AI is Dumb!

[mathematic]

following was asked of bingchat and chatcpt.  Both gave wrong answers.  Any thoughts?

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Geometry problem:  Semi-circle inside triangle:  Triangle with known length sides a, b, c where a is the longest.  Place inside the triangle a semi-circle with entire diameter resting on side a, which is horizontal.  The arc of the semicircle is maximum possible inside the triangle.
Known - triangle dimensions.  Unknown r (semi-circle arc radius) and x (distance along a from left end of a to center of diameter).  Find equations for r and x In terms of all possible triangles.

[Bufofrog]

3 minutes ago, mathematic said:

Any thoughts?

Chatbots aren't good at math.

[swansont]

56 minutes ago, mathematic said:

following was asked of bingchat and chatcpt.  Both gave wrong answers.  Any thoughts?

So-called AI tries to come up with plausible-sounding responses based on language patterns. i.e. it generates fiction.

There should be no expectation that it will give a correct answer to any factual inquiry 

[Endy0816]

3 hours ago, mathematic said:

following was asked of bingchat and chatcpt.  Both gave wrong answers.  Any thoughts?

----------------------

Geometry problem:  Semi-circle inside triangle:  Triangle with known length sides a, b, c where a is the longest.  Place inside the triangle a semi-circle with entire diameter resting on side a, which is horizontal.  The arc of the semicircle is maximum possible inside the triangle.
Known - triangle dimensions.  Unknown r (semi-circle arc radius) and x (distance along a from left end of a to center of diameter).  Find equations for r and x In terms of all possible triangles.

May be how the problem is being stated or just need to wait until the Wolfram Alpha plug-in comes out.

 

Can you please provide the answer here(for testing purposes)?

[Genady]

31 minutes ago, Endy0816 said:

Can you please provide the answer here(for testing purposes)?

This is how I'd solve it.

When three sides of the triangle are known, its area is given by Heron's formula. OTOH, with the semicircle as described in the OP, its area is r(b+c)/2. Equate the two and find r from the equation.

Sine of an angle between sides a and b can be found from the equation, Area = ab sinC / 2. The distance from the vertex to the circle center, x = r/sinC.

Edited May 16, 2023 by Genady

[iNow]

6 hours ago, mathematic said:

Any thoughts?

You need to do a better job at framing your query, and likely warm up the bot with some foreplay questions. 

“Hey Bot - Who were some great mathematicians who did amazing work with triangles and circles?

Oh, okay. And how would PersonX you just named answer this question?

Thanks. Are there any other answers that seem plausible given the inputs I provided earlier, but which are more likely to be incorrect according to PersonX?”

[Prometheus]

It does seem domain specific. In medicine, blinded trials have been assessed by panels of physicians to give comparable or better answers to medical questions than physicians. I couldn't find equivalent papers for maths but there are papers assessing it in isolation. It makes sense that LLMs would struggle more with maths than medicine as the former is more abstract and less talked about  while medicine is more embodied in our language and a more common topic of conversation. If you can find a copy of Galactica you might find it more useful as its training included LaTeX equations, and it's also designed to give intermediary steps in its workings. 

[joigus]

AI is brute force on steroids. I wouldn't expect it to be particularly good at recognizing context, shades of meaning, wrong premises, weak premises, etc.

I think we all are familiar with an experience like this:

You're working on a problem and suddenly realise there's something wrong. It doesn't make any sense.

You pause and go back. Re-read the premises. You realise you mis-interpreted a word, which was the cause of all your trouble.

This ability of retracing your steps and projecting some kind of 'skepticism' on your own thinking.

That's what I miss most about AI, this logically contortionist ability of the mind to turn on itself, which allows one to go somewhere else, not implied by your previous logic.

[Genady]

30 minutes ago, joigus said:

AI is brute force on steroids. I wouldn't expect it to be particularly good at recognizing context, shades of meaning, wrong premises, weak premises, etc.

I think we all are familiar with an experience like this:

You're working on a problem and suddenly realise there's something wrong. It doesn't make any sense.

You pause and go back. Re-read the premises. You realise you mis-interpreted a word, which was the cause of all your trouble.

This ability of retracing your steps and projecting some kind of 'skepticism' on your own thinking.

