So I have all sorts of associations with "apple" and spent a little time playing with it.

First in a raw physical sense I can imagine an apple in my head, spin it around, imagine its physics with near cylindrical symmetry etc. A red apple is what first pops into my head, although of course I know there are many apple variants and have opinions on their taste etc.

There are many cultural associations I have with apples from Newton to George Washington. The company Apple has its own set of ideas that I interact with when I hear the word.

In other words I can think of various associations I have to the word apple of various strengths. These associations and strengths are functions of my experience encountering the word and actual apples.

Is there a feeling of "appleness"?

I don't really know what this would mean. I would say no, unless it can perhaps be defined what appleness means and feels like. I don't really notice any strong set of emotions or feelings from this thought exercise.

Do you think that sense of meaning is equivalent to the numerical weights of an LLM?

Again I think I would need a definition of "sense of meaning". I don't seem to derive a singular pointlike meaning when contemplating a singular word. I never was contending that human and LLM cognition are exactly equivalent, but I could see these association strengths being represented in LLM weights. I would say then if an LLM has similar association strengths with "apple" then it "understands" apples as well as I do. Of course this is really hard to test, but frontier models could give you all sorts of apple facts and cultural associations and so on. It may slip up and hallucinate, and I'm sure that I also believe at least one false thing about apples.

So what is your brightline between LLM and human understanding in this example? I assume that your line of reasoning would argue that LLMs do not understand apples. Why don't LLMs understand the word "apple?

Or rather, maybe I don't understand what you mean :)

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To find the value of foo applied to bar, we need to first determine the values of both foo and bar. Let's start with bar, the circumference of a circle with radius 1:

Circumference (C) = 2 * π * r where r is the radius.

In this case, r = 1, so:

bar = C = 2 * π * 1 = 2π

Now, let's move on to foo. Since foo is a function that calculates the sinus of its first argument, we need to find the sine of bar (2π):

foo(bar) = sin(2π)

The sine function is periodic with a period of 2π, which means that sin(2π) is equal to sin(0). The value of sin(0) is 0. Therefore:

foo(bar) = sin(2π) = 0

======= So I think it evaluated correctly here unless I have made a dumb mistake in reading your prompt myself.