# Technological singularity, why would it NOT happen?

**URL:** <https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252>\
**Category:** Great Debates\
**Created:** [August 5, 2010, 11:56am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252 "2010-08-05T11:56:35Z")\
**Posts on this page:** 20\
**Page:** 2

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**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\
**Post date:** [August 5, 2010, 11:10pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/21 "2010-08-05T23:10:56Z")

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> [@Simplicio](#):
>
> True enough, but I think the scale of the effect is big enough that even with the lag time between initial conception and widespread implementation, its still pretty obvious that technological innovation has slowed. 1960 was a long time ago, stuff invented then has had a long time to percolate, I’m pretty skeptical that its just the slowness of the rate that stuff “catches on” that has made that decade and its successors seem less inventive then the previous century. Of course, maybe it just slowed for a couple decades, and the period 2000-2010 actually will turn out to have yielded a bunch of inventions that we don’t know are important yet. But in anycase, I think enough time has passed that I feel confident saying the pace of innovation was higher in the first half of the twentieth century then the second half, and that enough time has passed since 2000 that this isn’t just a selection effect due to the slowness of the importance of inventions being realized making more recent decades seem less technologically progressive.

You’re just too close to it. My grandfather was born in the early 1890s, and in 1960 he never much talked about being overwhelmed by changes. There were a few - airplanes, radio, TV, but his 1900 self wouldn’t have had that hard a time understanding the world his 1950 or even 1960 self went through.

My 1960 self would have had a lot harder time. Cars, planes and trains haven’t changed much. Lots of TV channels aren’t that big a difference, and I read Arthur C. Clarke, so satellite TV would have been fine. MP3 players and smartphones, on the other hand, would have blown my mind, and I read a lot of SF (though a bit after this.) We got GPS. We have people making calls from the top of Everest. We’ve got the research work I used to go to the library and spend hours on available in a few seconds. Count the results from your average Google search - we are throwing away information, it is so cheap. I bought my first car on my own in 1981. Buying a car today is totally different.

I’m watching Mad Men now. Except that they’d be selling ads on radio, not TV, their environment is not that different from 1950 and I can tell you it is not that technologically different from 1970. It is totally different today.

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**Author:** ![GIGObuster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gigobuster/32/421_2.png) [@GIGObuster](https://boards.straightdope.com/u/GIGObuster)\
**Post date:** [August 5, 2010, 11:27pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/22 "2010-08-05T23:27:27Z")

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> [@Simplicio](#):
>
> > [@GIGObuster](#):
> >
> > Seems to me that the OP is referring to the progress of technology, not much the development of newest forms of it. While technology is added to the definition, the focus is on the growth of it in relation to simulating or recreating human levels of intelligence.
> 
> But improving computation hasn’t led to an accelerated rate of technological development. We were advancing faster pre-computer, and then were doing better in the pre-transitor era of computation then we are now. Of course, maybe we will hit a point where computers do become enough such a boon that technological development takes off, but I’d say what historical evidence we have suggests that this isn’t the case.

Well, this seems to me that once again you are saying that \*\*new \*\*technologies need to appear to make the singularity possible, if I understood correctly that is not the point made by most proponents of the singularity. Their point is that the improvements made to current technologies are what is allowing them to make the extrapolation that it will be very likely that hard artificial intelligence will arrive as a result of the exponential improvement of the “current” technology.

Of course I have to add that “current” has caveats also because I do know that there are indeed new technologies (related to nanotechnology) that are making possible the progress made in computing power alone.

New theories on how human intelligence works are making possible to begin to make AIs that enable them to identify items that were never encountered before.

![](https://img.youtube.com/vi/P9ByGQGiVMg/maxresdefault.jpg)https://www.youtube.com/embed/P9ByGQGiVMg?feature=oembed&wmode=opaque

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**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\
**Post date:** [August 5, 2010, 11:50pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/23 "2010-08-05T23:50:35Z")

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I forgot the thing which I would consider the major difference in the world between the time I went to college in 1969 and when my youngest daughter did five years ago - the elimination of distance. When I went I called my parents once a week, made easier when we installed a bunch of illegal extension phones off one legal phone my junior year. Every so often we’d exchange letters. They knew very little of my life in college. My kids call and chat almost every day, on the way to class. When one was in Germany, we could chat for free on Skype and she could show me her room. My parents never saw my dorm room. When she had a problem with a graph in Excel, she could send me the file. When she was applying for various honors, we could proofread her essays. She is in constant contact with her friends from Germany, from college, and of course her friends from home when she was in college. She is going back to Germany next year, and was able to get an apartment on line, and see exactly how far it was from the school she is teaching at. She and my wife are going to Australia soon, and they get to keep their phone number and I can text them for almost no cost. In ten years it will be no cost. There used to be a thing called Long Distance - not any more.  
My daughter has a totally different attitude about distance and communication than I do. Still not a real singularity, though, but getting close.

