropagation, gradient descent, and thus neural networks. (At least until someone invents a clever alternative. But that’ll take a while.)”
I’m not sure whether “NoProp” uses the camel principle in its derivation, but it is a method for training ANNs without back prop or gradient descent. See…
https://ai.gopubby.com/you-dont-need-backpropagation-to-train-neural-networks-anymore-e989d75564cb
Heard about NoProp recently, looks interesting! Haven't read the paper though.
hate links that i cant read without paying.
The NoProp paper is on arXiv for free, check there!
I can see how the camel principal works using the first illustration.
Unfortunately, mathematics to me is like a woman's mind – I love it, I'm fascinated by it, I drown in its unfathomableness-
How on earth I managed to found a successful machinery design and manufacturing company without being able to understand a quadratic equation is a source of wonderment to me.
I guess I didn't know what impostor syndrome was x
Very cool, and well presented. Thank you!
Thanks!