Category Archives: Singularity

In the world of artificial intelligence, the idea of singularity looms large. This slippery concept describes the moment AI exceeds beyond human control and rapidly transforms society. The tricky thing about AI singularity (and why it borrows terminology from black hole physics) is that its enormously difficult to predict where it begins and nearly impossible to know whats beyond this technological event horizon.

However, some AI researchers are on the hunt for signs of reaching singularity measured by AI progress approaching the skills and ability comparable to a human. One such metric, defined by Translated, a Rome-based translation company, is an AIs ability to translate speech at the accuracy of a human. Language is one of the most difficult AI challenges, but a computer that could close that gap could theoretically show signs of Artificial General Intelligence (AGI).

Thats because language is the most natural thing for humans, Translated CEO Marco Trombetti said at a conference in Orlando, Florida, in December. Nonetheless, the data Translated collected clearly shows that machines are not that far from closing the gap.

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The company tracked its AIs performance from 2014 to 2022 using a metric called Time to Edit, or TTE, which calculates the time it takes for professional human editors to fix AI-generated translations compared to human ones. Over that 8-year period and analyzing over 2 billion post-edits, Translateds AI showed a slow, but undeniable improvement as it slowly closed the gap toward human-level translation quality.

Translated

On average, it takes a human translator roughly one second to edit each word of another human translator, according to Translated. In 2015, it took professional editors approximately 3.5 seconds per word to check a machine-translated (MT) suggestion today that number is just 2 seconds. If the trend continues, Translateds AI will be as good as human-produced translation by the end of the decade (or even sooner).

The change is so small that every single day you dont perceive it, but when you see progress across 10 years, that is impressive, Trombetti said on a podcast in December. This is the first time ever that someone in the field of artificial intelligence did a prediction of the speed to singularity.

Although this is a novel approach to quantifying how close humanity is to approaching singularity, this definition of singularity runs into similar problems of identifying AGI more broadly. Although perfecting human speech is certainly a frontier in AI research, the impressive skill doesnt necessarily make a machine intelligent (not to mention how many researchers dont even agree on what intelligence is).

Whether these hyper-accurate translators are harbingers of our technological doom or not, that doesnt lessen Translateds AI accomplishment. An AI capable of translating speech as well as a human could very well change society, even if the true technological singularity remains ever elusive.

Darren lives in Portland, has a cat, and writes/edits about sci-fi and how our world works. You can find his previous stuff at Gizmodo and Paste if you look hard enough.

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Singularity: Here's When Humanity Will Reach It, New Data Shows

sentinelOne expands singularity marketplace with new SOAR, insider threat, training, and prioritization integrations  ZAWYA

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sentinelOne expands singularity marketplace with new SOAR, insider threat, training, and prioritization integrations - ZAWYA

Biological? Post-biological? Something in between? What is humanity's future?

In a new paper published in The International Journal of Astrobiology, Joseph Gale from The Hebrew University of Jerusalem and co-authors make the point that recent advances in artificial intelligence (AI)particularly in pattern recognition and self-learningwill likely result in a paradigm shift in the search for extraterrestrial intelligent life.

While futurist Ray Kurzweil predicted 15 years ago that the singularitythe time when the abilities of a computer overtake the abilities of the human brainwill occur in about 2045, Gale and his co-authors believe this event may be much more imminent, especially with the advent of quantum computing. Its already been four years since the program AlphaGO, fortified with neural networks and learning modes, defeated Lee Sedol, the Go world champion. The strategy game StarCraft II may be the next to have a machine as reigning champion.

If we look at the calculating capacity of computers and compare it to the number of neurons in the human brain, the singularity could be reached as soon as the early 2020s. However, a human brain is wired differently than a computer, and that may be the reason why certain tasks that are simple for us are still quite challenging for todays AI. Also, the size of the brain or the number of neurons dont equate to intelligence. For example, whales and elephants have more than double the number of neurons in their brain, but are not more intelligent than humans.

The authors dont know when the singularity will come, but come it will. When this occurs, the end of the human race might very well be upon us, they say, citing a 2014 prediction by the late Stephen Hawking. According to Kurzweil, humans may then be fully replaced by AI, or by some hybrid of humans and machines.

