I think free will exists just because we can imagine a math object into being that is neither caused nor random.
Can you? I can only imagine world_state(t + ε) = f(world_state(t), true_random_number_source). And even in that case we do not know if such a thing as true_random_number_source exists. The future state is either a deterministic function of the current state or it is independent of it, of which we can think as being a deterministic function of the world state and some random numbers from a true random number source. Or a mixture of the two, some things are deterministic, some things are random.
But neither being deterministic nor being random qualifies as free will for me. I get the point of compatibilists, we can define free will as doing what I want, even if that is just a deterministic function of my brain state and the environment, and sure, that kind of free will we have. But that is not the kind of free will that many people imagine, being able to make different decisions in the exact same situation, i.e. make a decision, then rewind the entire universe a bit, and make the decision again. With a different outcome this time but also not being a random outcome. I can not even tell what that would mean. If the choice is not random and also does not depend on the prior state, on what does it depend?
The closest thing I can imagine is your brain deterministically picking two possible meals from the menu based on your preferences and the environment respectively circumstances, and then flipping a coin to make the final decision. The outcome is deterministically constraint by your preferences but ultimately a random choice within those constraints. But is that what you think of as free will? The decision result depends on you, which option you even consider, but the final choice within those acceptable options does not depend on you in any way and you therefore have no control over it.
> But neither being deterministic nor being random qualifies as free will for me
Not sure what you mean here, but non-random + non-caused is the very definition of free will. It is closely bound up with the problem of consciousness, because we need to define the "you" that has free will. It is certainly not your individual brain cells nor your organs.
But irrespective of what you define "you" to be, free will is the "you"'s ability to choose, influenced by prior state but not wholly, and also not random.
Not sure what you mean here, but non-random + non-caused is the very definition of free will.
Now describe something that is non-random and not-caused. I argue there is no such thing, i.e. caused and random are exhaustive just as zero and non-zero are, there is nothing left that could be both non-(zero) and non-(non-zero). Maybe assume such a thing exists, how is it different from caused things and random things?
[...] free will is the "you"'s ability to choose, influenced by prior state but not wholly, and also not random.
I am with you until including influenced by prior state but not wholly but what does and also not random mean? It means it depends on something, right? Something that forced the choice, otherwise it would be random and we do not want that. But just before we also said that it does not wholly depend on the prior state, so what gives?
I can only see one way out, it must depend on something that is not part of the prior state. But are we not considering everything in the universe part of the prior state? Does the you have some state that the choice can depend on but that is not considered part of the prior state of the universe? How would we justify that, leaving some piece of state out of the state of the universe?
> Now describe something that is non-random and not-caused. I argue there is no such thing, i.e. caused and random are exhaustive just as zero and non-zero are, there is nothing left that could be both non-(zero) and non-(non-zero).
That's my point. The fail to exist only in a certain axiomatic system that is familiar to us. But in a certain mathematical/platonic sense there is nothing essential about that axiomatic system.
Well, what does random mean? Unpredictable, right? Why is it unpredictable? Because the outcome is not determined by anything else. [1] So random just means not determined. And instead of caused I would say determined, because caused is a pretty problematic term, but for this discussions the two should be pretty much interchangeable. And this is probably the best place to attack my argument, to point out something wrong with that. Once you agree to this, it will be a real uphill battle.
So your non-random + not-caused just says non-(non-determined) and non-determined. Now you have to pick a fight with the law of excluded middle [2]. You are saying that there exists a thing that has some property but also does not have that property. Do you see the problem? Nothing makes sense anymore, having a property no longer means having a property, everything starts falling apart.
Maybe you can resolve that problem in a clever way, but you will have to do a lot more work than saying there is some axiomatic system where this is not an issue. Which one? Or at least a proof of existence? And even if you have one, does it apply to our universe?
[1] Things may also seem random because you do not have access to the necessary state, for example a coin flip is not truly random, you just do not have detailed enough information about the initial state to predict the outcome. Or you may not know the laws or have the computing power to use the laws and that bares you from seeing the deterministic truth behind something seemingly random. But all those cases are not true randomness, they are just ignorance making things look random.
Yep, the law of the excluded middle is one place to start attacking your argument, I assume you know not all philosophers accept it.
Then, you are also right that semantics intertwine with logic in a way that needs careful interrogation and is open to different perspectives. I'd be very careful making the leap you make from:
> non-random + not-caused
to:
> non-(non-determined) and non-determined.
Your arguments also contain an interesting thing to think about: True randomness. If you really think about it, true randomness should not exist. And yet we think radioactive decay at the quantum level is truly, fundamentally, irreducibly random. If that is so, here is an example of things happening that we, by definition, cannot explain in any more fundamental way.
