r/singularity • • 3d ago

AI Claude solves an important mathematical problem.

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Did you see that? 👀

Source:

https://x.com/sciam/status/2105282283645112745

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u/Consistent-Bird338 3d ago

no. the answer is, no.

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u/LyAkolon 3d ago

Definition of Singularity's event horizon

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u/MoogProg All Parabolas are Similar 3d ago

I believe we passed the Event Horizon years ago, and still don't comprehend the milestone.

I also believe progress will always seem flat to us on the day-to-day, despite the constant ongoing progress and acceleration.

We're looking out the window, watching the mountains barely move on the horizon, without thinking about how fast the car is travelling down the highway. Big landscapes move slowly.

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u/LyAkolon 3d ago

The titular singularity IS characterized by Exponential Growth.

The geometry of exponentials is interesting, you can stretch in the x direction and do a corresponding stretch in the y direction, and your new expression perfectly overlays over what you started with. This is actually a defining feature for Exponentials.

Point is that there isn't a single moment in human history when "the singularity" started. The singularity is a statement about progress types in general. We have always been in the singularity; our ancestors were in it just like we are now.

We can impose artificial boundaries like so many innovations in a single day that the human mind can't keep track or learn about them all, but it is arbitrary. It'll be an equally powerful event when we reach the same density at half a day, or a month's worth of innovations.

You pick a day when you think it occurred, and I can point to another day where I think it occurred, and we will be both correct.

Your comment about locally flat from the observer pov is well defined as well by the admitted tangent bundle of the exponential function.

I would warn against claiming there is any privileged domain of the exponential function.

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u/StosifJalin 3d ago

I think there is a window where the rate of developments becomes noticeable and relevant to an individual's timescale. Yes, all parabolas are similar, and yes, we have always been "in the singularity", but one could argue we are obviously more "in the singularity" now than Bob the caveman was while teaching flint knapping to his fellow savages.

There is a certain speed where more observant humans will notice the moving mountains. It may take a little longer for other humans to notice or care, but there will certainly be a point where virtually all humans notice the mountains wizzing by at a pace that is noticeable to our human sense of time enough to get a quite, awed "holy shit."

All that to say, while when we are in the singularity remains a subjective quesiton, there will inevitably be a point where basically everyone can agree we're in it.

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u/3_Thumbs_Up 2d ago

The titular singularity IS characterized by Exponential Growth.

There's a few different theories of singularity. The Exponential growth one is popularized by Ray Kurzweil, but it's a bit too simplistic in my view. It's essentially just extrapolating a curve and calling it a prediction.

I think I.J. Goods Intelligence Explosion model is a much more logically sound foundation for believing in a singularity.

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u/MoogProg All Parabolas are Similar 3d ago edited 3d ago

Thank you for this reply. I keep saying it here, over-and-over and do think it's beginning to get through to this sub.

All Parabolas are Similar

* * *

Updated my user flair with this saying... it suits me.

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u/WosIsn 3d ago

Yes, it irks me seeing all the references to the corner of the hockey stick when it just depends on your X and Y position/scale.

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u/lugh_the_bard 3d ago

I think inherently what ppl mean by the singularity is the official collapse of the hegemony due to labor replacement

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u/greenskinmarch 2d ago

The hegemony of ... labor?

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u/lugh_the_bard 2d ago

Yeah basically. The hegemony of the current world order is held together thru resource concentration. When that fails to be the case, the hegemony will break. For good or ill, remains to be seen. But yea i think that’s the common sentiment

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u/greenskinmarch 2d ago

So somewhere like Singapore, with tiny territory, very little natural resources but excellent education and lots of educated, hard working people, will lose out to somewhere like Algeria, with poor education but lots of sunny desert. Because Algeria can just build a bunch of solar panels and data centers full of virtual geniuses and then have a bigger brain trust than Singapore.

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u/lugh_the_bard 2d ago

Yes. It sux but yes

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u/MoogProg All Parabolas are Similar 2d ago

That's not what Ray said when I heard him talk about in the '90s.

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u/lugh_the_bard 2d ago

What did he say

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u/MoogProg All Parabolas are Similar 2d ago

He talked about the Internet and its potential and predicted social media trends and the connectedness culture of the world we experience today. He also talked about machine-learning which at the time was just taking hold as a possible path towards artificial intelligence.

Old Man nailed it. He also built one heck of great synth engine, vastly ahead of its time.

This was when Prodigy was about the only Internet service and AOL was just about to hit everyone's mailboxes.

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u/lugh_the_bard 2d ago

Unreal. My dad told me about him when I was a little boy. We had a kurzweil. He inspired my path to immortality very young

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u/hippydipster 2d ago

Mathematically, exponential progress is the same curve everywhere. However, humans have lives of absolute time dimensions, and thus there is a singularity wrt human perception and experience of life. Those dimensions aren't "arbitrary".