> Depression can be caused by a chemical imbalance and no amount of exercise or talking about it will fix it.
This is a debatable. As far as I understand things: 'chemical imbalance' has no tests to confirm that's actually true, That's just a story they tell to relax people.
Which is orthogonal to the point that antidepressants can work for some people.
We don't know how depression works. It very well may be many little things dressed in a trench coat.
An analogy is asking someone who is colorblind how many colors are on a sheet of paper. What you are probing isn't reasoning, it's perception. If you can't see the input, you can't reason about the input.
> What you are probing isn't reasoning, it's perception.
Its both. A colorblind person will admit their shortcomings and, if compelled to be helpful like an LLM is, will reason their way to finding a solution that works around their limitations.
But as LLMs lack a way to reason, you get nonsense instead.
What tools does the LLM have access to that would reveal sub-token characters to it?
This assumes the colorblind person both believes it is true that they are colorblind, in a world where that can be verified, and possesses tools to overcome these limitations.
You have to be much more clever to 'see' an atom before the invention of a microscope, if the tool doesn't exist: most of the time you are SOL.
> Most people who (quite reasonably) hate corporate personhood would probably have a knee-jerk reaction that personhood for a river can/should be normalized.
Three replies now, all saying that this is nonsense (including this one). I would venture to say it's the other way around: if you are okay with a river having 'personhood' then that logically leads to being okay with a group of people having 'personhood'.
Elephants, on the other hand, have a better case for 'personhood' than a river. An elephant has autonomy, is thinking, can feel pain, has emotions... a river has none of these things, nor does a corporation (even if the parts {humans} consisting of a corporation do).
Personhood for non-persons is definitely absurd. But if you're actually stuck with a broken system, then the most logical thing to do is at least apply your broken logic consistently. That's an important part of the difference between rule of law and wild corrupt barbarism. Of course it's much better to actually fix absurdities, but if you can't or won't, inconsistency still has to be forbidden or else the whole thing is a farce
I'm a bit reminded of the days before Unix-style pipelining and abstract I/O streams like "standard input and output". Mainframe operating systems would instead support devices like "virtual card readers" and "virtual line printers". When you created a COBOL program on disk and scheduled a compile job for it, the system would set up a virtual card reader to accept the program as input and direct the logs to a virtual printer. How to set this up was specified using JCL on IBM iron.
It seems that "virtual personhood" was set up to address deficiencies in our legal system regarding who or what may be party to a lawsuit, etc.
Perhaps it is a mental process you can train and get better at. I understand the 'back of the head', location for imagination. And now - for me - it's at the front with some specific training. Drawing (and specific techniques within) have been the cause of the biggest shifts to 'where/how' my imagination is.
Some people can project the image of an apple into the real world. As in, they are able to imagine an apple on the table that they see with their eyes. They 'see' it, but see that it's a projection. It's a lot like when you have two very similar images (except one change), and you cross your eyes such that they overlap to highlight the change (it's ghostly, as it's only seen in one eye). Same Idea, only instead of the other eye, that projection is coming from your brain.
Try the crossed eyes 'find the difference' technique. Which is crossing your eyes such that a third image (a blending of the two images: one from each eye) appears between those two images.
You can easily understand where the difference is because the data is different between the eyes. The difference appears 'ghostly'. In a similar way, data from the mind's eye is different from data from the physical eyes when those two 'streams of data' are blended.
Yes I can do this. I can see the image in the middle the same way as I see each individual image. (But not both at the same time, the outside images get blurry when I focus on the one in the middle).
Anyways, this is nothing like what I experience when I imagine something.
That's what it's like to 'overlay' imagination onto your vision.
But that requires - like the eyes focusing correctly - for the 'imagination vision' and the physical vision to 'line up'
your imagination is more like it's in the the back of the head, yeah?
What helped me 'move' where my imagination was (to the front and center), was to do the flame meditation. Which is to focus on a flame in a dark room for a few seconds, close your eyes, and try to retain the phosphene afterglow in the flame shape. and repeating that until you are able to retain image of the flame while your eyes are closed.
Similarly: 'drawing from memory' - particularly from recent short term memory - was another method that had a profound impact on my ability to visualize.
Both of these take time and commitment, but they have worked for me. They may work for you.
"where" the mind's eye is also variable. And may be moveable.
For a time, my mind's eye was 'on the floor, sideways, behind "my driver seat"'. With some effort, it is now 'in front' of me, closer than where my vision is, occupying some space between where my vision is, and where I perceive my sense of self to be.
