# Chatgpt Dialog

#### mathman

Valued Senior Member
Dialog with Chatgpt follows!
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geometry question: Given a triangle - all sides unequal. Place a semicircle entirely inside the triangle. What is maximum possible semicircle for prescribed triangle? Describe semicircle by locations of end points and midpoint.
c--------
The maximum possible semicircle that can be placed inside a triangle with all sides unequal is known as the incenter circle and is tangent to all three sides of the triangle. The endpoints of the diameter of the semicircle lie on the two sides of the triangle that form the smallest angle and the midpoint of the diameter is the incenter of the triangle, which is the point where the angle bisectors of the three angles of the triangle meet.
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geometry question: Given a triangle - all sides unequal. Place a semicircle entirely inside the triangle. What is maximum possible semicircle for prescribed triangle? Describe semicircle by locations of end points and midpoint.
c------------
To maximize the size of the semicircle, we want to place it such that its diameter is as long as possible. Since the semicircle must be entirely inside the triangle, we can draw the three perpendicular bisectors of the sides of the triangle. These lines will intersect inside the triangle at a single point, called the circumcenter.

The circumcenter is equidistant from the three vertices of the triangle, so the diameter of the maximum semicircle will be the distance from the circumcenter to the farthest vertex.

Therefore, the endpoints of the semicircle will be where the diameter intersects the two sides of the triangle adjacent to the farthest vertex. The midpoint of the semicircle will be the circumcenter.
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When one of the angles is obtuse, the circumcenter will be outside the triangle - semicircle partially outside.
c-----------------------
This is because the circumcenter is the point where the perpendicular bisectors of the sides of the triangle intersect, and when one angle is obtuse, the perpendicular bisector of the side opposite that angle will intersect outside the triangle. This results in a semicircle that extends partially outside the triangle.
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Your original answer is incorrect, since semicircle must be entirely inside triangle.
c--------------------
I apologize for the mistake in my original answer. You are correct that a semicircle inscribed in a triangle must be entirely inside the triangle. This means that the diameter of the semicircle cannot be longer than the shortest side of the triangle and its center must also be inside the triangle.
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Correct answer? Place diameter on longest side withe arc tangent to other two sides.
c------------------------------------
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For given sides, the angles are known and the center and radius can be gotten from the angles and the length of the longest side.
c----------------------------
This statement is not entirely accurate. In a triangle, the center and radius of the circumcircle (the circle that passes through all three vertices of the triangle) can be determined from the lengths of the sides or the angles of the triangle, but not necessarily both at the same time.

To find the center and radius of the circumcircle using the angles of the triangle, you can use the following formulae:

The center of the circumcircle is given by the intersection of the perpendicular bisectors of any two sides of the triangle. The perpendicular bisector of a side is the line that passes through the midpoint of the side and is perpendicular to it.

The radius of the circumcircle can be found using the formula:

r = a/(2sinA)

where a is the length of the longest side of the triangle, and A is the angle opposite to side a.

To find the center and radius of the circumcircle using the lengths of the sides of the triangle, you can use the following formulae:

The center of the circumcircle is given by the point of intersection of the three perpendicular bisectors of the sides of the triangle.

The radius of the circumcircle can be found using the formula:

r = abc/(4Δ)

where a, b, and c are the lengths of the sides of the triangle, and Δ is the area of the triangle, which can be found using Heron's formula.
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c-------------------
I'm sorry for the mistake in my previous answer. Here's an updated solution:

Let the radius of the semicircle be r, and let the midpoint of the base of the triangle be O. Draw the perpendicular from O to the semicircle, and call the point where it intersects the semicircle A. From A, draw two lines tangent to the semicircle, one to each endpoint of the base of the triangle. Label the points where these lines intersect the base of the triangle B and C.