What will this mean for astrobiology? Not much, if were searching only for microbial extraterrestrial life. But it might have a drastic impact on the search for extraterrestrial intelligent life (SETI). If other civilizations are similar to ours but older, we would expect that they already moved beyond the singularity. So they wouldnt necessarily be located on a planet in the so-called habitable zone. As the authors point out, such civilizations might prefer locations with little electronic noise in a dry and cold environment, perhaps in space, where they could use superconductivity for computing and quantum entanglement as a means of communication.

We are just beginning to understand quantum entanglement, and it is not yet clear whether it can be used to transfer information. If it can, however, that might explain the apparent lack of evidence for extraterrestrial intelligent civilizations. Why would they use primitive radio waves to send messages?

I think it also is still unclear whether there is something special enough about the human brains ability to process information that casts doubt on whether AI can surpass our abilities in all relevant areas, especially in achieving consciousness. Might there be something unique to biological brains after millions and millions of years of evolution that computers cannot achieve? If not, the authors are correct that reaching the singularity could be humanitys greatest and last advance.

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Reaching the Singularity May be Humanitys Greatest and Last ...

Supercomputers to Superintelligence

Heres an experiment that fits all ages: approach your mother and father (if theyre asleep, use caution). Ask them gently about that time before you were born, and whether they dared think at that time that one day everybody will post and share their images on a social network called Facebook. Or that they will receive answers to every question from a mysterious entity called Google. Or enjoy the services of a digital adviser called Waze that guides you everywhere on the road. If they say they figured all of the above will happen, kindly refer those people to me. Were always in need of good futurists.

The truth is that very few thought, in those olden days of yore, that technologies like supercomputers, wireless network or artificial intelligence will make their way to the general public in the future. Even those who figured that these technologies will become cheaper and more widespread, failed in imagining the uses they will be put to, and how they will change society. And here we are today, when youre posting your naked pictures on Facebook. Thanks again, technology.

History is full of cases in which a new and groundbreaking technology, or a collection of such technologies, completely changes peoples lives. The change is often so dramatic that people whove lived before the technological leap have a very hard time understanding how the subsequent generations think. To the people before the change, the new generation may as well be aliens in their way of thinking and seeing the world.

These kinds of dramatic shifts in thinking are called Singularity a phrase that is originally derived from mathematics and describes a point which we are incapable of deciphering its exact properties. Its that place where the equations basically go nuts and make no sense any longer.

The singularity has risen to fame in the last two decades largely because of two thinkers. The first is the scientist and science fiction writer Vernor Vinge, who wrote in 1993 that

Within thirty years, we will have the technological means to create superhuman intelligence. Shortly after, the human era will be ended.

The other prominent prophet of the Singularity is Ray Kurzweil. In his book The Singularity is Near, Kurzweil basically agrees with Vinge but believes the later has been too optimistic in his view of technological progress. Kurzweil believes that by the year 2045 we will experience the greatest technological singularity in the history of mankind: the kind that could, in just a few years, overturn the institutes and pillars of society and completely change the way we view ourselves as human beings. Just like Vinge, Kurzweil believes that well get to the Singularity by creating a super-human artificial intelligence (AI). An AI of that level could conceive of ideas that no human being has thought about in the past, and will invent technological tools that will be more sophisticated and advanced than anything we have today.

Since one of the roles of this AI would be to improve itself and perform better, it seems pretty obvious that once we have a super-intelligent AI, it will be able to create a better version of itself. And guess what the new generation of AI would then do? Thats right improve itself even further. This kind of a race would lead to an intelligence explosion and will leave old poor us simple, biological machines that we are far behind.

If this notion scares you, youre in good company. A few of the most widely regarded scientists, thinkers and inventors, like Steven Hawking and Elon Musk, have already expressed their concerns that super-intelligent AI could escape our control and move against us. Others focus on the great opportunities that such a singularity holds for us. They believe that a super-intelligent AI, if kept on a tight leash, could analyze and expose many of the wonders of the world for us. Einstein, after all, was a remarkable genius who has revolutionized our understanding of physics. Well, how would the world change if we enjoyed tens, hundreds and millions Einsteins that couldve analyzed every problem and find a solution for it?

