I am of the belief that we will experience a Technological Singularity around 2050 or shortly thereafter. Many top futurists all arrive at prediction dates between 2045 and 2075. The bulk of Singularity debate revolves not so much around 'if' or even 'when', but rather 'what' the Singularity will appear like, and whether it will be positive or negative for humanity.

To be clear, some singularities have already happened.  To non-human creatures, a technological singularity that overhauls their ecosystem already happened over the course of the 20th century.  Domestic dogs and cats are immersed in a singularity where most of their surroundings surpass their comprehension.  Even many humans have experienced a singularity - elderly people in poorer nations make no use of any of the major technologies of the last 20 years, except possibly the cellular phone.  However, the Singularity that I am talking about has to be one that affects all humans, and the entire global economy, rather that just humans that are marginal participants in the economy.  By definition, the real Technological Singularity has to be a 'disruption in the fabric of humanity'. 

In the period between 2008 and 2050, there are several milestones one can watch for in order to see if the path to a possibile Singularity is still being followed.  Each of these signifies a previously scarce resource becoming almost infinitely abundant (much like paper today, which was a rare and precious treasure centuries ago), or a dramatic expansion in human experience (such as the telephone, airplane, and Internet have been) to the extent that it can even be called a transhuman experience.  The following are a random selection of milestones with their anticipated dates. 

Technological :

Hours spent in videoconferencing surpass hours spent in air travel/airports : 2015

Video games with interactive, human-level AI : 2018

Semi-realistic fully immersive virtual reality : 2020

Over 5 billion people connected to the Internet (mostly wirelessly) at speeds greater than 10 Mbps : 2022

Over 30 network-connected devices in the average household worldwide : 2025

1 TeraFLOPS of computing power costs $1 : 2026

1 TeraWatt of worldwide photovoltaic power capacity : 2027

1 Petabyte of storage costs $1 : 2028

1 Terabyte of RAM costs $1 : 2031

An artificial intelligence can pass the Turing Test : 2040

Biological :

Complete personal genome sequencing costs $1000 : 2020

Cancer is no longer one of the top 5 causes of death : 2025

Complete personal genome sequencing costs $10 : 2030

Human life expectancy achieves Actuarial Escape Velocity for wealthy individuals : 50% chance by 2040

Economic :

Average US household net worth crosses $2 million in nominal dollars : 2024

90% of humans living in nations with a UN Human Development Index greater than 0.800 (the 2008 definition of a 'developed country', approximately that of the US in 1960) : 2025

10,000 billionaires worldwide (nominal dollars) : 2030

World GDP per Capita crosses $50,000 in 2008 dollars : 2045

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Each of these milestones, while not causing a Singularity by themselves, increase the probability of a true Technological Singularity, with the event horizon pulled in closer to that date.  Or, the path taken to each of these milestones may give rise to new questions and metrics altogether.  We must watch for each of these events, and update our predictions for the 'when' and 'what' of the Singularity accordingly. 

Related : The Top 10 Transhumanist Technologies