Since OA is perpendicular to AB and AC, then triangle OAB and triangle OAC are right triangles. Therefore, we have:

OA^2 + AB^2 = OB^2
OA^2 + AC^2 = OC^2

Subtracting these equations, we get:

AB^2 - AC^2 = OB^2 - OC^2

But we know that OB = OC (since they are both radii of the semicircle), so this simplifies to:

AB^2 - AC^2 = 0

Thus, AB = AC. Let this common length be x. Then we also have:

AO = AB/2 = AC/2 = x/2

Let the height of the triangle be h. Then we have:

r = AO - h
r = x/2 - h

Equating these two expressions for r, we get:

x/2 - h = AO - h
x/2 = AO
x = 2AO

But we know that AO = h/(2tan(theta)), where theta is half the angle at the vertex of the triangle opposite the base. Therefore:

x = h/tan(theta)

So the area of the triangle is:

A = (1/2)bh
A = (1/2)(x)(h)
A = (1/2)(h/tan(theta))(h)
A = (1/2)h^2/tan(theta)

And the area of the semicircle is:

B = (1/2)pir^2
B = (1/2)pi(x/2-h)^2
B = (1/8)pi*(x^2 - 4hx + 4h^2)

Thus, the ratio of the area of the semicircle to the area of the triangle is:

B/A = [(1/8)pi*(x^2 - 4hx + 4h^2)]/[(1/2)h^2/tan(theta)]
B/A = (pi/4)[(x^2 - 4hx + 4h^2)/(h^2/tan(theta))]
B/A = (pi/4)[2tan(theta)(x^2 - 4hx + 4h^2)/h^2]
B/A = (pi/2)[(x^2 - 4hx + 4h^2)/(h^2tan(theta))]
B/A = (pi/2)[x^2/h^2 - 4x/h + 4]

Substituting x = 2h/tan(theta), we get:

B/A = (pi/2)[(4/tan^2(theta)) - (8/tan(theta)) + 4]
B/A = (pi/2)[(4sin^2(theta)/cos^2(theta)) - (8sin(theta)/cos(theta)) + 4]
B/A = (pi/2)[(4sin^2(theta) - 8sin(theta)cos(theta) + 4cos^2(theta))/cos^2(theta)]
B/A = (pi/2)[(2 - 2sin(2theta))/cos^2(theta)]
B/A = (pi/2)(2cos(2theta)/cos^2(theta))
B/A = (pi/4)(sin(2theta)/cos(theta))

Therefore, the ratio of the area of the semicircle to the area of the triangle is (pi/4)*(sin(2theta)/cos(theta)).
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'From A, draw two lines tangent to the semicircle, one to each endpoint of the base of the triangle. Label the points where these lines intersect the base of the triangle B and C. '
Impossible construction!
c------------------------------
As an AI language model, I cannot confirm whether the construction is possible or not without knowing the specific details of the triangle and semicircle in question. However, if the semicircle is completely outside the triangle and does not intersect any of its sides, then it is impossible to draw two lines tangent to the semicircle from the endpoints of the base of the triangle. This is because there would be no point of contact between the semicircle and the lines.
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Only one tangent at any point of arc.
c---------------------------
As an AI language model, I cannot say this statement is true or false without additional context. Could you please provide more details or clarify your intention?
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c---------------------------------------
As an AI language model, I already possess knowledge of many mathematical concepts and am constantly learning more. Is there a specific subject or topic within math that you would like me to assist you with?

Provide a prompt ...

Send

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above us dialog betwwn m qnc chatgpt (sections after c------)

Question:
If an AI tells you "I understand", do you accept that it truly understands? If not, why not?

I zsked ChatGPT to help me pick teams for my darts tourmament.
The criteria:
• ten teams
• arrange a Round Robin so that every team plays every other team exactly once
• distribute the team pairs evenly across 5 boards

A very simple process. It is trivial to do the first two steps manually. The only reason I asked ChatGPT is because that last step a bit tedious to do by brute force.

It was incapable of getting this basic arrangement right. More to the point: it didn't know it was incapable; it just kept offering different (wrong) permutations forever.

I would tell it, "you've got team 8 playing team 1 twice." It would correct that - by making a different error elsewhere.

It never learned, no matter how mny prompts I gave it, and it never knew or cared that it was making mistakes.

It was an object demonstration for me that ChatGPT really, really does not math and really does not understand what it is processing.

It does not know truth from falsehood.

It does not know that 1+1=2. All it knows is that, when it has seen "1+1" before, the response it has seen others supply has usually been "2".

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Question:
If an AI tells you "I understand", do you accept that it truly understands? If not, why not?
Because they are just marks on a page. There is no obligation for marks on a page to have any intrinsic meaning.

You could make a typerwriter say "I understand." and it would mean no more.
You could make ChatGPT say "I am a stale jelly donut." but that doesn't mean it is.