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**Author:** ![Evil\_Captor](https://avatars.discourse-cdn.com/v4/letter/e/f17d59/32.png) [@Evil\_Captor](https://boards.straightdope.com/u/Evil_Captor)\
**Post date:** [August 5, 2010, 11:59pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/24 "2010-08-05T23:59:35Z")

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I think with all the concentration on medicine and aging as rich people continue to age and get sick, the medical place is where the singularity type stuff is beginning to hit. Things like MRI scanning of living bodies, the tricks they can do with hearts, not clumsy mechanical replacements, but things using optic fibers and lasers to see what’s happening inside the heart while it’s working and to clear out clogged arteries while the heart works … and that’s just the tip of the iceberg. Sooner or later stem cell research is gonna do miraculous things, it’s just a matter of time.

I personally will call the Singularity arrived when they have pills, nanotech, artificial virusoids, whatever, that will get rid of fat cells at will.

I’m not even sure hard AI is needed for the singularity, though it would be very nice. We seem to be getting closer to DNI every year … that might produce some STARTLING stuff …

And finally, we are gonna figure out some nifty tricks as the oil continues to run out. Already have, but you can be sure that even cooler stuff runs down the pike.

BTW, have you noticed how much longer lasting and brighter LED flashlights are than the old fashioned flashlights?

The Singularity is gonna creep up on us, and I think it IS creeping up on us … and that’s a good thing. When tech moves so fast not even hard core conservatives can do flip about it, I really think the world will be a better place.

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**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\
**Post date:** [August 6, 2010, 7:40am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/25 "2010-08-06T07:40:16Z")

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> [@GIGObuster](#):
>
> Well, this seems to me that once again you are saying that \*\*new \*\*technologies need to appear to make the singularity possible, if I understood correctly that is not the point made by most proponents of the singularity. Their point is that the improvements made to current technologies are what is allowing them to make the extrapolation that it will be very likely that hard artificial intelligence will arrive as a result of the exponential improvement of the “current” technology.

And maybe not. I was on a business trip when the 386 was released, and The USA Today said on its front page that this powerful 16 bit processor would give us AI real soon now.

> [@](#):
>
> Of course I have to add that “current” has caveats also because I do know that there are indeed new technologies (related to nanotechnology) that are making possible the progress made in computing power alone.

Which technologies are those? 28 nanometer is coming, but it isn’t all that very much different from the design point of view than previous nodes - it just requires some more interesting design rules and will no doubt have fascinating failure modes. MEMs are real nanotechnology, and are really cool, but don’t do much for computing power. The big new thing is 3D (nothing to do with Avatar) where you stack chips. That isn’t nanotech either.

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**Author:** ![Evil\_Captor](https://avatars.discourse-cdn.com/v4/letter/e/f17d59/32.png) [@Evil\_Captor](https://boards.straightdope.com/u/Evil_Captor)\
**Post date:** [August 6, 2010, 8:11am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/26 "2010-08-06T08:11:51Z")

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I’d say that when you have chip dimensions down to the level that [electron tunneling](http://computer.howstuffworks.com/nehalem-microprocessor-microarchitecture5.htm) is a problem, you’re doing nanotech whether you want to admit it or not.

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**Author:** ![Baboonanza](https://avatars.discourse-cdn.com/v4/letter/b/f475e1/32.png) [@Baboonanza](https://boards.straightdope.com/u/Baboonanza)\
**Post date:** [August 6, 2010, 9:34am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/27 "2010-08-06T09:34:25Z")

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> [@Oakminster](#):
>
> > [@Baboonanza](#):
> >
> > It’s possible that we may never be able to create a an artificial intelligence that’s smarter than we are for instance.
> 
> Nor should we. That rarely ends well, as any sci-fi fan can tell ya.

I diagree, I think we should always build to the limits of our capability. That’s what humans do, anything less is a diservice to ourselves.

And Science Fiction is just that, fiction.

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**Author:** ![Gukumatz](https://avatars.discourse-cdn.com/v4/letter/g/74df32/32.png) [@Gukumatz](https://boards.straightdope.com/u/Gukumatz)\
**Post date:** [August 6, 2010, 9:38am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/28 "2010-08-06T09:38:22Z")

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> [@Evil\_Captor](#):
>
> I’d say that when you have chip dimensions down to the level that [electron tunneling](http://computer.howstuffworks.com/nehalem-microprocessor-microarchitecture5.htm) is a problem, you’re doing nanotech whether you want to admit it or not.

