I like this analogy! I think it relates to what he was saying in the video about theorems now being 'data points' that you observe and build into wider theories. The change is that now the theorem proving itself, which used to require deep understanding, can now be done very quickly. There are lots of parallels to when genAI for image generation came out, artists were frustrated their work is seen as just an end result - AI obliterates the elegance and the process.
I am not a mathematician, but I imagine it will provide a huge landscape of possibilities to explore, and be a very different field. Almost like an observational science with links to all kinds of other disciplines. Maybe it reduces the satisfaction from proofs, but people climb mountains that other people have climbed, because they learn a lot on the way.
Interesting... is it overkill to use a multimodal model like this on just audio? Could the model size be decreased dramatically, or does the multimodality help the accuracy and speed in some way?
The benefit is that you can take input in one "mode" and extract output in another; that is, the input is audio mode and the output is text mode. The intermediate representation is the "embedding".
I suppose it depends on the words in question... language knowledge and general world knowledge may not always both be necessary to transcribe accurately.
It's a breathing app that uses your phone to recognise and measure breathing in real-time. Breathing also drives interactive visuals, e.g. fluid, cloth sims and soft body sims.
I have been meaning to make an Android version, but as an interim I started building a web version of simple breathing patterns here: https://lungy.app/breathe/
Exactly - context is everything in art, in how it's experienced and how it is created.
I think it's important to note that a jpg of Monet is not fully experiencing the painting in any sense. Colours will not be accurately captured, the texture, the framing, the scale - it's sort of like getting a heavily watered down version of the expensive wine, saying it's cheap wine, and asking what people think.
This reminds me the day I went to see in person Starry Night Over The Rhone.
I am not exactly an art person, but I once was explained why that painting is a big deal, the whole impasto thing, etc.
I get there and there's an horde of morons taking selfies next to the painting, and another horde of morons taking photos of the painting. I just wanted to observe a bit the depth of the carved layers of ink and how light reflected on them.
Why bother taking a photo when I can find professional high definition photos of it online?
In the end I was unable to observe anything. It was sort of a let down, and the experience made me hate people a wee bit more than before. Nobody wanted to fucking look at the painting.
I love deeply observing paintings and also love taking a photo while in a museum. It helps me remember the details and review like spaced repetition the things I saw, or spend more time observing nuance later. Are many people ticking boxes? Probably, but the issue is the too many people. Even with people just looking, I feel uncomfortable spending time if there’s a line.
> The act of taking photos of paintings in museums is meaningless.
No. I found some paintings I liked in a museum and took photos of them with a serious-at-the-time camera and uploaded them to wikimedia and found the endeavour worthwhile. Not all the paintings are super-famous and been scanned at infinite resolution!
This is why John Cage's 4'33" mentioned above is genius. If you listen to the composition with sincerity and seriousness, you get the full, unadulterated (non-silent) experience as opposed to an interpretation.
I feel really sorry for people that find context is key for art.
For them often context is more important than the actual art. Lie about the context and their view of art changes completely. I would say these people have objectively bad taste in art. These are the worst kinds of people.
In respect to your point about jpeg, you could have had a jpeg marked as real and one ai, and you would have had all the same comments about how the real jpeg was much better for all kinds of reasons. There is going to be almost zero chance anyone commented how they did due to it being a JPEG, vs them thinking it was ai.
I'd be a little bit careful here - being a jerk is quite different to non-conformity / red sneaker effect in surgery and it is not a quality you should look for.
The truly compassionate surgeons will want to improve their skills because they care about their patients. They care if they develop complications and may feel terrible if they do, the jerk may not. Being a jerk may mean that the surgeon can rise to the top, but it may not be due to surgical skill at all, they may be better at navigating politics etc.
I'm surprised at both the article and the paper - both seem very hyperbolic. This is LLMs competing against doctors in a way that is heavily weighted in the LLMs favour, which does not represent clinical practice. These reasoning cases are not benchmarks for doctors, they are learning tools.
I think it's important to note that diagnosis also relies on accurate description of the patient in the first place, and the information you gather depends on the differential diagnosis. Part of the skill of being a doctor is gathering information from lots of different sources, and trying to filter out what is important. This may be from the patient, who may not be able to communicate clearly or may be non verbal, carers and next of kin. History-taking is a skill in itself, as well as examination. Here those data are given.
For pattern recognition from plain text, especially on questions that may be in the o1's training data, I'm not surprised at all that it would outperform doctors, but it doesn't seem to be a clinically useful comparison. Deciding which investigations to do, any imaging, and filtering out unnecessary information from the history is a skill in itself, and can't really be separated from forming the diagnosis.
Also, you need to see an analysis of the incorrect calls. The goal of a human Dr is not to get the highest accuracy, it's to limit total harm to the patient. There can be cases where the odds favor picking X (but it may not be by that much), but the safe thing to do is to rule out some other option first, or start a safe treatment that covers several other possible options.