Which is to say, the universe is not bound by the logic of our experience. In the same way we had to break out of our basic intuition about numbers to create new ones that gave us more power, in the same way we could never have logically reasoned our way into quantum mechanics and needed experimental evidence to accept something so radical, yes in the same way math does not care that our minds/logic is currently too weak to conceive of a mechanism for free will.
Here is mind twister for you: Imagine a chain of antecedents for an action. In our intuition, the chain stretches backwards infinitely. But what is it could somehow wrap around to form a ring at infinity? Analogous to the way cosmologists think the universe is not infinite in all dimensions
I was wrong about the law of excluded middle, that is not an issue. Intuitionistic logic rejects it, because it says P or not P is definitely true, whether or not we have any proof for P or not P. But that is not really relevant here, the real question is whether there are things that are neither determined nor random. If random means not determined, then no such thing can exist, unless you accept a violation of the law of noncontradiction [1]. So are random things and determined things complementary sets with respect to some universe of things under consideration?
I assistance produces significant productivity gains across professional domains, particularly for novice workers.
We find that AI use impairs conceptual understanding, code reading, and debugging abilities, without delivering significant efficiency gains on average.
Are the two sentences talking about non-overlapping domains? Is there an important distinction between productivity and efficiency gains? Does one focus on novice users and one on experienced ones? Admittedly did not read the paper yet, might be clearer than the abstract.
Not seeing the contradiction. The two sentences suggest a distinction between novice task completion and supervisory (ie, mastery) work. "The role of workers often shifts from performing the task to supervising the task" is the second sentence in the report.
The research question is: "Although the use of AI tools may improve productivity for these
engineers, would they also inhibit skill formation? More specifically, does an AI-assisted task completion workflow prevent engineers from gaining in-depth knowledge about the tools used to complete these tasks?" This hopefully makes the distinction more clear.
So you can say "this product helps novice workers complete tasks more efficiently, regardless of domain" while also saying "unfortunately, they remain stupid." The introductiory lit review/context setting cites prior studies to establish "ok coders complete tasks efficiently with this product." But then they say, "our study finds that they can't answer questions." They have to say "earlier studies find that there were productivity gains" in order to say "do these gains extend to other skills? Maybe not!"
The first sentence is a reference to prior research work that has found those productivity gains, not a summary of the experiment conducted in this paper.
In that case it should not be stated as a fact, it should then be something like the following.
While prior research found significant productivity gains, we find that AI use is not delivering significant efficiency gains on average while also impairing conceptual understanding, code reading, and debugging abilities.
That doesn't really line up with my experience, I wanted to debug a CMake file recently, having done no such thing before - AI helped me walk through the potential issues, explaining what I got wrong.
I learned a lot more in a short amount of time than I would've stumbling around on my own.
Afaik its been known for a long time that the most effective way of learning a new skill, is to get private tutoring from an expert.
This highly depends on your current skill level and amount of motivation. AI is not a private tutor as AI will not actually verify that you have learned anything, unless you prompt it. Which means that you must not only know what exactly to search for (arguably already an advanced skill in CS) but also know how tutoring works.
From school you are used to think of function in their explicit form y = f(x) but you can easily turn that into the implicit form f(x) - y = 0 or more generally f(x, y) = 0. With that you can plot the graph of f(x, y) either as a 3D surface with f(x, y) being the height at point (x, y) or encode the function value at (x, y) into some color at (x, y). Where that surface is equal to zero, i.e. where it intersects the z = 0 plane, that are the points of y = f(x). Points (x, y) at which the value of f(x, y) has small non-zero magnitude are what the article calls low error points or regions, points or regions that almost satisfy y = f(x).
f(x, y) = 0 is true only for some combinations of x and y. It’s an equation to be solved, not a universal statement like ∀ x, y : f(x, y) = 0, nor a definition like f(x, y) ≔ 0 (or “≝”). The solutions to the equation are the points (x, y) where the graph has height 0. Which points these are depends on how f is defined.
For example, f might be defined as f(x, y) ≔ x² + y² – 1. Then the points (x, y) for which f(x, y) = 0 are those on the unit circle (those for which x² + y² = 1). The graph will have height 0 only for those points.
They're really two different types of equal signs.
f(x,y) = x+y might be better written as f(x,y) := x+y where := means "is defined as". Then f(x,y) = 0 is an equation that expands to x+y = 0, or in familiar intro algebra form, y=-x.
I will say that in programming it's commonly used as assignment, which isn't quite the same thing as definition. golang uses it to declare variables so that's pretty close
When we say "f(x, y) = 0" in this context, we also usually have a separate definition for f(x, y) provided, where that f(x, y) is not necessarily 0 at for all x,y. And so this constraint "f(x, y) = 0" means "find pairs of x and y such that it makes f(x, y) become 0".
If "f(x, y) = 0" is actually the definition of f(x, y), then yes, it would be a pretty boring graph.
But only if you are looking at the revised goals, if you look back at the original goals, things look different. It was supposed to fly around the moon with people on board two years ago.
