I'm not specifying them, I'm referencing their existence. You can take them not to exist, but in that case good luck explaining the measurable consistency that every human on earth observes. In fact, if you truly believed this, there would be no point in even speaking leaving a comment because then you could not believe in the ability of language to communicate ideas or even in the existence of language itself.
> Epistemology has been studied by some of the greatest thinkers since the ancient greeks ( probably even before ) and not just college freshmen.
Yes but it is somehow seems to always be the college freshman that raise this question for fields that have contributed the most to humanity like mathematics and physics, all the while not feeling the need to question any number of academic fields built on an absolutely pathetic scientific process in comparison. It is simply because of their failure of intuition and understanding of mathematics and physics that they raise these questions - I'm not saying that these questions are not part of a worthwhile conversation in general.
> If you have to intuitively understand them, it isn't very objective is it?
I'm not understanding your argument here. The failure of a human mind to understand something does not mean that this thing is not objective. Nobody on Earth understood why lightning occurs for most of human history. This does not mean that the existence of lightning and the reasons for its occurrence are not objective qualities of nature.
> What in math are objective facts about the nature of reality?
The existence of concepts that map to reality in producing models that yield consistent, effective, and measurable results.
If there were no conscious beings, the Earth would continue its orbit around the sun and this order is what is captured by the human-invented language of mathematics. Saying that "mathematics" isn't objective may be true depending on how you define mathematics, but there is no denying that there are objective relationships which exist beyond human experience. If you deny this, you are left with cogito ergo sum which was my original argument.
I have no idea what "true" means if it does not mean "a quality of a statement as being an accurate description of objective reality". While mathematics itself may be a human invention, it clearly describes a fundamental truth as evidenced by its continued reliance in producing effective models that describe the measurable world, which must be taken as a reflection of objective reality. Again, you can feel free to deny this, but all you are left with is cogito ergo sum.
How is it a leap of faith when mathematical models that describe reality demonstrate continued reliance in making predictions? Does this not demonstrate that there exist mathematical relationships between certain physical quantities?
If by "objective truth" we mean the qualities of nature that exist irrespective of any individual's perception, then I think the continued reliance of our scientific knowledge in producing effective and consistent results are at least some measure of that.
> The best that we can do is probably say something along the lines of "these are the best methods of getting closer to the truth that we have available - if anyone claims to have better methods, they are very likely wrong", but you still need to have the humility to accept that even the best models that we have to date are not infallible.
This last sentence slightly conflates the scientific method with the models they produce. I am not claiming that the models are "true", I am claiming that the scientific method is the only reasonable means of gaining a reliable understanding of the objective nature of reality, assuming it exists; and that you cannot pick and choose what you believe in based on your intuition.
Quantum principles have been proven in experiments that have as tight a margin of error as measuring the width of the United States to one human hair, producing shockingly consistent and effective models that were absolutely critical to the development of modern technology. Yet some people somehow refuse to accept these models as an "accurate" reflection of reality, whereas they'll take, at face value, psych/sociological/economic studies that are frankly nothing short of pathetic in comparison.
In regards to science, I am saying that there is a hierarchy of belief. You can draw the line wherever you like in terms of what you think is "true", but you cannot reorder this hierarchy and believe these sorts of psych studies while at the same time questioning the physical models that power the technology that is used to publish them.
And this isn't speaking about math, which is a particularly special case given that it is not scientific but still produces shockingly effective results.
Is the fact that these systems cannot prove their own consistency actually a feature of the incompleteness theorem? I thought it effectively boiled down to "you can keep either consistency or completeness, not both". It's been a while since my metamathematics course ...
Not that you were, but I don't quite understand why people get so caught up on this fact. There are objective facts about the nature of reality, and we are all (or at least competent practitioners in the field) are thoroughly convinced that we have identified a subset of these facts.
These presumed facts have helped us do things like go to the moon and build skyscrapers, but then someone comes along with the old "but how do you actually know" argument of a college freshman, and then we get into a conversation about the potential social relativism of math.
All the while, people will see a half-assed psychology study with a questionable procedure, weak at best, erroneous at worst statistics and therefore tenuous at best conclusions, and this study is taken to be "true" and might legitimately impact notable institutions. Yet when we're talking about extremely complicated topics that exist on the edge of the horizon of human intuition, no matter how obvious the impact some people just refuse to accept things as objective simply because they fail to intuitively understand them.
Foundational fields like mathematics and physics are as objective as we can get. If you don't accept that, your belief about what is objectively true ends at cogito ergo sum and that's that. This has always been such a pointless conversation in my mind.
One use case is in the training of Diffusion Models. In the original formulation, the likelihood-maximizing objective is recast in terms of KL divergences. This is done because the KL divergence between Gaussians has a closed form, and the transition distributions in Diffusion Models are taken to be Gaussian, which makes the problem tenable.
Fantastic article - I would love to see an analysis comparing larger quantized models to smaller unquantized models. e.g. is a 14b quantized model better than a 7b unquantized model?
many books will have a page in the preface that lays out the notation, even for very common objects. it's hard to make a cheat sheet for something like this because many symbols are used in different fields, and even if different subfields of the same field.
When did we start talking about the airline industry?
But seriously, the reason it works for the airline industry is because there is literally no other alternative, unlike in this case.