rb-2

To add to delhanty's reply, a "degree of freedom" can be thought of as a dimension of the drawing that can be changed or "stretched" or moved without violating a constraint (this is slightly inaccurate, but it's a good start). In a CAD program, a fully constrained drawing can't be freely stretched or dragged around; the program won't let you and the drawing will feel "rigid".

It's very intuitive if you play around with a CAD program for a bit. There is a free (GPLv3) 2D and 3D CAD program called Solvespace (https://solvespace.com/) that is probably easiest one to obtain and learn. There are detailed tutorials on the website, and you could probably download it and finish the first tutorial in an hour.

It's a difficult idea to put into words, but I'll try to elaborate on what I mean.

There are many things which respond to stimuli that most people wouldn't consider "conscious". When you press the gas pedal on your car, the car goes faster, for example. The means by which the stimuli causes a response is entirely mechanical here (the gas pedal causes more fuel to be injected into the engine, causing more energy to be released when it combusts, etc).

Most people don't think of the car as "feeling" that the gas pedal was pushed, because it's a machine. It's a bunch of parts connected in such a way that they happen to function together as a vehicle. If the car could feel, would a pressed gas pedal feel painful? Wood it feel good or satisfying?

There are also times when people are unconscious, yet still respond to stimuli. For example, what does it feel like when you are in deep sleep at night and you aren't dreaming? Well, it doesn't really feel like anything; your "conscious" self sort of fades out as you fall asleep and then it jumps forward to when you wake up. But if while you're asleep someone sneaks into your room and slaps you, you wake up right away (unconscious response to stimuli).

I hope this helps.

I've noticed that conversations about "consciousness" tend to go in circles because the participants are using different definitions of the word without realizing it.

Some people use the word "conscious" almost interchangeably with terms like "intelligent", "creative", or "responds to stimuli". Then people start saying things like LLMs are conscious because they pass the turing test.

However, others (including the authors of this paper and myself) use the term "consciousness" to refer to something much more specific: the inner experience of perceiving the world.

Here's a game you can play: describe the color red.

You can give examples of things that are red (that other people will agree with). You can say that red is what happens when light of a certain wavelength enters your eyeball. You can even try saying things like "red is a warm color", grouping it with other colors and associating it with the sensation of temperature.

But it is not possible to convey to another person how the color red appears to you. Red is completely internal experience.

I can hook a light sensor up to an arduino and it can tell me that an apple is red and that grass is not red. But almost no one would conclude that the arduino is internally "experiencing" the color red like they themselves do.

While the paper is using this more precise definition of consciousness, it seems to be trying to set up a framework for "detecting" consciousness by comparing external observations of the thing in question to external observations of adult human beings, who are widely considered by other adult human beings to be conscious entities [1]. I don't see how this approach could ever produce meaningful results because consciousness is entirely an internal experience.

[1] There is a philosophical idea that a person can only ever be sure of their own consciousness; everyone else could be mindless machines and you have no way of knowing (https://en.wikipedia.org/wiki/Solipsism). Also related is the dead internet theory (https://en.wikipedia.org/wiki/Dead_Internet_theory).

I wonder if it would be possible to mathematically define (in a theorem proving language like Coq) a bunch of accessor methods as well as a bunch of implementation primitives and then "compile" a custom graph implementation with whatever properties you need for your application. Some accessor methods will be very efficient for some implementations and very inefficient for others, but every method will still be available for every implementation. Profiling your application performance can help adjust the implementation "compiler" settings.

Ironically, this is a graph problem.