It's possible you could at least mitigate the problem by checking that what you've proven isn't trivial. If you slightly change a mathematical statement, it frequently becomes either trivially true or trivially false. So if you accidentally proved the wrong thing, there's a good chance that your proof can be shortened to a point that it becomes obviously wrong.
For example, if you accidentally put "there exists" instead of "for all" in Fermat's last theorem, the proof is 1^3 + 1^3 != 1^3. That is obviously too short to prove FLT - it would have fit in Fermat's margin.
That's true, but we should acknowledge that this question is generally regarded as unsettled.
If you accept the conclusion that AGI (as defined in the paper, that is, "solving [...] problems at a level of quality that is at least equivalent to the respective human capabilities") is impossible but human intelligence is possible, then you must accept that the question is settled in favor of Penrose. That's obviously beyond the realm of mathematics.
In other words, the paper can only mathematically prove that AGI is impossible under some assumptions about physics that have nothing to do with mathematics.
> then you must accept that the question is settled in favor of Penrose. That's obviously beyond the realm of mathematics.
Not necessarily. You are assuming (AFAICT) that we 1. have perfect knowledge of physics and 2. have perfect knowledge of how humans map to physics. I don't believe either of those is true though. Particularly 1 appears to be very obviously false, otherwise what are all those theoretical physicists even doing?
I think what the paper is showing is better characterized as a mathematical proof about a particular algorithm (or perhaps class of algorithms). It's similar to proving that the halting problem is unsolvable under some (at least seemingly) reasonable set of assumptions but then you turn around and someone has a heuristic that works quite well most of the time.
Where am I assuming that we have perfect knowledge of physics?
To make it plain, I'll break the argument in two parts:
(a) if AGI is impossible but humans are intelligent, then it must be the case that human behavior can't be explained algorithmically (that last part is Penrose's position).
(b) the statement that human behavior can't be explained algorithmically is about physics, not mathematics.
I hope it's clear that neither (a) or (b) require perfect knowledge of physics, but just in case:
(a) is true by reductio ad absurdum: if human behavior can be explained algorithmically, then an algorithm must be able to simulate it, and so AGI is possible.
(b) is true because humans exist in nature, and physics (not mathematics) is the science that deals with nature.
So where is the assumption that we have perfect knowledge of physics?
Nobody should care what ANY physicists say about consciousness.
I mean seriously, what? I don't go asking my car mechanic about which solvents are best for extracting a polar molecule, or asking my software developer about psychology.
"Gender" referred only to grammar before it gained its modern meaning. The modern meaning was introduced in the 1950s/60s to differentiate social aspects (gender) from biological (sex). Of course people then started using it to just mean "sex", but if you use social definition I don't think it's a bad name for the concept.
Are you sure? That’s almost the opposite of what I heard, which was that “gender” being used to refer to -inity arose as a euphemism to avoid using the word “sex”, because the word “sex” came to be more associated with specifically “sex-acts” (and that prior to it being used as a euphemism in this way, it essentially meant something like kind/type/sort), and only after “gender” began being used as a euphemism in this way, did people begin using it to distinguish between “gender roles” and “sexes”.
> Note that it's not necessarily simple to pick an element from a set. For instance, how would one pick an element from the set of uncomputable numbers?
In ZF without choice, you can pick an element from any non-empty set, so it actually is simple to pick an element from a set. Choice is only needed when you have an infinite number of sets to pick elements from.
> All of these produce valid video output and show dynamic or structured data.
While they will usually produce video on old CRTs, the video signal they generate is technically not valid. The VSync signal needs to be generated in software, and random programs are unlikely to do so correctly. Different TVs will behave differently (usually rolling on old TVs, blank on new TVs), and probably none would look like what the emulator is showing.
I tried running the game-like ROM in Stella and couldn't get it to work. It seems to depend on the startup state, which means it likely wouldn't run on an actual console.
> I once, for a side gig, had to write a 16-bit long-division routine on a processor with only one 8-bit accumulator. That was the point at which I declared that I'd never write another assembly program.
This is exactly the kind of job I'd enjoy! A perfectly doable technical challenge with clear requirements. Some people like solving Sudoku puzzles, I like solving programming puzzles.
I guess I'm just not "the overwhelming majority of programmers".
> doable technical challenge with clear requirements
That's a Project Management issue, not an implementation concern.
