I foolishly sat in 8.821 [0] while at MIT thinking I could make sense out of quantum gravity. Most of the math went over my head, but the way I understand this paper, it’s basically a cosmic engineering fix for a geometry problem. Please correct me if necessary.
String theory usually prefers universes that want to crunch inwards (Anti-de Sitter space). Our universe, however, is accelerating outwards (Dark Energy).
To fix this, the authors are essentially creating a force balance. They have magnetic flux pushing the universe's extra dimensions outward (like inflating a tire), and they use the Casimir effect (quantum vacuum pressure) to pull them back inward.
When you balance those two opposing pressures, you get a stable system with a tiny bit of leftover energy. That "leftover" is the Dark Energy we observe.
You start with 11 dimensions (M-theory) and roll up 6 of them to get this 5D model. It sounds abstract, but for my engineer brain, it's helpful to think of that extra 5th dimension not as a "place" you can visit, but as a hidden control loop. The forces fighting it out inside that 5th dimension are what generate the energy potential we perceive as Dark Energy in our 4D world. The authors stop at 5D here, but getting that control loop stable is the hardest part
The big observatiom here is that this balance isn't static -- it suggests Dark Energy gets weaker over time ("quintessence"). If the recent DESI data holds up, this specific string theory solution might actually fit the observational curve better than the standard model.
This is a bit of a technicality, but we don't live in a 4D world, we live in a 3+1D world - the 3 spacial dimensions are interchangeable, but the 1 time-related dimension is not interchangeable with the other three (the metric is not commutative).
I'm bringing this up because a lot of people seem to think that time and space are completely unified in modern physics, and this is very much not the case.
To expand on this a little for those interested, time has properties space doesn't. For example, you can turn left to swap your forward direction for sideways in space. You cannot turn though, in a way that swaps your forward (as it were) direction in space for a backward direction in time.
Equally, cause always precedes effect. If time were exactly like space, you could bypass a cause to get to an effect, which would break the fundamental laws of physics as we know them.
There's obviously a lot more, but that's a couple of examples to hopefully help someone.
Not really. Even the electric force is not purely time symmetric - you have to flip the sign of the charge if you want to flip the direction between forwards vs backward in time.
Even worse, the weak force breaks another symmetry as well, parity symmetry (which basically means that moving backward in time, weak force particles "look" like their mirror image, instead of looking the same).
Can you expand on this? I’m guessing that it’s something to do with preservation of mass & energy? Like mass doesn’t have to be preserved over a spatial dimension (eg rotating an object) but does over time.
I explained in another comment, but it's more fundamental than that.
In pure mathematical terms, the vector space used in special relativity (and in theories compatible with it, such as QM/QFT), while being 4 dimensional, is not R^4, it's not a 4D cartesian vector space.
Specifically, the scalar product of two vectors in R^4 (4D space) is [x1,y1,z1,h1] dot [x2,y2,z2,h2] = x1x2 + y1y2 + z1z2 + h1h2. You can order the coordinates however you like - you could replace x with h in the above and nothing would change.
However, SR space-time is quite different. The scalar product is defined as [x1,y1,z1,t1] dot [x2,y2,z2,t2] = c^2 * t1t2 - x1x2 - y1y2 - z1z2. You can still replace x with y without any change with the result; but you can't replace x with t in the same way. This makes it clear from the base math itself that the time dimension is of a different nature than the 3 space dimensions in this representation. This has a significant impact on how distances are calculated, and how operations like rotations work in this geometry.
How is the difference between them characterised in physics?
It seems like it would be hard to distinguish from the point of view of a 4D unit vector XYZT if T was massively larger. Is it distinguished because it's special or is it just distinguished just because the ratio to the other values is large.
Imagine if at the big bang there was stuff that went off in Z and XY and T were tiny in comparison? What would that look like? Part of me says relativity would say there's no difference, but I only have a slightly clever layman's grasp of relativity.
The difference is this: in regular 4D space, the distance between two points, (X1 Y1 Z1 T1) and (X2 Y2 Z2 T2) is (X1-X2)^2 + (Y1-Y2)^2 + (Z1-Z2)^2 + (T1-T2)^2), similar to 3D distances you may be more familiar with.