Similarly, how would things look like if each of us could enjoy his very own Doctor House, that constantly analyzed his medical state and provided ongoing recommendations? And which new ideas and revelations would those super-intelligences come up with, when they go over humanitys history and holy books?

Already we see how AI is starting to change the ways in which we think about ourselves. The computer Deep Blue managed to beat Gary Kasparov in chess in 1997. Today, after nearly twenty years of further development, human chess masters can no longer beat on their own even an AI running on a laptop computer. But after his defeat, Kasparov has created a new kind of chess contests: ones in which humanoid and computerized players collaborate, and together reach greater successes and accomplishments than each wouldve gotten on their own. In this sort of a collaboration, the computer provides rapid computations of possible moves, and suggests several to the human player. Its human compatriot needs to pick the best option, to understand their opponents and to throw them off balance.

Together, the two create a centaur: a mythical creature that combines the best traits of two different species. We see, then that AI has already forced chess players to reconsider their humanity and their game.

In the next few decades we can expect a similar singularity to occur in many other games, professions and other fields that were previously conserved for human beings only. Some humans will struggle against the AI. Others will ignore it. Both these approaches will prove disastrous, since when the AI will become capable than human beings, both the strugglers and the ignorant will remain behind. Others will realize that the only way to success lies in collaboration with the computers. They will help computers learn and will direct their growth and learning. Those people will be the centaurs of the future. And this realization that man can no longer rely only on himself and his brain, but instead must collaborate and unite with sophisticated computers to beat tomorrows challenges well, isnt that a singularity all by itself?

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Singularity: Explain It to Me Like I'm 5-Years-Old - Futurism

SINGULARITY FUTURE TECHNOLOGY LTD. : Notice of Delisting or Failure to Satisfy a Continued Listing Rule or Standard; Transfer of Listing, Change in Directors or Principal Officers, Other Events, Financial Statements and Exhibits (form 8-K)  Marketscreener.com

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Apple co-founder Steve Wozniak on Artificial Intelligence: Not worried about The Singularity, well still be in control  MacDailyNews

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Apple co-founder Steve Wozniak on Artificial Intelligence: Not worried about The Singularity, well still be in control - MacDailyNews

Method for assigning values to certain improper integrals which would otherwise be undefined

In mathematics, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined.

Depending on the type of singularity in the integrand f, the Cauchy principal value is defined according to the following rules:

In some cases it is necessary to deal simultaneously with singularities both at a finite number b and at infinity. This is usually done by a limit of the form

Let C c ( R ) {displaystyle {C_{c}^{infty }}(mathbb {R} )} be the set of bump functions, i.e., the space of smooth functions with compact support on the real line R {displaystyle mathbb {R} } . Then the map

To prove the existence of the limit

Therefore, 0 1 u ( x ) u ( x ) x d x {displaystyle int _{0}^{1},{frac {u(x)-u(-x)}{x}},mathrm {d} x} exists and by applying the mean value theorem to u ( x ) u ( x ) , {displaystyle u(x)-u(-x),} we get:

And furthermore:

we note that the map

Note that the proof needs u {displaystyle u} merely to be continuously differentiable in a neighbourhood of 0 and x u {displaystyle x,u} to be bounded towards infinity. The principal value therefore is defined on even weaker assumptions such as u {displaystyle u} integrable with compact support and differentiable at 0.

