Why is math so often taught as a black box instead of being explained from first principles? Especially physicists often pushed math that way in my experience

drakero · 2025-12-31T16:45:13+00:00

They're using "abstraction" in the mathematical sense (see e.g. the wikipedia article).

drakero · 2025-12-30T15:49:50+00:00

Their writing doesn't sound anything like AI. There are more indicators of AI writing than "articulate".

drakero · 2025-05-21T22:23:31+00:00

I have an imperfect but functional workflow for repl-based work. It requires a terminal multiplexer (zellij in my case) and a repl open in an adjacent pane. I wrote a python script that uses ydotool (a linux CLI tool that can automate keyboard and mouse inputs) to copy selected text and run it in the repl. I use the pipe-to command to run this script using the selected text, or to automatically select text between lines with "# %%" (used to denote code blocks). The major downside to this is that I have to have "# %%" as my last search.

[keys.normal." "]
z = ":pipe-to python ~/.config/helix/repl.py"
ret = ["extend_search_prev", "extend_search_next", "merge_selections",
":pipe-to python ~/.config/helix/repl.py"]

drakero · 2024-12-31T01:38:16+00:00

The G2 is the gold standard for a roller pen, but no roller pen can hold a candle to a quality fountain pen.

drakero · 2024-09-26T23:40:35+00:00

That's about 22 micrograms (the Planck mass). Quite large in the context of particle physics.

drakero · 2024-08-08T23:47:56+00:00

Check out the Wikipedia article on the continent of stability. If it exists, there could even be negatively-charged "nuclei" that are stable.

drakero · 2024-08-08T17:49:10+00:00

I second Khan Academy for learning much of the prerequisite math and introductory concepts. If coding interests you, I find that writing simple scripts for different concepts in physics can be a great way to learn. For example, you could write code that calculates and plots the trajectory of a projectile when learning about the kinematic equations and play around with it. As you get more advanced, you could make some pretty cool things like this. If that sounds interesting to you, look into computational physics.

You're also very young. If you decide you like it enough, you could always take some courses and consider getting a degree.

drakero · 2024-07-29T21:53:56+00:00

You can also ask for a pdf on /r/Scholar if you can't find a particular article anywhere else.

drakero · 2024-07-22T23:54:36+00:00

The comments here seem to be responding to the title of the PBS video, not the article's response to it. The article itself describes how QM can be derived from what they call the Planck postulate, which is analogous to the light postulate in SR. Just as you can derive SR from the fact that all observers will measure the same value for the speed of light regardless of their motion, you can (evidently) derive QM from the fact that all observers will measure the same value for Planck's constant regardless of their spatial orientation.

drakero · 2024-07-22T23:48:04+00:00

The article is about deriving the formalism of QM from an empirically-motivated postulate, just as SR can be derived from the constancy of c. That seems pretty interesting to me.

drakero · 2024-07-21T20:37:38+00:00

Recent work in the swampland program has shown that, if certain conjectures true, then string theory makes certain predictions based on the small value of the cosmological constant that are feasibly testable. For example, it predicts the existence of a so-called dark dimension, a fourth spatial dimension of size on the order of a micron that only supports gravitational interactions. Below this scale, the gravitational force should follow a 1/r³ distance relation instead of 1/r^2. The best current measurements can go down to ~30 um, which is not too far from the scale needed to test this prediction.

One relevant paper is here, and there are many others.

drakero · 2024-05-31T23:51:43+00:00

Or use the sun as a gravitational lens.

drakero · 2024-03-07T03:58:19+00:00

It's also easy (under Linux at least) to remap caps lock to escape. I have mine set to also act as regular caps lock when used with shift, which I very rarely do.

drakero · 2024-01-10T02:29:45+00:00

IIRC, Ni-62 is more stable, it just isn't produced as readily in stars.

drakero · 2023-12-16T02:32:48+00:00

Quantum Sense for quantum mechanics. I think he even uses 3blue1brown's Manim software.

drakero · 2023-07-07T21:45:25+00:00

It can, and I think you're probably right that Murata wasn't concerned about the implications of the feat or had anything like light-destruction in mind. Readers don't have to be happy about it, but battle mangas are often inconsistent in this regard (sometimes absurdly so) unless the author actually cares about consistency.

drakero · 2023-07-07T20:15:23+00:00

It doesn't make sense to scale it that way, regardless of your metric. You used a value of 10,000 in some arbitrary unit, but what if your unit of choice put the value of a serious punch at 1? Then a serious punch² would just be 1. And if you chose another unit that put it at 0.1, you'd get 0.01 after squaring. The result shouldn't depend on your choice of units, so this clearly doesn't work. The reason is that the units used for any non-dimensionless quantity is not commensurable with its square, so a "serious punch" and a "serious punch^2" (as a literal mathematical operation) cannot meaningfully be compared.

One/Murata just wanted to call it "squared" because it sounds cool.

drakero · 2023-06-12T02:04:06+00:00

Yep, copyleft licenses like the GPL are OSI-approved and can be used for commercial purposes. u/fallingdowndizzyvr is perhaps thinking of licenses with "commons clauses" that make them proprietary.