However, this is NOT the case in Special Relativity (or in QM or QFT). Instead, the distance between two points ("events") is (cT1-cT2)^2 - (X1-X2)^2 - (Y1-Y2)^2 - (Z1-Z2)^2. Note that this means that the distance between two different events can be positive, negative, or 0. These are typically called "time-like separated" (for example, two events with the same X,Y,Z coordinates but different T coordinates, such as events happening in the same place on different days); "space-like separated" (for example, two events with the same T coordinate but different X,Y,Z coordinates, such as events happening at the same time in two different places on Earth); or light-like separated (for example, if (cT1-cT2) = (X1 - X2), and Y, Z are the same; these are events that could be connected by a light beam). Here c is the maximum speed limit, what we typically call the speed of light.
This difference in metric has many mathematical consequences in how different points can interact, compared to a regular 4D space. But even beyond those, it makes it very clear that walking to the left or right is not the same as walking forwards or backwards in time.
Edit to add a small note: what I called "the distance" is not exactly that - it's a measure of the vector that connects the two points (specifically, it is the result of its scalar product with itself, v . v). Distance would be the square root of that, with special handling for the negative cases in 3+1D space, but I didn't want to go into these complications.
The turkey is fed by the farmer every morning at 9 AM.
Day 1: Fed. (Inductive confidence rises)
Day 100: Fed. (Inductive confidence is near 100%)
Day 250: The farmer comes at 9 AM... and cuts its throat. Happy thanksgiving.
The Turkey was an LLM. It predicted the future based entirely on the distribution of the past. It had no "understanding" of the purpose of the farmer.
This is why Meyer's "American/Inductive" view is dangerous for critical software. An LLM coding agent is the Inductive Turkey example. It writes perfect code for 1000 days because the tasks match the training data. On Day 1001, you ask for something slightly out of distribution, and it confidently deletes your production database because it added a piece of code that cleans your tables.
Humans are inductive machines, for the most part, too. The difference is that, fortunately, fine-tuning them is extremely easy.
> The Turkey was an LLM. It predicted the future based entirely on the distribution of the past. It had no "understanding" of the purpose of the farmer.
But we already know that LLMs can do much better than that. See the famous “grokking” paper[1], which demonstrates that with sufficient training, a transformer can learn a deep generalization of its training data that isn’t just a probabilistic interpolation or extrapolation from previous inputs.
Many of the supposed “fundamental limitations” of LLMs have already been disproven in research. And this is a standard transformer architecture; it doesn’t even require any theoretical innovation.
I'm a believer that LLMs will keep getting better. But even today (which might or might not be "sufficient" training) they can easily run `rm -rf ~`.
Not that humans can't make these mistakes (in fact, I have nuked my home directory myself before), but I don't think it's a specific problem some guardrails can solve currently. I'm looking for innovations (either model-wise or engineering-wise) that'd do better than letting an agent run code until a goal is seemingly achieved.
LLM's have surpassed being Turing machines? Turing machines now think?
LLM's are known properties in that they are an algorithm! Humans are not. PLEASE at the very least grant that the jury is STILL out on what humans actually are in terms of their intelligence, that is after all what neuroscience is still figuring out.
That’s where Bayesian reasoning comes into play, where there are prior assumptions (e.g., that engineered reality is strongly biased towards simple patterns) which make one of these hypotheses much more likely than the other.
Deciding that they are both equally likely is also a deciding a prior.
Yes, "equally likely" is the minimal information prior which makes it best suited when you have no additional information. But it's not unlikely that have some sort of context you can use to decide on a better prior.
> The difference is that, fortunately, fine-tuning them is extremely easy.
Because of millions of years of generational iterations, by which I mean recursive teaching, learning and observing, the outcomes of which all involved generations perceive, assimilate and adapt to in some (multi-) culture- and sub-culture driven way that is semi-objectively intertwined with local needs, struggles, personal desires and supply and demand. All that creates a marvelous self-correcting, time-travelling OODA loop. []
Machines are being finetuned by 2 1/2 generations abiding by exactly one culture.