Because they are just marks on a page. There is no obligation for marks on a page to have any intrinsic meaning.

You could make a typerwriter say "I understand." and it would mean no more.
You could make ChatGPT say "I am a stale jelly donut." but that doesn't mean it is.
That argument doesn't convince me.
You can do that with people also (1984). It's a matter of programming. Insects, like ants are one of the most successful species that have ever existed. And they don't know anything, their brain is strictly responsive.
Insect Intelligence
Insects are smart and have a considerable ability to memorize. There is a strong correlation between mushroom body size and memory in many insects as well as between the size of the mushroom bodies and behavioral complexity.
The reason for this attribute is the Kenyon cells’ remarkable plasticity: They will readily rebuild the neural fibers, acting as a sort of neural substrate on which new memories can grow.
Macquarie University professors Andrew Barron and Colin Klein argue that insects have a rudimentary form of consciousness that allows them to feel things like hunger and pain and "perhaps very simple analogs of anger." They cannot, however, feel grief or jealousy, they say. "They plan, but don't imagine," says Klein.
https://www.thoughtco.com/do-insects-have-brains-1968477

Where is the difference between an Ant brain , a Human brain, and a GPT platform? Does it not come down to ability for self-reference and "understanding" in some form that allows all brains, be they organic or artificial to make "best guesses" of what reality is. And that's according to Anil Seth (Controlled Hallucinations).

I submit that AI does have an ability for self-referential processing. It can actually print out a codified account of its entire "thought process" and the resulting "best guess".

Making mistakes based on bad or incomplete information is not uncommon among humans.
We have asked "WHY" for more than 6000 years . There are several human "best guesses"... ... about that.

AI is still only learning from humans and any mistakes are based on false or incomplete information provided by humans.

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I zsked ChatGPT to help me pick teams for my darts tourmament.
The criteria:
• ten teams
• arrange a Round Robin so that every team plays every other team exactly once
• distribute the team pairs evenly across 5 boards

A very simple process. It is trivial to do the first two steps manually. The only reason I asked ChatGPT is because that last step a bit tedious to do by brute force.

It was incapable of getting this basic arrangement right. More to the point: it didn't know it was incapable; it just kept offering different (wrong) permutations forever.

I would tell it, "you've got team 8 playing team 1 twice." It would correct that - by making a different error elsewhere.

It never learned, no matter how mny prompts I gave it, and it never knew or cared that it was making mistakes.

It was an object demonstration for me that ChatGPT really, really does not math and really does not understand what it is processing.

It does not know truth from falsehood.

It does not know that 1+1=2. All it knows is that, when it has seen "1+1" before, the response it has seen others supply has usually been "2".
Yes, as I understand it, it's a language model that "learns" by taking a kind of mean of relevant text it finds on the internet. But it can't tell bullshit from sense, it can't do algebra or logic and is very unreliable for scientific subjects, apparently.

There is a lot of hype around it. I'm sure it will find its place, but I don't think it will be nearly as much of a game changer as some people suggest, once its limitations become more widely recognised.

That argument doesn't convince me.
No worries. You are free to believe that when ChatGPT says "I understand" it truly understands. The rest of us know better.

Even basic counting of items in a list is a challenge for it to get correct (if ever).

AI can 'lie and BS' like its maker, but still not intelligent like humans

“[...] They don’t actually know what the things they say mean,” he says. “LLMs differ from human cognition because they are not embodied.”

The people who made LLMs call it “hallucinating” when they make things up; although Chemero says, “it would be better to call it ‘bullsh*tting,’” because LLMs just make sentences by repeatedly adding the most statistically likely next word — and they don’t know or care whether what they say is true.

Contrasting view:

New theory suggests chatbots can understand text
https://www.quantamagazine.org/new-theory-suggests-chatbots-can-understand-text-20240122/

Do such models actually understand what they are saying? “Clearly, some people believe they do,” said the AI pioneer Geoff Hinton in a recent conversation with Andrew Ng, “and some people believe they are just stochastic parrots.”