In my case, there was no requirement that said "use 16-bit long division." However, we had committed to a particular processor family (MC68HC05), and the calculation precision required 16-bit math. IIRC, there was a compiler available, but it cost more than the rest of the project and the code it produced wouldn't have fit into the variant of the processor that I was using anyway.
The actual requirement would have looked more like "detect a 0.1% decrease in signal that persists for 10 seconds, then do X."
I feel the same way, but I also can't help but imagine the boss jumping up and down and throwing chairs and screaming "how can you not be done yet? You're a programmer and this is a program and it's been three _hours_ already".
I think the majority of programmers would enjoy it, but most would first need to pick an ISA (something older is probably going to be more approachable for beginners), learn enough about it to understand basic arithmetic instructions, learn enough about the dev tools to be able to assemble, link, and execute their code, etc.
For most folks, that's going to be a couple days of prep work before they can get to the fun part of solving the puzzle.
"I guess I'm just not the "overwhelming majority of programmers"."
The "overwhelming" majority of programmers may be underwhelming
Some readers may be unimpressed by programmers who complain about and criticise assembly language, e.g., claiming it offers "no benefit" to others, especially when no one is forcing these programmers to use it
Rule 110 is only Turing-Complete if you have an infinitely large array of cells, and are able to initialize it with an infinite repeating pattern. If I'm not mistaken, HTML+CSS can only do a fixed-sized array.
With a Turing-Complete language, if a program runs out of memory on one machine, you can run the same code on a bigger machine without modifying it, and it can use the additional memory. With fixed-length rule 110, you need to modify the code if you want to use more memory.
"Stuff which is somehow limited (stack overflows, arbitrary configuration, etc) is still considered Turing complete, since all "physical" Turing machines are resource limited."
In my opinion, worrying about infinite memory, in regards to Turing completeness, makes the task of implementing computation much less interesting.
Also, I'm pretty sure CSS only does one generation (or a finite number of them) before stopping anyway.
Awesome [hunted [___ crackers are ironically vegan]]! I found the d[[not amateur, abbreviated]gramming construct preceding "else"]ficulty just [___ to remain [___ but deadly]].
> Background/Objectives: Egg consumption in adults has been linked with a modestly increased risk of all-cause and CVD mortality. However, evidence on adults aged 65 y+ is limited.
So, according to the authors of the study, it has already been established that egg consumption in adults is linked with increased mortality, but they wanted to see if this is still true for those 65 years and older.
The study found lower mortality in those who reported eating eggs weekly compared to those who ate eggs never or infrequently. It did not establish causality. So it could be that eggs improve the health of the elderly, or it could be that healthy elderly people are more able to cook for themselves, and people who cook for themselves are more likely to eat eggs. The study does not distinguish between these possibilities.
The same findings have been made with other animal protein in general, the going theory is that animal foods are protein dense and protect against sarcopenia which is very well established to contribute a lot to all cause mortality in the elderly.
It seems almost impossible to get the elderly to eat enough protein. Even those aware that they should be changing their diet. A lifetime of habit and greatly diminished appetite means pushing protein dense foods. I've very grateful for studies such as this, to help with my thankfully scientifically minded seniors. If you can only fit in a spoonful or two, you have to make it count.
Adding and mixing some protein powder, e.g. whey protein concentrate, into various kinds of foods can enrich them greatly in protein, with a very small increase in bulk, so one can have an adequate protein intake without eating much.
Presumably the increased cardiovascular disease risk from animal protein in general, most evident in processed meat, then red meat, then other sources in order of effect size.
Not so sure about cancer risk outside of the colorectal cancer risk associated with processed meat and unprocessed red meat.
So far the studies that appear to show a correlation between meat consumption and negative health outcomes have all been barely a step above junk science. We're talking about observational studies with poor controls (healthy subject effect), multiple uncontrolled variables, and small effect sizes.
I would say that the evidence on red and processed meat and CVD and CRC is at least a “B”, so we’re meeting your goalposts here.
When we look at the totality of the evidence via meta analysis, we see effect sizes in the 10-20% range for IHD. If 20% change in one of the leading killers in the western world is “small” to you then fair enough, but I’d suspect that’s a fairly proprietary use of the word that wouldn’t accord with what most people mean when they use it.
I’m not sure what variables you think are uncontrolled in these studies, you’ll have to be specific about which uncontrolled variables you think are having an effect.
This answer seems plausible, but I also see no control for people who eat eggs through their entire life being more likely to die prematurely or those taking measures like not eating eggs being deeply unhealthy.
