Sure. Let’s take quantum theory. There are lots of concepts that are based in math but can be reasoned about non-mathematically.

The reason that chatGPT can write quantum computer programs to in any domain (despite the lack of existing programs!) is because it can deal with the concepts of quantum computing and the concepts in a domain (eg, predicting housing prices) and align them.

Not everything is logic and math; very little of human reasoning is. And this despite the fact that, as a Pythagorean at heart, I believe the world is made of math.

Now you are making things up

Want to be specific?

Adding quantum to whatever you are doing always makes it better!

>There are lots of concepts that are based in math but can be reasoned about non-mathematically.

Can you be more specific? I literally don't know what you mean. What can you say about quantum mechanics that is not mathematical or logical in nature? Barring metaphysical issues of interpretation, which I assume is not what you mean.

Rarely do I think responding with chatGPT is appropriate, but this is one of those times. * Of course! When discussing concepts from quantum mechanics without getting into the mathematical details, we can focus on the general ideas and principles that underlie the theory. Here are some key concepts in quantum mechanics that can be explained in a non-mathematical way:

1. Superposition: In quantum mechanics, particles can exist in multiple states simultaneously, until they are measured. This is called superposition. It's like a coin spinning in the air, being both heads and tails at the same time, until it lands and shows one face.

2. Wave-particle duality: Particles like electrons, photons, and others exhibit both wave-like and particle-like properties. This means they can sometimes behave as particles, and at other times, as waves. This dual nature has been experimentally demonstrated through phenomena like the double-slit experiment.

3. Quantum entanglement: When two particles become entangled, their properties become correlated, regardless of the distance between them. If you measure one of the entangled particles, you'll immediately know the state of the other, even if they are light-years apart. This phenomenon is often referred to as "spooky action at a distance."

4. Heisenberg's uncertainty principle: This principle states that we cannot simultaneously know the exact position and momentum of a particle. The more precisely we know one of these properties, the less precisely we can know the other. This inherent uncertainty is a fundamental aspect of quantum mechanics.

5. Quantum tunneling: In quantum mechanics, particles can "tunnel" through barriers that would be insurmountable in classical physics. This is because the particle's wave function, which describes its probable location, can extend beyond the barrier, allowing the particle to appear on the other side.

6. Quantum superposition of states: Quantum systems can exist in multiple states at once, and when you measure a property of the system, it "collapses" into one of the possible states. This is a fundamental difference between quantum and classical mechanics, where systems have definite properties even before measurement.

These concepts can be discussed and reasoned about without delving into the complex mathematical equations that govern quantum mechanics. While a mathematical understanding is necessary for rigorous study and application of the theory, non-mathematical discussions can still provide valuable insights into the strange and fascinating world of quantum mechanics.*

QED

Mate, not only is every single one of those concepts a mathematical one, the explanations it gives are misleading or incorrect! E.g. the typical pop-sci misleading lines of "it's a wave and a particle at the same time" (it isn't both, it's neither) or "it's in two states at the same time, like a coin which is heads and tails" (no it's not, the point is precisely that it doesn't behave according to classical probabilities).

Claiming these concepts are not mathalematical is like saying addition is not mathematics because you can explain it with words or diagrams to a child!

> logic underpins everything we think.

I hate to break it to you, but humans aren't thinking logically, or exclusively logically. In fact I would say that humans are not using logic most of the time, and we go by intuition most of our lives (intuition is shorthand for experience, pattern matching and extrapolation). There is a reason of why we teach formal logic in certain schools....

i dunno man, I asked it about that chord and it told me it was an F diminished 7th chord. I asked it what a d flat major chord was and it told me. I then asked it what the relationship between the two was. It didnt catch it immediately but when I told it to think about inversions it got it. That's decent for a music student.

It even told me about the role of each in a chord progression and how even though they share the same notes they resolve differently

Humans clearly don't think logically anyhow. Thats why we need things like abacus to help us concretely store things, in our head everything is relative in importance to other things in the moment

> I asked it about that chord and it told me it was an F diminished 7th chord. I asked it what a d flat major chord was and it told me. I then asked it what the relationship between the two was. It didnt catch it immediately but when I told it to think about inversions it got it.

So it gave you a wrong answer and when you spelled out the correct answer it said "OK" x) Was that it? Or am I missing something.

it gave me a correct answer (but not the one GP expected), and then I asked it about another chord GP wanted it to say (D flat major) which can be stylistically replaced with this one (by "inverting" the top note). I asked it what the relationship between the two was and it told me about how they're used in songwriting correctly (gave information about the emotions they invoke and how they resolve to other chords), but didnt tell me the (frankly, trivia/irrelevant to songwriting) fact that they share notes if you happen to invert it in a particular way.

In music theory a set of the same notes can be one of several chords, the correct answer as to which one it is depends on the "key" of the song and context which wasnt provided, so the AI decided to define the root note of the chord as the bottom one which is a good and pretty standard assumption.

It's kind of like asking the AI about two equivalent mathematical functions expressed in different notation, and it saying a bunch of correct facts about the functions like their derivative, x intercept and stuff and how it can be used, but needing a prod to explicitly say the fact that they are interchangable. It's the kind of trivial barely-qualifies-as-an "oversight" I would expect actual human people who fully understand the material to make.

A diminished 7th above F is B, not B flat. Also a 7th chord is understood to be a triad plus the 7th (and therefore the diminished 5th above the F is also missing). Unless I'm missing something it did indeed produce a wrong answer.