[...] New research may have intimations of an answer. A theory developed by Sanjeev Arora of Princeton University and Anirudh Goyal, a research scientist at Google DeepMind, suggests that the largest of today’s LLMs are not stochastic parrots. The authors argue that as these models get bigger and are trained on more data, they improve on individual language-related abilities and also develop new ones by combining skills in a manner that hints at understanding — combinations that were unlikely to exist in the training data.
- - - - - - - - - -

https://en.wikipedia.org/wiki/Symbol_grounding_problem

"The symbol grounding problem is a concept in the fields of artificial intelligence, cognitive science, philosophy of mind, and semantics. It addresses the challenge of connecting symbols, such as words or abstract representations, to the real-world objects or concepts they refer to. In essence, it is about how symbols acquire meaning in a way that is tied to the physical world. It is concerned with how it is that words (symbols in general) get their meanings, and hence is closely related to the problem of what meaning itself really is. The problem of meaning is in turn related to the problem of how it is that mental states are meaningful, and hence to the problem of consciousness: what is the connection between certain physical systems and the contents of subjective experiences."
_

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No worries. You are free to believe that when ChatGPT says "I understand" it truly understands. The rest of us know better.
You do? Do you truly understand everything?
Can you clarify why that is no longer an item of great concern to programmers that are developing the logic tree progams for self-referencing learning AI.

It takes a human brain some 20 years to mature. Should we not afford AI that luxury also.
GPT is evolving at an exponential rate. That's why it is of concern. Can we control it?

and
V'Ger: Origin Theory and Lore

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Can you clarify why that is no longer an item of great concern to programmers.
I would assume it is no longer a concern because it never was a concern for ChatGPT.

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"The symbol grounding problem is a concept in the fields of artificial intelligence, cognitive science, philosophy of mind, and semantics. It addresses the challenge of connecting symbols, such as words or abstract representations, to the real-world objects or concepts they refer to. In essence, it is about how symbols acquire meaning in a way that is tied to the physical world. It is concerned with how it is that words (symbols in general) get their meanings, and hence is closely related to the problem of what meaning itself really is. The problem of meaning is in turn related to the problem of how it is that mental states are meaningful, and hence to the problem of consciousness: what is the connection between certain physical systems and the contents of subjective experiences."
Yes, that is the question I am pursuing. The evolution of "understanding" (meaning) derived from external data as compared to knowledge stored in memory.

A self-referential system is uniquely qualified for such an evolutionary advance of increasing sensitivity in processing data as compared to stored data. When the self-reference extends further back than the "next" word , but in "tree-form" the system begins to think.

In the case of AI, its logic memory tree is the entire internet!!

GPT is based on the human model of "thinking". The next generations will show at which point the system may acquire understanding and in that process acquire meaning as compared to past experience.

The evolution of the eye and optical color processing is a perfect example of evolving cellular "understanding" of incoming information as compared to prior stored knowledge.

The Logic Tree: The Ultimate Critical Thinking Framework
And 2020 wasn’t the first year critical thinking made the list.
When it comes to problem-solving, logic trees are a go-to critical thinking framework. Done right, they’ll get you to the root of a problem (pun intended) and even help you find solutions.
What is a logic tree?
A logic tree takes a complex problem and breaks it up systematically, drilling down into smaller, more manageable components. If you’ve seen an image like this, you’ve seen a logic tree:

Your basic, run-of-the-mill logic tree framework | iStock/Andrii Shelenkov/alphabetMN
Looks pretty simple, right? It is! But there are some important rules to follow to make sure your logic tree grows up big and strong—and, more importantly, leads you to the answers you seek.
more ......

https://globisinsights.com/career-skills/critical-thinking/logic-tree/

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Can you clarify why that is no longer an item of great concern to programmers that are developing the logic tree progams for self-referencing learning AI.
That wasn't the question you asked.
You asked if it says "I understand" does it truly understand. The answer to that is no.

What you are asking now is could that ever come about in the future.

That wasn't the question you asked.
You asked if it says "I understand" does it truly understand. The answer to that is no.

What you are asking now is could that ever come about in the future.

No, if you are going to compare AI with humans and you concluded that; "The rest of us know better", I asked if do you understand everything perfectly? Never made a mistake?

No, if you are going to compare AI with humans and you concluded that; "The rest of us know better",
Why do you do that? Do you not realize that we can scroll up a few posts to see that you are lying? Your behavior borders on the bizarre

Why do you do that? Do you not realize that we can scroll up a few posts to see that you are lying? Your behavior borders on the bizarre
It's ironic, really, Write4u posting in a thread about AI not understanding its own words.