Sweet damn, you’re right.

That level of physics just makes my head hurt.

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**Author:** ![Sitnam](https://avatars.discourse-cdn.com/v4/letter/s/6a8cbe/32.png) [@Sitnam](https://boards.straightdope.com/u/Sitnam)\
**Post date:** [August 6, 2010, 12:32pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/29 "2010-08-06T12:32:34Z")

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I love this part from the OP’s link:

> [@](#):
>
> …it might eventually be possible to build a machine that is more intelligent than humanity.[citation needed]

Breakthroughs take creativity and that’s something I don’t think can be outsourced.

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**Author:** ![Sablicious](https://avatars.discourse-cdn.com/v4/letter/s/bbce88/32.png) [@Sablicious](https://boards.straightdope.com/u/Sablicious)\
**Post date:** [August 6, 2010, 1:11pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/30 "2010-08-06T13:11:00Z")

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> [@](#):
>
> “_The term Technological Singularity reflects the idea that the change may happen suddenly, and that it is very difficult to predict how such a new world would operate. It is also unclear whether there would be any place for humans in a world containing very intelligent machines._”

[http://i33.tinypic.com/30w8pky.jpg](http://i33.tinypic.com/30w8pky.jpg)

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**Author:** ![Baboonanza](https://avatars.discourse-cdn.com/v4/letter/b/f475e1/32.png) [@Baboonanza](https://boards.straightdope.com/u/Baboonanza)\
**Post date:** [August 6, 2010, 1:13pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/31 "2010-08-06T13:13:06Z")

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> [@Sitnam](#):
>
> I love this part from the OP’s link:
> 
> > [@](#):
> >
> > …it might eventually be possible to build a machine that is more intelligent than humanity.[citation needed]
> 
> Breakthroughs take creativity and that’s something I don’t think can be outsourced.

Or found on Wikipedia 🙂

It’s a popular theme that machine intelligence would lack ‘human creativity’ but there isn’t any real reason for this assumption. At the moment creativity seems like magic because we don’t understand how it works, but there must be some reason for it. Perhaps it’s just a massively parallel hybrid pattern recognition / brute-froce problem solving algorithm, or it is an emergent system that occurs by itself in suffiently complex cognitive systems. Or whatever.

Or maybe (quite likely IMO) creativity is an innate feature of what we consider sentience, and without it something doesn’t really qualify.

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**Author:** ![Baboonanza](https://avatars.discourse-cdn.com/v4/letter/b/f475e1/32.png) [@Baboonanza](https://boards.straightdope.com/u/Baboonanza)\
**Post date:** [August 6, 2010, 1:16pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/32 "2010-08-06T13:16:29Z")

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> [@Sablicious](#):
>
> > [@](#):
> >
> > “_The term Technological Singularity reflects the idea that the change may happen suddenly, and that it is very difficult to predict how such a new world would operate. It is also unclear whether there would be any place for humans in a world containing very intelligent machines._”
> 
> [http://i33.tinypic.com/30w8pky.jpg](http://i33.tinypic.com/30w8pky.jpg)

Well one things for certain: If the AI take over they won’t plug us into a giant simulation so that they can harvest ‘bio-electrical energy’, despite having fusion technology.

Because that would be fucking retarded.

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**Author:** ![The\_Tao\_s\_Revenge](https://avatars.discourse-cdn.com/v4/letter/t/73ab20/32.png) [@The\_Tao\_s\_Revenge](https://boards.straightdope.com/u/The_Tao_s_Revenge)\
**Post date:** [August 6, 2010, 1:45pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/33 "2010-08-06T13:45:01Z")

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I think people are looking at the AI issue in a really weird way. No one is smart enough to build gigahertz cpu from scratch, yet we have them. A long time ago someone built a crappy computer out of vacuum tubes. Then eventually someone built one transistors, then ICs, then a lot of little of improvements over time, and now we have gigahertz cpus.

Humans didn’t spring from the ground like a seed, but we’re a refinement of a much dumber ape, which is a smarter version of a monkey, all way back to the ancestral slime critter.

I don’t see why AI is any different. We figure out how to build stupid AI, then we figure out how to make it a little smarter, and keep at it and eventually the Cosmic AC reverses entropy.

