On Solving Einstein's Field Equation

[Alan Grayson]

Basic question; when a solution is sought, what exactly can we solve for? TY, AG

[Alan Grayson]

What I mean is not some simple minded answer such as solving for this or that tensor in the field equation, but something like this; suppose we consider a star of mass M, with all mass contained in its center for simplicity. How would we calculate the spacetime curvature in a region around this star? TY, AG

[Brent Meeker]

Geodesics, the force-free trajectories, would be one thing to solve for.

Brent

On 2/12/2025 9:23 PM, Alan Grayson wrote:

Basic question; when a solution is sought, what exactly can we solve for? TY, AG --

[Alan Grayson]

On Thursday, February 13, 2025 at 1:06:48 PM UTC-7 Brent Meeker wrote:

Geodesics, the force-free trajectories, would be one thing to solve for.

Brent

That's more or less what I figured. Now, what's the very first thing you'd do to acomplish that? TY. AG 

[spudb...@aol.com]

Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach

https://arxiv.org/abs/2502.05171

 https://twitter.com/akazlev/status/1890193777526292745

 We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This stands in contrast to mainstream reasoning models that scale up compute by producing more tokens. Unlike approaches based on chain-of-thought, our approach does not require any specialized training data, can work with small context windows, and can capture types of reasoning that are not easily represented in words. We scale a proof-of-concept model to 3.5 billion parameters and 800 billion tokens. We show that the resulting model can improve its performance on reasoning benchmarks, sometimes dramatically, up to a computation load equivalent to 50 billion parameters.

New research paper shows how LLMs can "think" internally before outputting a single token! Unlike Chain of Thought, this "latent reasoning" happens in the model's hidden space. TONS of benefits from this approach. Let me break down this fascinating paper...

[Alan Grayson]

This is wothless. Stop wasting our time. AG

[John Clark]

I agree. I don't see how any serious person could say that these AI's are not conscious, they're certainly smart as hell! 

John K Clark    See what's on my new list at  Extropolis

,,h

[John Clark]

On Thu, Feb 13, 2025 at 7:32 PM 'spudb...@aol.com' via Everything List <everyth...@googlegroups.com> wrote:

> Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach
https://arxiv.org/abs/2502.05171

 https://twitter.com/akazlev/status/1890193777526292745

Here's a video about that fascinating paper: 

New AI Model "Thinks" Without Using a Single Token

John K Clark    See what's on my new list at  Extropolis

myz

 

 

[Brent Meeker]

That's effectively the Schwarzschild solution unless the a star is rotating very fast.  You don't even have to make the assumption that the mass is concentrated at the center, you just assume spherical symmetry.

Brent

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[Alan Grayson]

On Thursday, February 13, 2025 at 6:15:08 PM UTC-7 John Clark wrote:

I agree. I don't see how any serious person could say that these AI's are not conscious, they're certainly smart as hell! 

John K Clark    See what's on my new list at  Extropolis

Serious question; how can a person with zero clue about the source of consciousness claim any insight about AI's consciousness? AG

Question about discrimination; in a horse race, according to the MWI, multiple worlds come into existence for all possible winners in a particular race. But for one given race, are there are not multiple worlds which come into existence for every possible way in which the winner wins, even retaining the finishing order of the loosing horses? I think so, and is the reason I find the interpretations and its devotees, lacking in discrimination. AG 

[Alan Grayson]

On Thursday, February 13, 2025 at 9:59:31 PM UTC-7 Brent Meeker wrote:

That's effectively the Schwarzschild solution unless the a star is rotating very fast.  You don't even have to make the assumption that the mass is concentrated at the center, you just assume spherical symmetry.

Brent

TY, but what's the first thing one must DO, who never heard of Schwartzchild, to derive a geodesic path?  AG

[John Clark]

On Fri, Feb 14, 2025 at 12:06 AM Alan Grayson <agrays...@gmail.com> wrote:

> in a horse race, according to the MWI, multiple worlds come into existence for all possible winners in a particular race. But for one given race, are there are not multiple worlds which come into existence for every possible way in which the winner wins, 

There are. In some worlds you win your bed in the other worlds you don't. In the world where you win sometimes your horse wins in a photo finish by half an inch, in other worlds your horse wins by half a mile. 

John K Clark    See what's on my new list at  Extropolis

jgh

[John Clark]

On Fri, Feb 14, 2025 at 12:11 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, February 13, 2025 at 9:59:31 PM UTC-7 Brent Meeker wrote:

 

>> That's effectively the Schwarzschild solution unless the a star is rotating very fast.  You don't even have to make the assumption that the mass is concentrated at the center, you just assume spherical symmetry.

 

 > but what's the first thing one must DO, who never heard of Schwartzchild,

Open a book and learn about the Schwarzschild solution.

 John K Clark    See what's on my new list at  Extropolis

bo9 

 

[Alan Grayson]

On Friday, February 14, 2025 at 6:09:52 AM UTC-7 John Clark wrote:

On Fri, Feb 14, 2025 at 12:11 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, February 13, 2025 at 9:59:31 PM UTC-7 Brent Meeker wrote:

 

>> That's effectively the Schwarzschild solution unless the a star is rotating very fast.  You don't even have to make the assumption that the mass is concentrated at the center, you just assume spherical symmetry.