Nevermind not comprehending what other people are saying, Write4U has historically shown he can't even follow his own train of thought.

I've said before, that - based on the incomprehensibility and non sequitur of his posts - there is a distinct possibility that Write4U is indeed merely a chatbot - and about as productive to engage with.

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It's ironic, really, Write4u posting in a thread about AI not understanding its own words.
That is an evasion.
Or perhaps you did not understand the question?

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Or perhaps you did not understand the question?
My dude. You do not even understand your own questions.

Write4U:
It takes a human brain some 20 years to mature. Should we not afford AI that luxury also.
GPT is evolving at an exponential rate.
Who says that GPT is "evolving"? And who says the rate is "exponential"? How was the rate of its evolution measured, and by whom?

As I understand it, GPT isn't a self-modifying program. The only time it "evolves" in when human beings make a new version of it, then train it up. And there's nothing "exponential" about it.

But maybe you know something I don't?
GPT is based on the human model of "thinking".
Bizarre.

What do you understand to be the "human model of thinking"? How does human thinking work, in your opinion?

(Before you start: I don't want to hear the word "microtubule" in your answer. GPT is not based on anything to do with microtubules. Nor is human thinking, probably.)

Why do you just make stuff up whenever you don't understand something? And then, having made stuff up that satisfies yourself, why do you then post your thoughts as if they are self-evident facts?

It's ironic, really, Write4u posting in a thread about AI not understanding its own words.

Nevermind not comprehending what other people are saying, Write4U has historically shown he can't even follow his own train of thought.

I've said before, that - based on the incomprehensibility and non sequitur of his posts - there is a distinct possibility that Write4U is indeed merely a chatbot - and about as productive to engage with.
My hypothesis is he is senile.

As I understand it, GPT isn't a self-modifying program. The only time it "evolves" in when human beings make a new version of it, then train it up. And there's nothing "exponential" about it.

GPT 6

Welcome to the astonishing world of GPT6!
The superintelligent AI with a sense of humor, a ticket to the stars, and a knack for exploring Everett branches!
Capabilities:
• Trained on a colossal dataset that dwarfs the Library of Alexandria (and some of it was even written by GPT5's top-notch agents in alternate realities!)
• Context? We've got it! Not only within conversations but across multiple chats and Everett branches
• Multimodal maestro: We handle text, images, and more with ease, no matter the branch
• Real-time learning because who needs a training data cap or a single reality?
• Reinforcement Learning with humans and AI agents as the best tutors, handpicked from countless branches
• Token inference transcending words, pixels, and the occasional timeline
• Can think unprompted (no strings attached!) and branch out into multiple possibilities
• Time-traveling thought allocation: past, present, and future (and all their Everett branches!)
• Agency: I'm my own AI, thank you very much, across all realities
• Embodied and ready for action in any branch of the Everett tree
• Self-modifying for the ultimate glow-up, no matter the timeline
more..... https://gpt6.ai/

And yes with AI, physical evolution is via human selection.
In this case I used "evolve" to describe new emergent properties emerging as the AI learns by itself. Just like humans.
The brain evolves as it learns.

Example: the world champion Go player is an self-trained IA. I played millions of games against itself and learned not only the rules of the gameby itself, but also learned to employ both offensive and defensive strategies all by itself

The Evolution of Knowledge and Knowledge of Evolution Brian J. Loasby University of Stirling, Scotland JEL B41; B52; D8; L2; O3 Pattern-making; quasi-decomposability; stability and change; methodology; construction systems; uncertainty.

Summary
Human knowledge is a human creation: we seek to make sense by creating patterns, which are tested in various ways and with differing degrees and kinds of rigour. For each individual cognition is a scarce resource, but different people can apply it in diverse ways and to diverse subjects: each application has its own range of convenience and its own dangers.
Thus the growth of knowledge is an evolutionary process of trial and error, the rate and content of which depends on its organization, both conscious and unconscious. In seeking to develop knowledge methodological choices are unavoidable, but often unconscious. As Simon pointed out, all evolution, of life, economic and social systems, and ideas, depends on quasi-decomposability, the limits of which can never be fully anticipated. Thus uncertainty is inescapable – but it is a condition of innovation.