I'm in the "there won't ever be a singularity" camp, a prime example being the human brain, Hugo De Garis calculates using the rate of neuron fireing, number of neurons and number of synapses each neuron is capable of forming, this gives a very large number (unsuprisingly). If his calculations are correct for the speed of the human brain, then we should get there in 20 years or so, but at its base, his calculation runs off only three variables, which for the "most complex structure in the known universe" seems a little dubious.
Memory formation and storage require long-lasting changes in memory-related neuronal circuits. Recent evidence indicates that DNA methylation may serve as a contributing mechanism in memory formation and storage. These emerging findings suggest a role for an epigenetic mechanism in learning and long-term memory maintenance and raise apparent conundrums and questions. For example, it is unclear how DNA methylation might be reversed during the formation of a memory, how changes in DNA methylation alter neuronal function to promote memory formation, and how DNA methylation patterns differ between neuronal structures to enable both consolidation and storage of memories. Here we evaluate the existing evidence supporting a role for DNA methylation in memory, discuss how DNA methylation may affect genetic and neuronal function to contribute to behavior, propose several future directions for the emerging subfield of neuroepigenetics, and begin to address some of the broader implications of this work.
Right there is proof that memory function and storage is far more complex than many anticipated (and certainly Hugo de Garis), so now we have to factor in epigenetic reading and writing processes into the storage of memory.
According to Garis:
Number of neurons=100 billion (1011)
Number of possible synapses per neuron=10,000 (104)
Number of action potentials (fireings) per second=101s-1
Hugo de Gariss calulation for speed of the human brain= 1011 X 104 X 101 =1016 bits per second
Amount of base pairs in human DNA per cell= 6 billion (of which 98% of it is believed to be "non-coding")=~ 6x109 bp
Amount of base pairs in human brain = 6x109 X 1011 =6x1020 bits can be stored at any one time
This is also assuming that only methylation can encode memory, which my hunch is would not be the case.
How this would affect the "RAM" i have no idea, that's question for mathematicians, and neurologists.