IQ (moved subtopic)
^^Hey Luciom, can you remind me again how smart JD Vance is? Above, same, or below the average MAGA chode?
I have no problem with schools using affirmative action to help people like Vance with humble backgrounds.... but maybe not in law school where these idiots start becoming dangerous. And they got to find smarter people then Vance or the whole thing just looks ridiculous and all you're doing is de-valuing your own department.
Here is my definitions of math intelligence using a super simple question and answer.
The idea that you can tell if a number of several digits is divisible by three by adding up the digits and seeing if that sum is divisible by three.
Most of the millions of people who know this trick and memorize it have displayed zero smartness.
Those who were told why it works and quickly understand the explanation are semi smart.
Those who are told the tick without explanation, go on to contemplate it and quickl
It doesn't really matter for your point, but as a matter of fact, very few people are told there is a trick but not told what the trick is.
Whatever algorithm you used is also not guaranteed to get the optimum answer in any reasonable amount of computing time if the problem wasn't a toy example. There is no such algorithm for all complex tasks. There are real tradeoffs one can make, even while maximizing intelligence.
So is that what is referred to as "Artificial General Intelligence"? As in, basically a lab-grown human brain?
The concept of AGI is so absurd. If AGI is said to exist, how would we be able to prove it? We still don't understand human consciousness, and we're not even close to figuring it out; probably never will.
Had a guitar teacher once who tried to transcribe all four parts of Jesu, Joy of Man's Desiring on classical guitar. Don't think he ever worked out an arrangement that was realistically playable.
The concept of AGI is so absurd. If AGI is said to exist, how would we be able to prove it? We still don't understand human consciousness, and we're not even close to figuring it out; probably never will.
Why would it be any different than determining if one person is more intelligent overall than another, or at least more intelligent at a given set of tasks? You don't need to prove it mathematically, you just need empirical evidence.
Why would it be any different than determining if one person is more intelligent overall than another, or at least more intelligent at a given set of tasks? You don't need to prove it mathematically, you just need empirical evidence.
Maybe I don't understand what AGI is—I'm not up to speed on AI developments and only pay so much attention—but my understanding is that it's not just about intelligence but about being able to gain intelligence and understanding without that being predetermined by algorithms. I don't see how that is possible.
Why would it be any different than determining if one person is more intelligent overall than another, or at least more intelligent at a given set of tasks? You don't need to prove it mathematically, you just need empirical evidence.
Show me consciousness and I'll give you a million dollars.
It doesn't really matter for your point, but as a matter of fact, very few people are told there is a trick but not told what the trick is.
The "trick" is that the remainder of the digit sum on division by 9 is the same as the remainder of the original number on division by 9, and exact divisibility by 3 follows as a corollary, so I feel if you were going to go down that route saying that there is a "division by 3" trick might be a bit misleading, almost to the point of misdirection.
The "trick" is that the remainder of the digit sum on division by 9 is the same as the remainder of the original number on division by 9, and exact divisibility by 3 follows as a corollary, so I feel if you were going to go down that route saying that there is a "division by 3" trick might be a bit misleading, almost to the point of misdirection.
The way I thought about it was, you start with the conclusion that the sum of the digits is divisible by 3. Then, to get back the original number, you add the appropriate power of ten, 10^n, times its associated digit, to get back the original number less 1 for the digit that was already counted. So you add digit*(10^n - 1) which will always have the form digit*9, digit*99, digit*999, etc., and those are all also divisible by 3, so if you keep adding numbers divisible by 3 then the whole thing stays divisible by 3.
The way I thought about it was, you start with the conclusion that the sum of the digits is divisible by 3. Then, to get back the original number, you add the appropriate power of ten, 10^n, times its associated digit, to get back the original number less 1 for the digit that was already counted. So you add digit*(10^n - 1) which will always have the form digit*9, digit*99, digit*999, etc., and those are all also divisible by 3, so if you keep adding numbers divisible by 3 then the whole thing s
This looks about right, although seems like a bit of a roundabout way of explaining it. There is nothing special about 3 other than it's the only divisor of 9 though. In its general form, the trick works in base b for n = b - 1 and its divisors. So, for example, in base 16, the trick would work for 3,5 and 15.
Just for a slightly more straightforward explanation, take a 3 digit number as an example although it's easy enough to see how this generalises to any number of digits and to any base.