If you want to look long term, well, they're still stellar :) Considering everything they're achieving, and how they're so much better than everybody else in the field.
It's a failure only if you look at a rather small time range and criteria. Which I don't think was a surprise for anybody - Elon is famous for going for moon shots and failing, but still delivering better than anybody else.
.NET supports this because [Visual] Basic supports it. This can be used from C# - and other languages - but there is no nice syntax supporting it.
// This also supports multidimensional arrays, that is why the parameters are arrays.
var array = Array.CreateInstance(elementType: typeof(Int32), lengths: [ 5 ], lowerBounds: [ -2 ]);
// This does not compile, the type is Int32[*], not Int32[].
// Console.WriteLine(array[0]);
array.SetValue(value: 42, index: -2);
Console.WriteLine(array.GetValue(-2));
What would happen in a hypothetical scenario where Microsoft cut off everything [1] they can for all of Israel - no Azure, no Office, no Outlook, no Exchange, no SQL Server, no Windows, no Xbox, no ...? Depending on how many things they can make unusable, I would imagine that this would be pretty bad, probably even causing some deaths because of affected infrastructure.
[1] Not sure what they could actually make unusable by revoking licenses, blocking logins, and whatnot. It probably also matters how quickly the effects are felt, Azure would be gone immediately but I am not sure how often Office checks whether its license has been revoked, if at all. If license checks make things stop working over weeks and months, it would still not be pretty, but it would provide at least some time to prepare and avoid the worst.
IDK but Mossad is quite possibly the world's most effective spy agency and SV software corporations rarely have effective safeguards to protect against rogue employees so we must conclude that there are many sleeper agents planted throughout major corporations on behalf of just about every intelligence agency in the world including but not limited to mossad.
I have not seen any hard evidence of this nor have i ever suspected a fellow employee at any of my employers of being a double-agent loyal to a state intelligence agency but it's easy enough to do that there must be hundreds, maybe even thousands of sleeper agents all over santa clara and redmond.
I do not understand how this could possibly work. From a camera with RGB filters we get essentially three different integrals over the spectrum per pixel, how would we recover the spectrum from that? Even assuming you can account for the spectrum of the light sources and the color filters in the camera - which should be doable with a color chart with known spectra - I do not see how you could go from three data points to a full spectrum without making assumptions about the possible object spectra.
EDIT: Okay, after going to the actual paper I at least get transmission mode - you photograph the color chart through the sample and this will of course imprint the absorption spectrum onto the know spectrum of the color chart and you can then look at the difference to the color chart without the sample in between. But I do not get the logic behind their reflectance mode.
For point one the reason is of course that π(p) has a [global] minimum at 2. Actually showing that is not that easy because the involved integrals have no closed form solution but in principle it is not too hard. The circumference of the circles is 2 π(p) and equals four times the length of the quarter circle in the first quadrant which has all x and y positive and allows dropping the absolute values. The quarter circle is y(x) = (1 - x^p)^(1/p) with x in [0, 1]. Its length is the integral of ds over dx from 0 to 1 where ds is the arc length in the Lp norm ds = (dx^p + dy^p)^(1/p) which yields ds = (1 + (dy/dx)^p)^(1/p) dx. For dy/dx you insert the derivative of the quarter circle dy/dx = -x^(p - 1)(1 - x^p)^(1/p - 1) and finally you have to compute the derivative of the integral with respect to p and find the zeros to figure out where the extrema are. Well, technically you have to also look at the second and third derivative to confirm that it is a minimum and check the limiting behavior. The referenced paper works around the integral by modifying the function in a way such that it still agrees with the original function in some relevant points but yields a solvable integral and shows that using the modified function does not alter the result.
Because the goal of the Zionists has always been to conquer all of Palestine and the State of Israel has been following those foot steps since day one. From the river to the sea. This has been declared illegal under international law more than half a century ago but Israel does not care about the law. Therefore Israel should be forced to comply, which means boycotts and sanctions or military force. And we should probably try boycotts and sanctions first before we send tanks. Which is unlikely to happen any time soon anyway as that would mean opposing the USA and we have seen in recent history what happens to people and countries supporting the Palestinians.
To the dead comment Israel agreed to the UN partition in 1947, and then Arabs started a war to kill all the Jews there.
You do not even understand what the UN general assembly does, it expresses majority opinions, it does not make legally binding decisions. That means the UN partition plan is only what a majority considered the best solution, not a legal decisions to divide Palestine. And the Palestinians vehemently opposed that solution and later violently its implementation.
And should one really be surprised that the Arab neighbors attacked Israel? The Jews had just occupied half of the Palestinian land, violently displaced hundred thousands of Palestinians, and established their own state on Palestinian land.
[1] https://www.youtube.com/watch?v=yOmcP9sMwIE
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