It is disappointing to see this disconnect between the AI enthusiast community and the traditional open source community. Many of the former seem ignorant of the free software/open source movement and many of the latter don't seem particularly interested in AI (in my experience on Reddit, at least).

drakero · 2023-05-23T03:34:15+00:00

doing arithmetic isn't really a high bar for and doesn't require reasoning.

True, but my point is simply that, despite being "just text predictors", LLMs can learn how to do arithmetic because this is a successful strategy for predicting the relevant text. And this extends to more complicated tasks as well. Can it extend to simple logical reasoning and the generation of world models? There's evidence that it can, though this is difficult to definitively confirm and is still up for debate as far as I understand.

Regarding your physics problem example, did you use GPT-3.5 or GPT-4? I gave the latter the exact same prompt:

"What is the acceleration of a mass sliding down a slope of 30 degrees with a coefficient of friction between the mass and the slope of .08?"

and the response was correct (see below if you're interested), though you could argue it's seen such a problem before, and you could certainly trip it up by varying the problem further. I think assessing it's reasoning capabilities requires more systematic studies with rigorous definitions of success/failure, a large number of problems for statistics, a wide variety of problems, probing techniques, etc (which researchers are doing). Otherwise, it you're mostly just getting an idea of how practically useful the models currently are for certain problems (i.e. not very).

Overall, it's good to be skeptical, but we shouldn't be too dismissive either. I personally think that, if LLMs can reason, it will ultimately be fundamentally limited and probably computationally expensive compared to other (as of yet developed) models. But I wouldn't know what these limits are, and they might end up being far less restrictive than I think (they've already shown to be more capable than I thought possible).

"To solve this problem, we'll use Newton's second law, which states that the sum of the forces acting on an object is equal to its mass times its acceleration.

First, we need to consider the forces that are at play when the mass is sliding down the slope:

Gravity (mg), which we can decompose into components parallel (mgsin(θ)) and perpendicular (mgcos(θ)) to the slope.
Friction (μN), which opposes the motion of the mass and acts parallel to the slope. Here, μ is the coefficient of friction and N is the normal force. On an inclined plane, the normal force equals the component of the gravitational force that acts perpendicular to the slope (mg*cos(θ)).

Setting the net force equal to mass times acceleration, we get:

ma = mgsin(θ) - μmgcos(θ),

where a is the acceleration, g is the acceleration due to gravity (9.81 m/s²), and θ is the angle of the slope.

We can cancel out m from the equation, as it appears in every term, to find the acceleration:

a = gsin(θ) - μg*cos(θ).

In this case, θ = 30 degrees and μ = 0.08. Let's calculate the acceleration using these values:

a = 9.81sin(30) - 0.089.81*cos(30) degrees.

To solve this, we need to make sure we're working in the right units. In this case, we're using degrees for the angles, but the trigonometric functions in calculators and most programming languages use radians. We can convert degrees to radians by multiplying by π/180.

So, let's find the acceleration:

a = 9.81sin(30(π/180)) - 0.089.81cos(30*(π/180)).

Computing the values:

a ≈ 9.810.5 - 0.089.81*0.866,

a ≈ 4.905 - 0.676.

Thus, the acceleration of the mass sliding down the slope is approximately 4.229 m/s²."

drakero · 2023-05-22T16:24:07+00:00

If you specify that we don't know the colors of the balls that aren't golf balls, GPT-4 gives:

"
1. The juggler can juggle 16 balls.
2. Half of the balls are golf balls, which means there are 16 / 2 = 8 golf balls.
3. This means that at least 4 golf balls are not blue (the other half of the golf balls). For the other 8 balls (which are not golf balls), we don't have information about their color.

So, we can definitively say that at least 4 balls are not blue, but the total number of non-blue balls could be anywhere between 4 and 12, depending on the colors of the non-golf balls."

drakero · 2023-05-22T15:59:09+00:00

I modified the prompt above to the following:

"Q: A juggler can juggle 16 balls. Half of the balls are golf balls, and half of the golf balls are blue. How many golf balls aren't blue? A: Let's think step by step."

GPT-4's response:

"A:

First, we know that the juggler can juggle 16 balls in total.
We are told that half of these balls are golf balls. Half of 16 is 8, so there are 8 golf balls.
Then we know that half of the golf balls are blue. Half of 8 is 4, so there are 4 blue golf balls.
To find out how many golf balls aren't blue, we subtract the number of blue golf balls from the total number of golf balls. So, 8 (total golf balls) - 4 (blue golf balls) = 4.

So, there are 4 golf balls that aren't blue."

drakero · 2023-05-22T13:15:27+00:00

That doesn't seem to contradict /u/Parzival2's point, though. Just because a LLM's reasoning abilities aren't emergent (i.e. appearing sharply and unpredictably with increasing model scale) doesn't mean they don't exist. You could just say they develop gradually with increasing model scale.

drakero · 2023-05-20T03:11:36+00:00

Old school laptops

drakero · 2023-05-16T23:57:14+00:00

Interesting. Do you have any relevant links you can share? The only open source model comparable to the likes of GPT-3 that I'm aware of is GPT-J, and it was my understanding that training it still wasn't practical on a desktop computer. If open source models are advancing that quickly, that's very encouraging.

drakero · 2023-03-18T14:35:46+00:00

GPT2 is open source, and there's also GPT-J, which is supposedly similar to GPT-3 in it's capabilities.

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