 

 > but what's the first thing one must DO, who never heard of Schwartzchild,

Open a book and learn about the Schwarzschild solution.

Will the same book inform me of your horse racing fantasy? AG 

[spudb...@aol.com]

Ok, thanks, JC. Smart and conscious seem to be a Venn Diagram for me. A science book is not smart, but the author who wrote it certainly is conscious and smart. 

Thx. 

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.

[spudb...@aol.com]

I shan't! It's science from a scientist. 

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[Alan Grayson]

It belongs on a different discussion thread. AG

[Alan Grayson]

On Friday, February 14, 2025 at 6:09:52 AM UTC-7 John Clark wrote:

On Fri, Feb 14, 2025 at 12:11 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, February 13, 2025 at 9:59:31 PM UTC-7 Brent Meeker wrote:

 

>> That's effectively the Schwarzschild solution unless the a star is rotating very fast.  You don't even have to make the assumption that the mass is concentrated at the center, you just assume spherical symmetry.

 

 > but what's the first thing one must DO, who never heard of Schwartzchild,

Open a book and learn about the Schwarzschild solution.

I intend to, but first I want to know what's the very first thing one must do to solve Einstein's Field Equation. AG 

[Brent Meeker]

On 2/13/2025 12:45 PM, Alan Grayson wrote:

On Thursday, February 13, 2025 at 1:06:48 PM UTC-7 Brent Meeker wrote:

Geodesics, the force-free trajectories, would be one thing to solve for.

Brent

That's more or less what I figured. Now, what's the very first thing you'd do to acomplish that? TY. AG

Derive the set of differential equations describing a geodesic, starting from the metric if you've solved the field equations for the metric.

Brent

On 2/12/2025 9:23 PM, Alan Grayson wrote:

Basic question; when a solution is sought, what exactly can we solve for? TY, AG --

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[Brent Meeker]

On 2/13/2025 9:11 PM, Alan Grayson wrote:

On Thursday, February 13, 2025 at 9:59:31 PM UTC-7 Brent Meeker wrote:

That's effectively the Schwarzschild solution unless the a star is rotating very fast.  You don't even have to make the assumption that the mass is concentrated at the center, you just assume spherical symmetry.

Brent

TY, but what's the first thing one must DO, who never heard of Schwartzchild, to derive a geodesic path?  AG

Schwarzschild first assumed spherical symmetry.  Then using spherical coordinates, Einstein's equations are greatly simplified and Schwarzschild solved them for the metric.  Incidentally, Einstein, when he published his paper describing general relativity, Nov 25 1915, said he thought that no exact solutions to the equations would ever be found.  Karl Schwarzschild, while fighting as an artillery officer in WW1, found his solution on Dec 22 and sent it to Einstein.

https://www.einsteinrelativelyeasy.com/index.php/general-relativity/171-schwarzschild-metric-derivation

But lest you think it's easy to find an exact solution, the cylindrically symmetric, rotating star, case wasn't found until Roy Kerr did it in 1965 at University of Texas where I once played soccer against him at the Relativity Dept picnic.  It was Americans v. Foreigners.

Brent

[Brent Meeker]

On 2/14/2025 7:44 AM, 'spudb...@aol.com' via Everything List wrote:

Ok, thanks, JC. Smart and conscious seem to be a Venn Diagram for me. A science book is not smart, but the author who wrote it certainly is conscious and smart. 

Thx. 

On Thursday, February 13, 2025 at 08:15:09 PM EST, John Clark <johnk...@gmail.com> wrote:

I agree. I don't see how any serious person could say that these AI's are not conscious, they're certainly smart as hell!

Consciousness isn't a single thing.  There's consciousness OF different kinds of things.  These AI's are probably not conscious of their location.  They're not conscious of tactile or kinematic sensations.  They don't have a body to be conscious OF, although they may hallucinate one.  I doubt they experience many common emotions such as lust.  I'm not sure how they are self-conscious. 

Brent

[John Clark]

On Fri, Feb 14, 2025 at 9:22 PM Brent Meeker <meeke...@gmail.com> wrote:

> Consciousness isn't a single thing.  There's consciousness OF different kinds of things. 

I'm not conscious of being President of the United States, I am nevertheless conscious.  

 > They [AIs] don't have a body to be conscious OF, although they may hallucinate one. 

You can't have a hallucination without consciousness, it's a subjective experience. 

  John K Clark    See what's on my new list at  Extropolis

7yc

[Brent Meeker]

On 2/15/2025 5:08 AM, John Clark wrote:

On Fri, Feb 14, 2025 at 9:22 PM Brent Meeker <meeke...@gmail.com> wrote:

> Consciousness isn't a single thing.  There's consciousness OF different kinds of things. 

I'm not conscious of being President of the United States, I am nevertheless conscious.  

 > They [AIs] don't have a body to be conscious OF, although they may hallucinate one. 

You can't have a hallucination without consciousness, it's a subjective experience.

Are you hallucinating that you're arguing with me...while you examples prove my point?

Brent

  John K Clark    See what's on my new list at  Extropolis

7yc

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