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The problem with language models is that there's no thought behind what they say. It's just pattern recognition. If you ask it an original convoluted but simple

by mik1998 4y ago

The problem with language models is that there's no thought behind what they say. It's just pattern recognition. If you ask it an original convoluted but simple natural language question, it will spit out nonsense. There's no thought behind what it sees - when it sees 5x - 3 = 2x + 7, it doesn't think that the x represents the variable, you need to plug in a number such that both sides are equal etc. It just sees the symbols and looks up the answer in it's memory. There's zero intelligence here. It's like a hypothetical student who simply memorizes all definitions without understanding at all. You can ask it for the definition of a linear system of equations, and you can ask it how to solve one, but there is zero understanding or thought there, in spite of apparent knowledge. In a way, it reminds me of Feynman's anecdote about Brazilian universities.

ben_w 4y ago
Goalpost shifting aside, that presumes a definition of "thought". Perhaps these models are different from us in this regard (I'd assume so simply because it had to read more tokens than the total number of times an average single synapse in a human brain will fire in a lifetime), but I don't think humanity collectively yet has a concept of what it means to think that's good enough to prove the absence. Can submarines swim? And does it really matter?
- mik1998 4y ago
  I'm not shifting goalposts, simply elaborating on your results. You already showed that ChatGPT cannot handle elementary school math problems.
  - ben_w 4y ago
    Which of those do you think were elementary grade? Because I'm fairly sure those are GCSE level[0]. In fact, why don't you suggest 20 "basic elementary school math problems", if you suggest 20 that are at that level, I'll put them in and post what it says; no cherry picking results, but I will grade it. Also, when I was at school, 75%-82.5% was a good score, and looking up the current system, that percentage range is in the top three grades (out of 9) at that level, and can be top grade depending on year and exam board. That is why I say you are moving the goalposts. [0] UK secondary schools are different from US highschools: https://en.wikipedia.org/wiki/General_Certificate_of_Secondary_Education https://en.wikipedia.org/wiki/General_Certificate_of_Seconda...
    - mik1998 4y ago
      I haven't been in elementary school for some time, but I do remember linear equations being taught. Maybe except the sine question, since trigonometry is taught later. Getting 3/4th of simple elementary school questions right indicates that someone is really bad at math. These are not difficult questions. I don't have time to come up with 20 exercises, but I can suggest a few that I think the AI may have trouble with. All of these are trivial single-variable linear equations that a smart elementary school student should have no problem with. (Note that the numbers are intentionally scrambled; this does not increase the difficulty of the problem): 1. Solve for x: 113(6x - 45) = 92x 2. Multiply 13.4a - 18b by 18b + 13.4a 3. Four girls bought bus tickets. Anne bought seventeen 20-minute tickets and paid $323. Marianne bought twenty-eight 75-minute tickets and paid $784. Alice bought nineteen 20-minute tickets and eight 75-minute tickets, and Alex bought seven thousand eighty five 20-minute tickets and ninety six 75-minute tickets. How much did Alex pay? 4. An old man walked fifty nine kilometres in four hours through a flat field. He drove a car to France for nine hours, and then proceeded to walk for eighteen hours through a flat field at the same pace. How many kilometres did the old man walk in France? 5. Alice bought seventy-nine pens and twenty-six notebooks. The arithmetic mean of the cost of these articles was $9.31. The sum of the cost of the notebooks was $112.762. How much did a pen cost?
      - ben_w 4y ago
        Elementary school is for children who are four to eleven years of age. Basic elementary school maths is the start of that age range, so counting with your fingers, the idea of base-10, and adding two small numbers with perhaps one carry. Late elementary school (for me "middle school", but the UK reforms education too much and too often to keep track) was still only basic arithmetic, fundamental "roll 2 d6" probability, nets of the most basic polyhedra. Algebra and trig wasn't until secondary school for me ("year 7" we called it, school year beginning age 11), though I personally had a head start from having learned to read with the Commodore 64 user manual. Well, if you're not willing (or well calibrated enough), I should get some old exam papers, see how well it grades against students. I wonder if there even are any downloadable pre-GCSE exams…

ben_w 4y ago

Goalpost shifting aside, that presumes a definition of "thought". Perhaps these models are different from us in this regard (I'd assume so simply because it had to read more tokens than the total number of times an average single synapse in a human brain will fire in a lifetime), but I don't think humanity collectively yet has a concept of what it means to think that's good enough to prove the absence. Can submarines swim? And does it really matter?

mik1998 4y ago
I'm not shifting goalposts, simply elaborating on your results. You already showed that ChatGPT cannot handle elementary school math problems.
- ben_w 4y ago
  Which of those do you think were elementary grade? Because I'm fairly sure those are GCSE level[0]. In fact, why don't you suggest 20 "basic elementary school math problems", if you suggest 20 that are at that level, I'll put them in and post what it says; no cherry picking results, but I will grade it. Also, when I was at school, 75%-82.5% was a good score, and looking up the current system, that percentage range is in the top three grades (out of 9) at that level, and can be top grade depending on year and exam board. That is why I say you are moving the goalposts. [0] UK secondary schools are different from US highschools: https://en.wikipedia.org/wiki/General_Certificate_of_Secondary_Education https://en.wikipedia.org/wiki/General_Certificate_of_Seconda...
  - mik1998 4y ago
    I haven't been in elementary school for some time, but I do remember linear equations being taught. Maybe except the sine question, since trigonometry is taught later. Getting 3/4th of simple elementary school questions right indicates that someone is really bad at math. These are not difficult questions. I don't have time to come up with 20 exercises, but I can suggest a few that I think the AI may have trouble with. All of these are trivial single-variable linear equations that a smart elementary school student should have no problem with. (Note that the numbers are intentionally scrambled; this does not increase the difficulty of the problem): 1. Solve for x: 113(6x - 45) = 92x 2. Multiply 13.4a - 18b by 18b + 13.4a 3. Four girls bought bus tickets. Anne bought seventeen 20-minute tickets and paid $323. Marianne bought twenty-eight 75-minute tickets and paid $784. Alice bought nineteen 20-minute tickets and eight 75-minute tickets, and Alex bought seven thousand eighty five 20-minute tickets and ninety six 75-minute tickets. How much did Alex pay? 4. An old man walked fifty nine kilometres in four hours through a flat field. He drove a car to France for nine hours, and then proceeded to walk for eighteen hours through a flat field at the same pace. How many kilometres did the old man walk in France? 5. Alice bought seventy-nine pens and twenty-six notebooks. The arithmetic mean of the cost of these articles was $9.31. The sum of the cost of the notebooks was $112.762. How much did a pen cost?
    - ben_w 4y ago
      Elementary school is for children who are four to eleven years of age. Basic elementary school maths is the start of that age range, so counting with your fingers, the idea of base-10, and adding two small numbers with perhaps one carry. Late elementary school (for me "middle school", but the UK reforms education too much and too often to keep track) was still only basic arithmetic, fundamental "roll 2 d6" probability, nets of the most basic polyhedra. Algebra and trig wasn't until secondary school for me ("year 7" we called it, school year beginning age 11), though I personally had a head start from having learned to read with the Commodore 64 user manual. Well, if you're not willing (or well calibrated enough), I should get some old exam papers, see how well it grades against students. I wonder if there even are any downloadable pre-GCSE exams…