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**Author:** ![Sablicious](https://avatars.discourse-cdn.com/v4/letter/s/bbce88/32.png) [@Sablicious](https://boards.straightdope.com/u/Sablicious)\
**Post date:** [August 6, 2010, 2:02pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/34 "2010-08-06T14:02:01Z")

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> [@Baboonanza](#):
>
> > [@Sablicious](#):
> >
> > [http://i33.tinypic.com/30w8pky.jpg](http://i33.tinypic.com/30w8pky.jpg)
> 
> Well one things for certain: If the AI take over they won’t plug us into a giant simulation so that they can harvest ‘bio-electrical energy’, despite having fusion technology.
> 
> Because that would be fucking retarded.

I actually like the idea. It’s novel, the ‘jelly-goo pods’ look comfy and the fields look very homely! To boot, we can have ultra-vivid dreams where we’re supermen/women fashionistas!

😃

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**Author:** ![XT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/xt/32/456_2.png) [@XT](https://boards.straightdope.com/u/XT)\
**Post date:** [August 6, 2010, 3:27pm UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/35 "2010-08-06T15:27:56Z")

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Haven’t read through the whole thread, so it’s quite possible that all this has already been addressed:

[QUOTE=Simplicio]  
Write down the most important technological innovations since 1900.

Now go look up the dates these items were first invented.

Really, do it. Its a pretty good exercise and only takes a few minutes.  
[/QUOTE]

The trouble with this thinking is that the time between invention and maturation of a technology is generally fairly long. Write down the most important technological innovations prior to the 1900’s and you’ll find that many of them were invented centuries or even millennium before. Generally, however, it took a great deal of time to refine those technologies to the level that they became truly important game changers for humans. During the period between when the technologies were invented and their development humans didn’t just sit around doing nothing…the maturation of the technologies themselves spurred on technological development.

Take, for example, gun powder. One of the biggest game changing technologies and invented well over a thousand years ago. It took centuries of development and change before it became useful as a tool both on and off the battlefield. During that period, it was constantly (though fitfully) developed and refined, and through that process it sparked multiple other branches of technological development, which sparked others, etc etc.

Now, take something like the Air Plane. From invention to useful to mature took less than a hundred years (granted, we continue to refine the technology even today). The pace of technological development is speeding up.

Ok…take the internet. This time, the pace from invention to useful to mature tech is less than 2 decades (again, we continue to refine it). The point here is that the pace of innovation is speeding up, and, of course, that these inventions are sparking new innovation and technological development both in parallel and in new directions.

So, to answer the OP, why would we not reach a technological singularity? The only reason I can think of is that we manage to wipe ourselves out first. Resources? I don’t think that will be a particular problem, to be honest. There are plenty of untapped energy resources right here on earth, let alone in our solar system…practically unlimited resources in that direction, in fact. That we won’t be smart enough, somehow? I highly doubt it. I think that technology and innovation are converging with science to tackle some of the last really big mysteries out there, and while I don’t think we’ll ever know everything, or that the journey of discovery will ever be done, I think that we won’t hit some kind of metaphysical brick wall that we can’t get around (always assuming we don’t wipe each other out, or get wiped out by our planet or by a really big rock).

-XT

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**Author:** ![Sitnam](https://avatars.discourse-cdn.com/v4/letter/s/6a8cbe/32.png) [@Sitnam](https://boards.straightdope.com/u/Sitnam)\
**Post date:** [August 7, 2010, 12:24am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/36 "2010-08-07T00:24:16Z")

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> [@Baboonanza](#):
>
> It’s a popular theme that machine intelligence would lack ‘human creativity’ but there isn’t any real reason for this assumption. At the moment creativity seems like magic because we don’t understand how it works, but there must be some reason for it. Perhaps it’s just a massively parallel hybrid pattern recognition / brute-froce problem solving algorithm, or it is an emergent system that occurs by itself in suffiently complex cognitive systems. Or whatever.

Everything seems so simple once it’s been discovered, the ability to see what isn’t there but should be is ingenuity. I sincerely doubt, even if we can get a self aware robot, that it’ll have that spark.

I remember reading and understanding Newton’s Method in college and falling in love with the human brain. His solution is so fucking simple and yet elegant that it boggles the mind anyone else couldn’t have just come up with it. And yet no one else had.

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**Author:** ![GIGObuster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gigobuster/32/421_2.png) [@GIGObuster](https://boards.straightdope.com/u/GIGObuster)\
**Post date:** [August 7, 2010, 1:53am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/37 "2010-08-07T01:53:46Z")

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> [@Sitnam](#):
>
> Everything seems so simple once it’s been discovered, the ability to see what isn’t there but should be is ingenuity. I sincerely doubt, even if we can get a self aware robot, that it’ll have that spark.