1. Call our number abc
2. abc = 100a + 10b + c
3. abc = 99a + a + 9b + b + c
4. abc = 9(some stuff) + a + b + c
5. abc mod 9 (the remainder of abc divided by 9) = 0 + (a + b + c) mod 9
6. abc mod 3 = 0 + (a + b + c) mod 3
This looks about right, although seems like a bit of a roundabout way of explaining it. There is nothing special about 3 other than it's the only divisor of 9 though. In its general form, the trick works in base b for n = b - 1 and its divisors. So, for example, in base 16, the trick would work for 3,5 and 15.
I just explained it the way I literally initially thought about it to display the different kinds of intelligence. I checked incrementally how the divisibility changes as you transform from one number to the other, whereas you're approaching it with static concepts.
I just explained it the way I literally initially thought about it to display the different kinds of intelligence. I checked incrementally how the divisibility changes as you transform from one number to the other, whereas you're approaching it with static concepts.
Not sure how I am approaching it using static concepts, I'd never really thought about it before and figured it out on the fly when Sklansky posted. I suppose the part I left implied when generalising to any base is that x^n - 1 is always divisible by x -1 which is true but requires a little algebra to prove, but it's easy enough to see intuitively that 999.... is always divisible by 9 in the case of base 10.
You wrote above:
The "trick" is that the remainder of the digit sum on division by 9 is the same as the remainder of the original number on division by 9, and exact divisibility by 3 follows as a corollary
This is static because none of the concepts or values that you're discussing are changing. They are static facts connected together.
When you got to the actual proof, after our interaction:
1. Call our number abc
2. abc = 100a + 10b + c
3. abc = 99a + a + 9b + b + c
4. abc = 9(some stuff) + a + b + c
5. abc mod 9 (the remainder of abc divided by 9) = 0 + (a + b + c) mod 9
6. abc mod 3 = 0 + (a + b + c) mod 3
Then you used some incremental changes because each line changes something from the previous line. It's interesting to me that, even though I would start with incremental change concepts and you would start with static concepts, either of us would have to add in more of the other concept to get an actual proof.
You wrote above:
This is static because none of the concepts or values that you're discussing are changing. They are static facts connected together.
When you got to the actual proof, after our interaction:
Then you used some incremental changes because each line changes something from the previous line. It's interesting to me that, even though I would start with incremental change concepts and you would start with static concepts, either of us would have to add in more of the other concept to get
Sorry man, I have no idea what you're talking about. In particular, this:
"This is static because none of the concepts or values that you're discussing are changing. They are static facts connected together."
seems like word salad to me.
If you mean that one of my posts contained a line by line proof and the other didn't, well, yeah, sure. One was a general observation and one was a sketch for a proof of that observation.
Sorry man, I have no idea what you're talking about. In particular, this:
"This is static because none of the concepts or values that you're discussing are changing. They are static facts connected together."
seems like word salad to me.
Just look at each part of the sentences and notice that none of them mention anything changing...Contrast that with something I said "so if you keep adding numbers divisible by 3 then the whole thing stays divisible by 3". The bolded words are considering how things are changing as some process occurs repeatedly.
Also, while your proof has changes since it's literally required, it does the bare minimum to get from a to b. The concept of a change or rate of change, or anything similar is avoided. I could generalize my initial version into a real proof while keeping parts that explicitly mention changes, though this whole example is more skewed toward static concepts. Something in calculus for example would be more naturally solved with changy concepts.
Just look at each part of the sentences and notice that none of them mention anything changing...Contrast that with something I said "so if you keep adding numbers divisible by 3 then the whole thing stays divisible by 3". The bolded words are considering how things are changing as some process occurs repeatedly.
Also, while your proof has changes since it's literally required, it does the bare minimum to get from a to b. The concept of a change or rate of change, or anything similar is avoided.
Ok, as I originally suspected, you are a word salad peddler.
Had a guitar teacher once who tried to transcribe all four parts of Jesu, Joy of Man's Desiring on classical guitar. Don't think he ever worked out an arrangement that was realistically playable.
**** that piece though. I’ve never understood why it’s popular, and I say that as a musician who was forced to study Bach chorales in depth.
People are ****ing stupid..
If you want to listen to bullshit oratorio, you know Handel exists, right? Right??
