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Use these computers not for the mundane tasks of today. Use them to provide alerts well in advance for natural disasters. I am sure the insurance companies will be able to support research and developement expenses. No need to use such powers for applications. My opinion.
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...I could finally win at World of WarCraft?
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It would be smarter to not make the future super computers to be backwardly compatible. It would be better to write the applications fresh than to attempt to upgrade an existing application built for a computer with a few cores.

This super computer looks like a solution for a problem we don't have, yet. It sounds like it would be best to model complicated systems like weather to improve weather forecasting. Using such a super computer to figure your check book balance or play video games could be fun but a waste of computational power, even most business needs would use less power than what this super computer is expected to handle.
but making computers backwards compatible is the reason why we are stuck with such trash personal computer systems, and every time microsoft tries to ditch outdated tech some idiots complain about not being able to use a 15 year old reporting application, because they like the graphical interface it offers better than current offerings they looked at. Not because of what it can do or how it does it. Everyone complains about MS making bloatware, but they only do it so there is enough backwards compatibility to keep enough of the people happy. (not that I often praise Apple, but...) Apple has it right by only supporting certain models when they release a new OS version, you have to ditch the crap if you want to progress to anything better. If we are lucky the next major OS releases from Apple and Microsoft will no longer come in 32 bit versions, considering a 32bit exclusive x86 CPU has not been manufactured for personal computers in the last 10 years.

Hopefully they will use such systems to help us design more efficient methods of doing the things we do today. No doubt someone will use one to "map the universe", I am sure they will be used to compute the math required to get a human to mars and back safely, in addition to predicting the survival rate of such a trip and able to recompute it with slight modifications in various conditions and time of year and planetary alignment.

I also expect them to be used to combat hackers

I would not be surprised at all if they are used to develop more efficient CPUs so that we can build bigger and better computers that can take over the world and remove the infestation known as humanity... yes I watch too many movies, but the real McCoy is in the books.
Back in 1985-6, Acorn computers had a problem - improving performance versus backward compatibility. They had to move on from their existing 6502 8-bit processor based computer (the BBC Micro) but they weren't willing to compromise on ANY of the properties of the 6502 when moving to a 16/32-bit processor. Both the Intel 8086 and the Motorola 68000 had inferior interrupt latency to the 6502 and neither was software compatible. Acorn made a brilliant decision - design their own processor and so ARM was born. It was totally non-backward-compatible with anything BUT it was so fast that it could run software emulations of processors such as the 6502 so fast that 6502 software ran at least as fast on the ARM emulation as on an original 6502.
This is the approach that any computer designer should take - forget hardware backward compatibilty and all the legacy overheads that it entails; go for speed and software emulation if backward compatibility is needed - it works, and you only have to look at the success of the ARM to see that such decisions can bring major success.
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The BIG problem with software is bugs and how to find them before the software is released. The more complex the software, the greater the chance of undetected bugs and the greater the difficulty in debugging. So the question arises - how do we exploit multi-processor systems yet keep the software simple? The obvious answer is SIMD - Single Instruction, Multiple Data - where the same program runs in every core but on different data. This way the processors can be simple which means that, for a given die size, there can be more in-core RAM. Such a system maps very well onto problems such as Air Traffic Control or Meteorology where vast quantities of data need the same work doing on each chunk of data. I worked on a simulation of an SIMD array processor with over 1000 cores back in 1985 where I looked into the operation of various standard algorithms (such as Fast Fourier Transform, Convolution, the Viterbi Algorithm - to name those I remember) on such an array. Unfortunately the company concerned, Anamartic, didn't survive to expoit the array processor but the potential was fascinating.
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