Simply getting the "high score" on this evaluation is not necessarily good medical treatment.
Exactly this. Most diagnosis isn’t about pinpointing the underlying exact cause, it’s ruling out the really bad stuff and minimising harm. Differential diagnosis just isn’t real world medicine.
Yeah 100% this. We've all used AI. It's obvious that it can sometimes outperform humans in a "did it get the right answer" benchmark while being wildly worse overall because of worse failure modes.
I bet the AI's incorrect answers are less "I don't know, let's get a second opinion" and more "you're perfectly fine, 0% chance this is cancer".
At many (otherwise) world-leading facilities even just reviewing the patient history is a slog. There is rarelly any ability to keyword search the records or even filter the records by location, title and occupation of the healthcare professional making it, etc. Especially very ill people will have hundreds and hundreds of recent entries.
And stepping through those entries isn’t like browsing a modern local-first app [1], where you will just scroll through dozens of entries in milliseconds. It’s not like the slightly older and slightly slower Gmail interface. You’re clicking on each record and waiting 400ms-3s for it to load, as if instead of a 25Gb fiber connection you’re on dialup requesting the record from Epic’s headquarters in the US and proxying them via Australia.
This is really great. I always saw those harmonic shapes as electron orbitals, I had no idea they could be used in lighting too - so cool.
It made me wonder - why do the electron orbitals take those shapes in say a hydrogen atom? Is there a constraint on the electron and proton together that make it fit only to spherical harmonic functions?
The reason is that electrons (like all quantum mechanical objects) are wavelike. In an isolated hydrogen atom, the electron is in a spherically symmetric environment, so the solutions to the wave equation have to be spherical standing waves, which are the spherical harmonics. The wave frequencies have to be integer divisions of 2pi or else they would destructively interfere. (Technically each solution is a product of a spherical harmonic function and a radial function that describes how fast the electron wave decays vs distance from the nucleus)
What’s interesting is if the environment is not spherically symmetric (consider an electron in a molecule) the solutions to the wave equation (the electronic wave functions) are no longer spherical harmonics, even though we like to approximate them with combinations of spherical harmonic basis functions centered on each nucleus. It’s kind of like standing waves on a circular drum head (hydrogen atom) vs standing waves on an irregular shaped drum head
Of course the nucleus also has a wave nature and in reality this interacts with the electrons, but in chemistry and materials we mostly ignore this and approximate the nucleus like a static point charge from the elctrons perspective because the electrons are so much lighter and faster
Ah amazing - thank you for the response! I have a couple of related questions - is it that the non 2 pi frequencies exist, but they destructively interfere so we can't see them? My understanding is that the radial function for the electron is zero at the nucleus - there is no possibility of it being found there - but why is that the case?
Admittedly my understanding of QM is a bit vibey but I’ll try to answer
In an atom, angular wavefunctions with wavelengths non-integer divisions of 2pi can’t exist because of the boundary conditions on the wave equation. A free electron can have any wavelength, but once you put it in a box (confine it to the potential around a proton in a Hydrogen atom) the non-integer wavelengths aren’t allowed
I think it’s instructive to think about what the wavefunction represents. It’s square is the electron probability density (technically the wavefunction is complex valued so it’s the wavefunction times it’s complex conjugate). If you have a non-integer multiple wavelength then the wavefunction goes out of phase with its complex conjugate after one period, and if you integrate over the angular domain the electron probability has to be zero everywhere.
This also answers your second question. The radial solution to the wave equation for hydrogen gives you the Laguerre polynomials. They don’t all go to zero at the nucleus though, actually the first one has a maximum at zero because it scales like exp(-r) (See fig 4.10.2 on chem.libretexts linked below). But when you do a volume integral to calculate the electron probability, the probability near the nucleus is low because the integration volume is small even though the wavefunction is large
Spherical harmonics are basically a fourier series. They're a complete orthonormal set of basis functions for functions for the unit sphere. Whereas the fourier series from calc 101 is a complete orthonormal set of basis functions on the unit interval (eg [0,1]).
In other words you can express any reasonable function on the unit sphere as a series of spherical harmonic terms. That makes them ideal for working with differential equations (eg schrodinger's equation for the hydrogen atom, or, emission from an arbitrary light source).
In the era im familiar with (ps3, 360) everyone used the first 9 coefficients. You can read the original Ramamoorthi paper for better theory applied to lighting.
But yes it’s an approximation. If you have a ton of terms it looks like a bitmap like you said.
I am not a mathematician, but I imagine it will provide a huge landscape of possibilities to explore, and be a very different field. Almost like an observational science with links to all kinds of other disciplines. Maybe it reduces the satisfaction from proofs, but people climb mountains that other people have climbed, because they learn a lot on the way.
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