The principal value is the inverse distribution of the function x {displaystyle x} and is almost the only distribution with this property:

In a broader sense, the principal value can be defined for a wide class of singular integral kernels on the Euclidean space R n {displaystyle mathbb {R} ^{n}} . If K {displaystyle K} has an isolated singularity at the origin, but is an otherwise "nice" function, then the principal-value distribution is defined on compactly supported smooth functions by

Consider the values of two limits:

This is the Cauchy principal value of the otherwise ill-defined expression

Also:

Similarly, we have

This is the principal value of the otherwise ill-defined expression

Different authors use different notations for the Cauchy principal value of a function f {displaystyle f} , among others:

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Cauchy principal value - Wikipedia

1. Singularity Future Technology Ltd. (SGLY) Stockholder Notice: Robbins LLP Reminds Investors of the Class Action Against Singularity Future Technology Ltd. f/k/a Sino-Global Shipping America Ltd.  GlobeNewswire
2. The Law Offices of Frank R. Cruz Announces the Filing of a Securities Class Action on Behalf of Singularity Future Technology Ltd. f/k/a Sino-Global Shipping America Ltd. (SGLY) Investors  Business Wire
3. Blockchain Supplier Singularity Hid CEO's Past Fraud, Suit Says  Bloomberg Law
4. Singularity Securities Fraud Class Action Lawsuit Pending: Contact Levi & Korsinsky Before February 7, 20  Benzinga
5. Lawsuit filed for Investors in shares of Singularity Future Technology Ltd. (NASDAQ: SGLY)  openPR
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Singularity Future Technology Ltd. (SGLY) Stockholder Notice: Robbins LLP Reminds Investors of the Class Action Against Singularity Future Technology...

1. ROSEN, A LEADING LAW FIRM, Encourages Singularity Future Technology Ltd. f/k/a Sino-Global Shipping America Ltd. Investors to Secure Counsel Before Important Deadline in First Filed Securities Class Action Initiated by the Firm - SGLY  PR Newswire
2. Singularity Investor Alert - EIN Presswire  EIN News
3. EQUITY ALERT: Rosen Law Firm Files Securities Class Action Lawsuit Against Singularity Future Technology Ltd. f/k/a Sino-Global Shipping America Ltd. SGLY  Business Wire
4. SHAREHOLDER ACTION ALERT: The Schall Law Firm Encourages Investors in Singularity Future Technology Ltd.  Benzinga
5. ROSEN, TOP RANKED INVESTOR COUNSEL, Encourages Singularity Future Technology Ltd. f/k/a Sino-Global Shipping America, Ltd. Investors to Inquire About Securities Class Action Investigation SGLY, SINO  GlobeNewswire
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ROSEN, A LEADING LAW FIRM, Encourages Singularity Future Technology Ltd. f/k/a Sino-Global Shipping America Ltd. Investors to Secure Counsel Before...

Point where a function, a curve or another mathematical object does not behave regularly

In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity.[1][2][3]

For example, the real function

has a singularity at x = 0 {displaystyle x=0} , where the numerical value of the function approaches {displaystyle pm infty } so the function is not defined. The absolute value function g ( x ) = | x | {displaystyle g(x)=|x|} also has a singularity at x = 0 {displaystyle x=0} , since it is not differentiable there.[4]

The algebraic curve defined by { ( x , y ) : y 3 x 2 = 0 } {displaystyle left{(x,y):y^{3}-x^{2}=0right}} in the ( x , y ) {displaystyle (x,y)} coordinate system has a singularity (called a cusp) at ( 0 , 0 ) {displaystyle (0,0)} . For singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry, see singularity theory.

In real analysis, singularities are either discontinuities, or discontinuities of the derivative (sometimes also discontinuities of higher order derivatives). There are four kinds of discontinuities: typeI, which has two subtypes, and typeII, which can also be divided into two subtypes (though usually is not).

To describe the way these two types of limits are being used, suppose that f ( x ) {displaystyle f(x)} is a function of a real argument x {displaystyle x} , and for any value of its argument, say c {displaystyle c} , then the left-handed limit, f ( c ) {displaystyle f(c^{-})} , and the right-handed limit, f ( c + ) {displaystyle f(c^{+})} , are defined by:

The value f ( c ) {displaystyle f(c^{-})} is the value that the function f ( x ) {displaystyle f(x)} tends towards as the value x {displaystyle x} approaches c {displaystyle c} from below, and the value f ( c + ) {displaystyle f(c^{+})} is the value that the function f ( x ) {displaystyle f(x)} tends towards as the value x {displaystyle x} approaches c {displaystyle c} from above, regardless of the actual value the function has at the point where x = c {displaystyle x=c} .