Well. I did agree before because the scandalous thing was that until recently there were no good theories regarding how the brain, specially the human, worked. This has [changed recently](http://books.google.com/books?id=Qg2dmntfxmQC&printsec=frontcover&dq=brain+theory+Jeff+Hawkins&source=bl&ots=6hFoJ7MopW&sig=bLG6oYTZqXEwd6yso-F9V5KijIw&hl=en&ei=SLZcTLiECcH78Ab97-XaAg&sa=X&oi=book_result&ct=result&resnum=8&ved=0CDUQ6AEwBw#v=onepage&q=brain%20theory%20Jeff%20Hawkins&f=false) and  
if you check the link I posted early, it demonstrated an early prototype of AI using ideas and concepts from the new theories. IMHO there is a spark there, not very bright I grant that, but I think it is getting there.

> [@Sitnam](#):
>
> I remember reading and understanding Newton’s Method in college and falling in love with the human brain. His solution is so fucking simple and yet elegant that it boggles the mind anyone else couldn’t have just come up with it. And yet no one else had.

:dubious:

Not for the specific method, but if you are talking about calculus, Newton was one of the biggest assholes in history when he almost stole all the credit from [Leibniz](http://en.wikipedia.org/wiki/Leibniz_and_Newton_calculus_controversy) that \*\*also \*\*came up with calculus. (IIRC Historians give the glory to both Newton and Leibniz; however, Leibniz’s methods are more generally adopted in our textbooks today)

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**Author:** ![GIGObuster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gigobuster/32/421_2.png) [@GIGObuster](https://boards.straightdope.com/u/GIGObuster)\
**Post date:** [August 7, 2010, 2:20am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/38 "2010-08-07T02:20:04Z")

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> [@Voyager](#):
>
> And maybe not. I was on a business trip when the 386 was released, and The USA Today said on its front page that this powerful 16 bit processor would give us AI real soon now.

IMHO we have to assign that as example #100004, of mainstream media getting it wrong, I’m still waiting for the ice age that they reported coming in the 70’s, and yes, the media got it wrong then, most climate scientists then actually thought that global warming was coming. It would not surprise me to find that USA Today also misinterpreted what actual AI researchers thought about the state of the research in those days.

> [@Voyager](#):
>
> Which technologies are those? 28 nanometer is coming, but it isn’t all that very much different from the design point of view than previous nodes - it just requires some more interesting design rules and will no doubt have fascinating failure modes. MEMs are real nanotechnology, and are really cool, but don’t do much for computing power. The big new thing is 3D (nothing to do with Avatar) where you stack chips. That isn’t nanotech either.

What **Evil Captor** said.

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**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\
**Post date:** [August 7, 2010, 2:27am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/39 "2010-08-07T02:27:54Z")

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A long time ago in a thread about science fiction, I posted what I thought would be some paradigm-changing innovations, ones which would fundamentally alter the human condition:  
[ul]  
[li]if no one ever grew old or died of old age[/li][li]if fast easy matter replication made material wealth almost limitless[/li][li]if total automation made work unnecessary except for top-level design[/li][li]if humans could be engineered to any physical or mental specification desired.[/li][/ul]So I can’t speak to technological singularities, but any technologies that made the above possible would certainly spark a sociological singularity.

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [August 7, 2010, 2:36am UTC](https://boards.straightdope.com/t/technological-singularity-why-would-it-not-happen/549252/40 "2010-08-07T02:36:23Z")

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> [@](#):
>
> Everything seems so simple once it’s been discovered, the ability to see what isn’t there but should be is ingenuity. I sincerely doubt, even if we can get a self aware robot, that it’ll have that spark.
> 
> I remember reading and understanding Newton’s Method in college and falling in love with the human brain. His solution is so fucking simple and yet elegant that it boggles the mind anyone else couldn’t have just come up with it. And yet no one else had.

Some time ago, some researchers wrote a computer program that could come up with geometrical proofs, and set it to duplicating Euclid’s _Elements_. It went as expected at first, until it came to the so-called “Bridge of Fools”, the proof that the base angles of an isosceles triangle are equal. Euclid’s proof of this theorem is sufficiently complicated that it’s generally the first point where students of geometry get lost, and requires an extended diagram resembling a bridge, hence the “Bridge of Fools” title. The computer, however, instead came up with a simple, elegant proof that’s both significantly shorter, and requires nothing but the triangle itself for a diagram. If that’s not creativity, then it’s something just as good.

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