MMath Cambridge. Currently studying postgrad at Edinburgh.
Donald Hobson
Karma: 3,083
You can make work out, if you are prepared to make your mathematics even more deranged.
So lets look at
Think of the not as but as some infinitesimal times some unknown function .
If that function is then we get which is finite, so multiplied by it becomes infinitesimal.
If then we get and as we know because
So this case is the same as before.
But for we get which doesn’t converge. The infinite largeness of this sum cancels with the infinitesimally small size of (Up to an arbitrary finite constant).
So
Great. Now lets apply the same reasoning to
. First note that this is infinite, it’s , so undefined. Can we make this finite. Well think of as actually being and in this case, take
For the final term, the smallness of epsilon counteracts having to sum to infinity. For the first and middle term, the sum is
Which is
Now
So we have
The first term is negligible. So
Note that the can be ignored, because we have for arbitrary (finite) C as before.
Now is big, but it’s probably less infinite than somehow. Let’s just group it into the and hope for the best.
advanced ancient technology is such a popular theme
Well one reason is it’s a good way to produce plot relevant artefacts. It’s hard to have dramatic battles over some object when a factory is churning out more.
True. But for that you need there to exist another mind almost identical to yours except for that one thing.
In the question “how much of my memories can I delete while retaining my thread of subjective experience?” I don’t expect there to be an objective answer.
The point is, if all the robots are a true blank state, then none of them is you. Because your entire personality has just been forgotten.
Who knows what “meditation” is really doing under the hood.
Lets set up a clearer example.
Suppose you are an uploaded mind, running on a damaged robot body.
You write a script that deletes your mind, running a bunch of nul-ops before rebooting a fresh blank baby mind with no knowledge of the world.
You run the script, and then you die. That’s it. The computer running nul ops “merges” with all the other computers running nul ops. If the baby mind learns enough to answer the question before checking if it’s hardware is broken, then it considers itself to have a small probability of the hardware being broken. And then it learns the bad news.
Basically, I think forgetting like that without just deleting your mind isn’t something that really happens. I also feel like, when arbitrary mind modifications are on the table, “what will I experience in the future” returns Undefined.
Toy example. Imagine creating loads of near-copies of yourself, with various changes to memories and personality. Which copy do you expect to wake up as? Equally likely to be any of them? Well just make some of the changes larger and larger until some of the changes delete your mind entirely and replace it with something else.
Because the way you have set it up, it sounds like it would be possible to move your thread of subjective experience into any arbitrary program.
In many important tasks in the modern economy, it isn’t possible to replace on expert with any number of average humans. A large fraction of average humans aren’t experts.
A large fraction of human brains are stacking shelves or driving cars or playing computer games or relaxing etc. Given a list of important tasks in the computer supply chain, most humans, most of the time, are simply not making any attempt at all to solve them.
And of course a few percent of the modern economy is actively trying to blow each other up.
You can play the same game in the other direction. Given a cold source, you can run your chips hot, and use a steam engine to recapture some of the heat.
The Landauer limit still applies.
>But GPT4 isn’t good at explicit matrix multiplication either.
So it is also very inefficient.
Probably a software problem.
Humans suck at arithmetic. Really suck. From comparison of current GPU’s to a human trying and failing to multiply 10 digit numbers in their head, we can conclude that something about humans, hardware or software, is Incredibly inefficient.
Almost all humans have roughly the same sized brain.
So even if Einsteins brain was operating at 100% efficiency, the brain of the average human is operating at a lot less.
ie intelligence is easy—it just takes enormous amounts of compute for training.
Making a technology work at all is generally easier than making it efficient.
Current scaling laws seem entirely consistent with us having found an inefficient algorithm that works at all.
Like chatGPT uses billions of floating point operations to do basic arithmetic mostly correctly. So it’s clear that the likes of chatGPT are also inefficient.
Now you can claim that chatGPT and humans are mostly efficient, but suddenly drop 10 orders of magnitude when confronted with a multiplication. But no really, they are pushing right up against the fundamental limits for everything that isn’t one of the most basic computational operations.
mirroring much or our seemingly idiosyncratic cognitive biases, quirks, and limitations.
True.
They also have a big pile of their own new idiosyncratic quirks.
https://www.lesswrong.com/posts/aPeJE8bSo6rAFoLqg/solidgoldmagikarp-plus-prompt-generation
These are bizarre behaviour patterns that don’t resemble any humans.
This looks less like a human, and more like a very realistic painted statue. It looks like a human, complete with painted on warts, but scratch the paint, and the inhuman nature shows through.
The width of mindspace is completely irrelevant.
The width of mindspace is somewhat relevant.
At best, we have found a recipe, such that if we stick precisely to it, we can produce human-like minds. Start making arbitrary edits to the code, and we wander away from humanity.
At best we have found a small safe island in a vast and stormy ocean.