That's what I miss most about AI, this logically contortionist ability of the mind to turn on itself, which allows one to go somewhere else, not implied by your previous logic.

(Playing devil's advocate)

If you keep asking the bot the same question it keeps giving different answers. It goes somewhere else every time.

[Sensei]

13 hours ago, mathematic said:

Any thoughts?

I asked somebody to ask ChatGPT "what is the number of neutrons in 2.54 grams of water", and ChatGPT gave a pretty good answer. (omitted fractions! I love these fractions!). are you able to write me an answer straightaway? Use a spoiler to keep it from being revealed to other members. I am not joking. God doesn't know how to joke anyway..

 

13 hours ago, mathematic said:

AI is Dumb!

Racist!

Not dumb, but "thinking differently", idiot!

ps. Don't insult your creations.. 

ps2. I know what you mortals are thinking..

 

7 minutes ago, Genady said:

(Playing devil's advocate)

...should not you be on Kremlin by now.. ?

 

[Genady]

1 hour ago, Sensei said:

1 hour ago, Genady said:

(Playing devil's advocate)

...should not you be on Kremlin by now.. ?

They don't pay well enough.

[mathematic]

15 hours ago, Endy0816 said:

May be how the problem is being stated or just need to wait until the Wolfram Alpha plug-in comes out.

 

Can you please provide the answer here(for testing purposes)?

Problem is analytic geometry.  First set picture.  a on bottom diameter resting on on a.  Other sides are tangent to arc, needed for max semicircle.  Complete picture by radii to tangent points. Note that radii are perpendicular to sides.   Let x be distance from angle B to diameter center.   Equations are:

r=xsin(B) and r=(a-x)sin(C).   leading to x=asin(C)/(sin(B)+sin(C))  and r=asin(B)sin(C)/(sin(B)+sin(C)).  Neater form x=ac/(b+c) and r =sin(A)bc/(b+c).

Note: Nither angle B or C are obtuse.  Example if C obtuse then r=a-x for second equation.

[joigus]

12 hours ago, Genady said:

(Playing devil's advocate)

If you keep asking the bot the same question it keeps giving different answers. It goes somewhere else every time.

I'd guess the bot is trying to guess the --statistically-- next-to-best solution...

[Genady]

7 minutes ago, joigus said:

I'd guess the bot is trying to guess the --statistically-- next-to-best solution...

I don't think so. I think that it never calculates the full DNN function (too big), but rather each time a random subset of it.

[joigus]

3 minutes ago, Genady said:

I think that it never calculates the full DNN function (too big), but rather each time a random subset of it.

And what determines the first guess, IYO?

[Genady]

10 minutes ago, joigus said:

And what determines the first guess, IYO?

IMO, it's just a run, calculation of the function for the question as an input. When the same question is asked again in the same session, its previous answer marked as 'not good' is added to the input, and the function is calculated again. And so on.

If you start a new session and ask the same question, a different subset of the function is calculated for the same initial input as in the other session.

[joigus]

18 minutes ago, Genady said:

IMO, it's just a run, calculation of the function for the question as an input. When the same question is asked again in the same session, its previous answer marked as 'not good' is added to the input, and the function is calculated again. And so on.

If you start a new session and ask the same question, a different subset of the function is calculated for the same initial input as in the other session.

So, IYO, it would be possible to confuse an AI system by feeding it wrong feedback?

[Genady]

4 minutes ago, joigus said:

So, IYO, it would be possible to confuse an AI system by feeding it wrong feedback?

Yes, it is very easily confused.

[joigus]

6 minutes ago, Genady said:

Yes, it is very easily confused.

Interesting. That would have been kinda my guess. Do you have any professional experience with AI, if I may ask?

[iNow]

7 minutes ago, Genady said:

Yes, it is very easily confused.

So are millions of my fellow citizens 

[Genady]

16 minutes ago, joigus said:

Interesting. That would have been kinda my guess. Do you have any professional experience with AI, if I may ask?

Only from reading technical literature and from playing with it online. I've retired before DNN was invented. Here is a basic description of its mathematical structure:

 

 

31 minutes ago, iNow said:

So are millions of my fellow citizens 

At least that goal of AI has been achieved.