> The difference is that, fortunately, fine-tuning them is extremely easy.
If this was true, educating people fast for most jobs would be a really easy and solved problem. On the other hand in March 2018, Y Combinator put exactly this into its list of Requests for Startups, which gives strong evidence that this is a rather hard, unsolved problem:
But never a second; the human learned from one instance, effectively forever, without even trying. ChatGPT had to be retrained and to not fall for the “r”’s trick, which cost much more than one prompt, and (unless OpenAI are hiding a breakthrough, or I really don’t understand modern LLMs) required much more than one iteration.
That seems to be the one thing that prevents LLMs from mimicking humans, more noticeable and harder to work around than anything else. An LLM can beat a Turing test where it only must generate a few sentences. No LLM can imitate human conversation over a few years (probably not even a few days), because it would start forgetting much more.
The problem with education is that existing ways of doing things are very strongly entrenched.
At the school level: teachers are trained, buildings are built, parents rely on kids being at school so they can go out to work....
At higher levels and in training it might be easier to change things, but IMO it is school level education that is the most important for most people and the one that can be improved the most (and the request for startups reflects that).
I can think of lots of ways things can be done better. I have done quite a lot of them as a home educating parent. As far as I can see my government (in the UK) is determined to do the exact opposite of the direction I think we should go in.
> The problem with education is that existing ways of doing things are very strongly entrenched.
Which is still a problem of educating humans. Just moved up the chain one step. Educators are often very hard to educate.
Even mathematics isn't immune to this. Calculus is pervasively taught with prematurely truncated algebra of differentials. Which means for second order derivatives and beyond, the "fraction" notation does not actually describe ratios, when this does not need to be the case.
But when will textbooks remove this unnecessary and complicating disconnect between algebra and calculus? There is no significant movement to do so.
Educators and textbook writers are as difficult to educate as anyone else.
You clearly underestimate the quality of people I have seen and worked with.
And yes guard rails can be added easily.
Security is my only concern and for that we have a team doing only this but that's also just a question of time.
Whatever LLMs ca do today doesn't matter. It matters how fast it progresses and we will see if we still use LLMs in 5 years or agi or some kind of world models.
> You clearly underestimate the quality of people I have seen and worked with.
I'm not sure what you're referring to. I didn't say anything about capabilities of people. If anything, I defend people :-)
> And yes guard rails can be added easily.
Do you mean models can be prevented to do dumb things? I'm not too sure about that, unless a strict software architecture is engineered by humans where LLMs simply write code and implement features. Not everything is web development where we can simply lock filesystems and prod database changes. Software is very complex across the industry.
I know plenty of people who are shittier in writing code than Claude. People with real jobs who are expensive like 50-100k/year.
People whom you have to always handhold and were code review is fundamental.
You can write tests, pr gates etc.
It's still a scale in what you can let them do unsupervised vs controlling them more closely but already better than real people I know. Because they are also a lot faster.
> You clearly underestimate the quality of people I have seen and worked with
"Humans aren't perfect"
This argument always comes up. The existence of stupid / careless / illiterate people in the workplace doesn't excuse spending trillions on computer systems which use more energy than entire countries and are yet unreliable
I assume this is satire, but that aside -- many of my friends who entered into big tech as new grads with "unlimited pto" are indeed very hesitant to take it. They are worried that it'd affect how their managers see them. The same idea with showing up before your manager and leaving after they leave.
Likely it was an expired domain. I have seen this trend happen quite a bit with semi-popular domains, e.g., International Olympiad in Informatics 2019 official website, ioi2019.az
Calling a Polymarket dashboard a "Bloomberg Terminal" is doing a lot of heavy lifting here.
The value of a Bloomberg Terminal isn't the UI (which is famously terrible/efficient); it's the latency, the hardware, the proprietary data feeds, the chat network, and the reliability.
Building a React frontend that fetches some JSON from an API in 2 hours is impressive, sure, but it’s not the hard part of fintech. We need to stop conflating "I built a UI that looks like X" with "I rebuilt the business value of X."
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