The efforts were a combination of trataka flame training, training to remain conscious through the process of falling asleep (for lucid dreaming), and drawing (seeing an image, quickly memorizing it, and drawing it from the mind's eye projection {as in, literally trying to see the image on the blank page without access to the reference image}).
I don't think a truly random sequence would necessarily halt under these rules. It's not enough to have arbitrarily long runs. As the sequence as a whole gets larger, the run length needed to end it also gets longer, and thus the probability gets smaller. The result should be something like a geometric sequence with a finite sum.
Consider a simpler version, where you flip a coin three times, then four times, then five times, etc., and you stop if you ever get the same side for every flip in a given turn. The probability that you'll stop is equal to 1/4 + 1/8 + 1/16 + ... which is 50%. If you do this forever then you'll eventually see a run of ten trillion heads or tails, but you probably won't see that run before your ten trillionth turn.
So I think the question is, does the anti-hydra sequence ever diverge sufficiently from randomness?
> As the sequence as a whole gets larger, the run length needed to end it also gets longer, and thus the probability gets smaller. The result should be something like a geometric sequence with a finite sum.
This is true.
But it would still halt. Infinity is weird like that.
To be clear, I mean the sequence of coin flips where the total value of heads/tails is 2:1.
The probability of having a 2:1 ratio of heads/tails - at some point - in an infinite sequence of fair flips is 1, is it not?
The anti-hydra may have a bias, and only if that bias is against the halt condition do we have a case where we can conclude that the anti-hydra does not halt.
No, I don't think it's 1. The weirdness of infinity can go both ways. A classic example being that a random walk on a line or a two-dimensional grid takes you back to your starting point an infinite number of times, but for a three dimensional grid you only return to the start a finite number of times, quite possibly zero.
This problem is equivalent to a one-dimensional random walk where the terminating condition is reaching a value equal to the number of steps you've taken divided by 3. I'm not quite sure how to calculate the probability of that.
Intuitively, I'd expect this to have a finite probability. The variance grows with sqrt(n), which gets arbitrarily far away from n/3.
Looking at it another way, this should be very similar to the gambler's ruin problem where the gambler is playing against an infinitely rich house and their probability of winning a dollar is 2/3. If the gambler starts with $1 then the probability of ever reaching zero is 1 - (1/3)/(2/3) = 50%. Reference for that formula: https://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GR.pdf
You can solve it with a linear recurrence relation [0]: the halting probability from position n is ((sqrt(5)-1)/2)^(n+1), where n is twice the number of odds minus the number of evens. (In fact, this +2/-1 random walk is precisely how the machine implements its termination condition.) The expected value of n is 1/3 the number of iterations. At the end of the longest simulation that has been computed, n is greater than 2^37, so the halting probability is less than 10^(-10^10).
Even if an event has probability 1 it is not inevitable, conversely probability 0 does not imply its impossibility.
For example, randomly picking the number 0.5 out of the interval of real numbers [0,1] has probability 0, and yet it might happen. The probability of picking an irrational number instead was 1 (because almost all real numbers are irrational), but that didn't happen.
Even if you consider a countably infinite number of events, as with the coinflip example, it might just happen that the coin flips to one side forever.
Since the machines under consideration just represent one specific sequence of events, probabilistic arguments may be misleading.
The peak run lengths of evens/odds 'should' go to infinity, but these runs become a smaller and smaller component of the overall average, so that it is expected to approach the long-term 50% regardless.
In other words, an unbiased random walk should almost surely return to the origin, but a biased random walk will fail to return to the origin with nonzero probability. This can be considered a biased random walk [0], since the halting condition linearly moves further and further away from the expected value of the 50/50 walk.
It is by definition not random. The Antihydra is generated by a fixed computable map, so it is compressible and would fail some effective statistical tests. You can't get true randomness via a deterministic algorithm; any computable infinite sequence fails Martin‑Löf randomness.
That said, empirically and in all current analyses, the Antihydra's parity behaves as if it were roughly fair over long spans (neither a proven odd nor even bias), and the short-range statistics look pseudo-random. Non-halting is overwhelmingly plausible... but a concrete proof seems out of reach.
This is a debatable. As far as I understand things: 'chemical imbalance' has no tests to confirm that's actually true, That's just a story they tell to relax people.
Which is orthogonal to the point that antidepressants can work for some people.
We don't know how depression works. It very well may be many little things dressed in a trench coat.
https://www.sciencedirect.com/science/article/pii/S266656032...
https://www.nature.com/articles/s41380-022-01661-0
https://www.neurocaregroup.com/news-insights/the-death-of-ch...
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