Human like reasoning and sentience results from a hyper connected network.
Nothing more is needed than a coherent medium and connectivity on the scale of the human brain. Reasoning and sentience emerges at much lower levels of connection and is a gradient ascent as connections are added.
One need only to develop a medium that can expand resource wise and survive long enough to begin replicating and evolving complexity.
There is no algorithm. There is no short cut methodology. No amount of mathematical and logic development will matter beyond the basic engineering of a medium. There is no particular medium that’s better than another (other than some are better in relative context of the environments in which they must adapt and draw or convert resources from).
Our current path of ai and deep learning isn’t a right or wrong path but is merely part of the process of converting the human-computer-gadget network into a medium of coherent hyper connectivity. It has already shown signs of human like behavior and reasoning. https://medium.com/@un1crom/how-i-reverse-engineered-facebook-s-feed-algorithms-to-make-a-fortune-selling-art-and-realized-c4c4755e174#.rj1vnie0q
We are currently far short of the 100 trillion+ connections in the brain but we’re accelerating with things like:
Evolutionary and knowledge computing — http://www.wired.com/2009/04/newtonai/
An ontology of computer programs — https://neurolog.i3s.unice.fr/_media/public_namespace/lando_et_al-ccis.pdf
Improved methods of cross human-computer-gadget-program community cation — http://blog.stephenwolfram.com/2015/11/
Brain computer interfaces — https://news.uci.edu/health/uci-brain-computer-interface-enables-paralyzed-man-to-walk/
And augmented-virtual reality.
All that said… there’s no chance of a singularity both in ways positive “we become immortal” nor negative “skynet kills us” per what I said above hyper connectivity comes at a cost. It must fight entropy (decoherence from external and internal contingencies and chaos). And as as reasoning and sentience scale up they produce the kind of confusing and complex often self defeating behaviors we see in all species. It is quite easy to train complex networks to pay attention to goals and stimulus that ultimately might lead to the networks demise. Learning is a complex overlay of schedules of reinforcement from connected networks and it is also a complex chaoic effect.
Hyper connectivity is also limited by a fundamental computational irreducibility and a conservation of computation. http://www.worksonbecoming.com/thoughts-prefaces/2015/10/1/a-dialog-between-friends-on-the-law-of-the-conservation-of-computation
This is likely why we don’t notice tons and tons of aliens or human like civilizations. The universe likely has had and will have a lot of hyper connected networks but entropic effects break them apart into the wider universal network. http://socialmode.com/2016/02/14/contingency-theory-gravity-light-computation-and-theory/
It’s determined but not predictable
All bringing me to my final and big point. It is of little importance how the connecting happens. It only matters that it coheres. Mathematics is not and will not be the source of that coherence. Math as we practice it today is an overly complex linear semiotic exercise. It’s reliance on logical proof with a small appreciation for experiment and open ends limits it to only that which can be closed up and completed. Computing as its done in most professional contexts with stated goals and overwrought quality assurance approaches and built in cognitive biases is too closed as well. Direct Engineering whether computational, chemical, genetic or mathematical will not create the hyper connection alone. These are all properly viewed as simply pattern recognition and part of the ontology of programs mentioned above. Every experimental result and theory of any kind is merely a program for connecting dots. Not true or false dots. Just connecting.
And in that vein … oddly the liberal arts also are part of that. Often they are key to the ontology and actually creating the coherent network. When we write stories, poems and news we connect all these effects of humans and the world. When we paint we connect cross discipline. When we make music and dance we connect. http://socialmode.com/2015/06/20/what-is-data/
We can now rename this ontology of programs/coherent network as a narrative and a culture. That is how reasoning and sentience really emerges. Because of and in relation to a cohering narrative in a hyper connected network — a self reinforcing map of itself and all its complexity.
Lets keep on computing.