There are some functions for which these limits do not exist at all. For example, the function

does not tend towards anything as x {displaystyle x} approaches c = 0 {displaystyle c=0} . The limits in this case are not infinite, but rather undefined: there is no value that g ( x ) {displaystyle g(x)} settles in on. Borrowing from complex analysis, this is sometimes called an essential singularity.

The possible cases at a given value c {displaystyle c} for the argument are as follows.

In real analysis, a singularity or discontinuity is a property of a function alone. Any singularities that may exist in the derivative of a function are considered as belonging to the derivative, not to the original function.

A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which can be removed by choosing a different frame. An example of this is the apparent singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole (in the case of the example, jumping from longitude 0 to longitude 180 degrees). This discontinuity, however, is only apparent; it is an artifact of the coordinate system chosen, which is singular at the poles. A different coordinate system would eliminate the apparent discontinuity (e.g., by replacing the latitude/longitude representation with an n-vector representation).

In complex analysis, there are several classes of singularities. These include the isolated singularities, the nonisolated singularities and the branch points.

Suppose that f {displaystyle f} is a function that is complex differentiable in the complement of a point a {displaystyle a} in an open subset U {displaystyle U} of the complex numbers C . {displaystyle mathbb {C} .} Then:

Other than isolated singularities, complex functions of one variable may exhibit other singular behaviour. These are termed nonisolated singularities, of which there are two types:

Branch points are generally the result of a multi-valued function, such as z {displaystyle {sqrt {z}}} or log ( z ) {displaystyle log(z)} , which are defined within a certain limited domain so that the function can be made single-valued within the domain. The cut is a line or curve excluded from the domain to introduce a technical separation between discontinuous values of the function. When the cut is genuinely required, the function will have distinctly different values on each side of the branch cut. The shape of the branch cut is a matter of choice, even though it must connect two different branch points (such as z = 0 {displaystyle z=0} and z = {displaystyle z=infty } for log ( z ) {displaystyle log(z)} ) which are fixed in place.

A finite-time singularity occurs when one input variable is time, and an output variable increases towards infinity at a finite time. These are important in kinematics and PDEs infinites do not occur physically, but the behavior near the singularity is often of interest. Mathematically, the simplest finite-time singularities are power laws for various exponents of the form x , {displaystyle x^{-alpha },} of which the simplest is hyperbolic growth, where the exponent is (negative) 1: x 1 . {displaystyle x^{-1}.} More precisely, in order to get a singularity at positive time as time advances (so the output grows to infinity), one instead uses ( t 0 t ) {displaystyle (t_{0}-t)^{-alpha }} (using t for time, reversing direction to t {displaystyle -t} so that time increases to infinity, and shifting the singularity forward from 0 to a fixed time t 0 {displaystyle t_{0}} ).

An example would be the bouncing motion of an inelastic ball on a plane. If idealized motion is considered, in which the same fraction of kinetic energy is lost on each bounce, the frequency of bounces becomes infinite, as the ball comes to rest in a finite time. Other examples of finite-time singularities include the various forms of the Painlev paradox (for example, the tendency of a chalk to skip when dragged across a blackboard), and how the precession rate of a coin spun on a flat surface accelerates towards infinitebefore abruptly stopping (as studied using the Euler's Disk toy).

Hypothetical examples include Heinz von Foerster's facetious "Doomsday's equation" (simplistic models yield infinite human population in finite time).

In algebraic geometry, a singularity of an algebraic variety is a point of the variety where the tangent space may not be regularly defined. The simplest example of singularities are curves that cross themselves. But there are other types of singularities, like cusps. For example, the equation y2 x3 = 0 defines a curve that has a cusp at the origin x = y = 0. One could define the x-axis as a tangent at this point, but this definition can not be the same as the definition at other points. In fact, in this case, the x-axis is a "double tangent."

For affine and projective varieties, the singularities are the points where the Jacobian matrix has a rank which is lower than at other points of the variety.

An equivalent definition in terms of commutative algebra may be given, which extends to abstract varieties and schemes: A point is singular if the local ring at this point is not a regular local ring.

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Singularity (mathematics) - Wikipedia