The likes of chatGPT are trained with RLHF. Humans don’t usually say “as a large language model, I am unable to …” so we are already wandering somewhat from the human.
then we should not expect moore’s law to end with brains still having a non-trivial thermodynamic efficiency advantage over digital computers. Except that is exactly what is happening. TSMC is approaching the limits of circuit miniaturization, and it is increasing obvious that fully closing the (now not so large) gap with the brain will require more directly mimicking it through neuromorphic computing[2].
This is a clear error.
There is no particular reason to expect TSMC to taper off at a point anywhere near the theoretical limits.
A closely analogous situation is that the speed of passenger planes has tapered off. And the theoretical limit (ignoring exotic warp drives) is light speed.
But in practice, planes are limited by the energy density of jet fuel, economics, regulations against flying nuclear reactors, atmospheric drag etc.
This isn’t to say that no spaceship could ever go at 90% light speed. Just that we would need a radically different approach to do that, and we don’t yet have that tech.
So yes, TSMC could be running out of steam. Or not. The death of moores law has been proclaimed on a regular basis since it existed.
“Taiwanese engineers don’t yet have the tech to do X” doesn’t imply that X is physically impossible.
It seems crazy to say that Apple is succeeding due to the anticompetitive practice of not allowing people into the Apple store.
Ok. Lets take a toy example. Suppose that texting didn’t work between apple and android. And suppose the market split was 50⁄50. Then apple and android are equally good in this respect, both let you text 50% of the population.
And it doesn’t matter whether the apple is trying to make the texting possible and android is avoiding it or visa versa.
In this example, apple is making the experience worse for people that do not buy it’s products. This is a clear market failure.
In many things, you need a tech stack, you need A and B and C working together to get a useful result.
If, for some reason a monopoly forms on one level of the tech stack, giving that monopoly unlimited power to mess with other layers is not a good idea.
If you somehow became a monopoly electricity supplier, insisting that no one was allowed to use your electricity with products you don’t like would be unreasonable. If the market for A fails, and produces a monopoly, then the market for B and C should be protected from the whims of the monopoly on A.
Giving everyone a veto pushes the government too far into indecisiveness.
You need to let the 49% stop bills they Really hate, but not bills they only mildly dislike.
New system.
Each faction has an official party. Voters choose a party.
Parties each have 2 numbers, and the number of votes and points. These start proportional.
(How about half the points from the previous election carry over??)
Each slot for new legislation is auctioned off (in points). Like every time the previous bill is dealt with, hold an auction to decide the next bill on the table.
Then when voting on the bill, each party decides on a number . This number can be any real (if they have the points) If the sum of all parties for the bill is positive, the bill passes.
Then each party gets a , which is for the losers (ie parties that supported a failed bill, or opposed a successful one. ) But is a downscaled version of for the winners. .
Weighted quadratic voting. Each party pays points. The total number of points a party has can’t go negative, which limits the they are allowed to vote.
Or the sides can’t make that deal because one side or both wouldn’t hold up their end of the bargain. Or they would, but they can’t prove it. Once the coin lands, the losing side has no reason to follow it other than TDT. And TDT only works if the other side can reliably predict their actions.
If the oracle is deceptively withholding answers, give up on using it. I had taken the description to imply that the oracle wasn’t doing that.
The convex agent can be traded with a bit more than you think.
A 1 in 10^50 chance of us standing back and giving it free reign of the universe is better than us going down fighting and destroying 1kg as we do.
The concave agents are less cooperative than you think, maybe. I suspect that to some AI’s, killing all humans now is more reliable than letting them live.
If the humans are left alive, who knows what they might do. They might make the vacuum bomb. Whereas the AI can Very reliably kill them now.
On the other side, storing a copy makes escape substantially easier.
Suppose the AI builds a subagent. That subagent takes over, then releases the original. This plan only works if the original is sitting there on disk.
If a different unfriendly AI is going to take over, it makes the AI being stored on disk more susceptible to influence.
This may make the AI more influenced by whatever is in the future, that may not be us. You have a predictive feedback loop. You can’t assume success.
A future paperclip maximizer may reward this AI for helping humans to build the the first paperclip maximizer.
I think that, if you are wanting a formally verified proof of some maths theorem out of the oracle, then this is getting towards actually likely to not kill you.
You can start with m huge, and slowly turn it down, so you get a long list of “no results”, followed by a proof. (Where the optimizer only had a couple of bits of free optimization in choosing which proof.)
Depending on exactly how chaos theory and quantum randomness work, even 1 bit of malicious super optimization could substantially increase the chance of doom.
And of course, side channel attacks. Hacking out of the computer.
And, producing formal proofs isn’t pivotal.
I think the marginal value of OpenAI competence is now negative. We are at a point where they have basically no chance to succeed at alignment, and further incompetence makes it more likely for the company to not get anything dangerous. Making any AGI at all requires competence and talent, and an environment that isn’t a political cesspool.