3 ms·

Yes, this remind me what one of my teachers used to say: hardware is what you kick when the software does not work. I don't believe that our solution space is

Yes, this remind me what one of my teachers used to say: hardware is what you kick when the software does not work. I don't believe that our solution space is limited by the hardware we run it on because our solution can be intended to run in different hardware, and when its adecuate enought it should produce the same results. Lets take math as an example. Lets say the axiom a + b = b + a We know that the expression is true in its essence, regardless the alphabet that we used to expressed. One can argue that ths expression does not makes sense to a chinesse personon because the chinesse alphabet does not have the letters 'a' or 'b'. But we know that if we use valid chinesse letters, then the concept is still true. You see? Is the concept that we express what remains valid, not the symbols that we use to express them. And this allows us to talk about commuting regardless of the language. The symbols are used to communicate an idea that is beyond the meaning of the particular symbol Same thing with software. Software development is not about the computer that it runs on anymore than astronomy is not about a particular telescope. Thus we need to separate the software solution from its implementation environment. The software is not bound by the architecture, a particular implementation is bounded by the hardware architecture and the ability to think out of the box of the developer; but the software it self it isn't (which is why we can do things like calculate the big O, which is hardware independent) Like in math, a particular implementation is just one way to express that software on that hardware using a particular programming language. For a different hardware (chinesse) you will use a different implementation for the same software concept. I cannot address how or why is the logical conclusion for you, but I can tell that it is not for me.

csense 14y ago
The principle you're trying to articulate is the Church-Turing thesis [1]: Every reasonable definition of computation can compute the same set of functions. [2] [3] [1] http://en.wikipedia.org/wiki/Church-Turing_thesis http://en.wikipedia.org/wiki/Church-Turing_thesis [2] Quantum computing may change the O() of some functions. I.e. maybe some O(n^2) problems become O(n) with a quantum computer, or NP problems become P; I'm not familiar enough with quantum computation to know for sure which classes are known to be reduced to smaller classes. But in principle you can always simulate a quantum computer on a classical computer given enough time -- of course, in practice "enough time" may be many orders of magnitude out of the realm of possibility. So quantum computation isn't a "new" form of computation as far as the Church-Turing thesis is concerned. [3] There are purely theoretical machines called "oracle machines" -- exactly like a regular computer/Turing machine, but equipped with a (theoretical) hardware device called an "oracle" which is able to solve some problem that is known to be impossible for Turing machines, like the halting problem [4]. An oracle machine can be more powerful than a Turing machine, but its violation of the Church-Turing hypothesis is sort of a technicality. Saying "Build magic hardware that does something a Turing machine can't, and attach it to a computer" is too vague about how the non-Turing computation is to be achieved to really constitute a fair definition of non-Turing computation. [4] http://en.wikipedia.org/wiki/Halting_problem http://en.wikipedia.org/wiki/Halting_problem
- jorgeleo 14y ago
  Cool! Thank you for the links, I didn't know that it had a name, mine were just mere observation. To me it stand to logic that different hardware has different capabilities, and if an implementation can use these characteristics then the implementation can have a different O. But my point still remains that as a theorical concept, the O does not depends of the hardware in the sense that it is not a necessary piece of information to make the calculation of O. Also i would like to point that in my original definition the math paint has a purpose of utility for society. To build magic hardware would be like telling Picasso here is infinite canvas and infinite degree of colors, what can you do with them? The magic is not in the resources or the tools, the magic is in thinking independent of those tools, and then using the tools to implement. I understand that people might come from the other end of the spectrum and think that we need to begin with the tools, i just don't share that view, and it has worked for me just fine.

csense 14y ago

The principle you're trying to articulate is the Church-Turing thesis [1]: Every reasonable definition of computation can compute the same set of functions. [2] [3] [1] http://en.wikipedia.org/wiki/Church-Turing_thesis http://en.wikipedia.org/wiki/Church-Turing_thesis [2] Quantum computing may change the O() of some functions. I.e. maybe some O(n^2) problems become O(n) with a quantum computer, or NP problems become P; I'm not familiar enough with quantum computation to know for sure which classes are known to be reduced to smaller classes. But in principle you can always simulate a quantum computer on a classical computer given enough time -- of course, in practice "enough time" may be many orders of magnitude out of the realm of possibility. So quantum computation isn't a "new" form of computation as far as the Church-Turing thesis is concerned. [3] There are purely theoretical machines called "oracle machines" -- exactly like a regular computer/Turing machine, but equipped with a (theoretical) hardware device called an "oracle" which is able to solve some problem that is known to be impossible for Turing machines, like the halting problem [4]. An oracle machine can be more powerful than a Turing machine, but its violation of the Church-Turing hypothesis is sort of a technicality. Saying "Build magic hardware that does something a Turing machine can't, and attach it to a computer" is too vague about how the non-Turing computation is to be achieved to really constitute a fair definition of non-Turing computation. [4] http://en.wikipedia.org/wiki/Halting_problem http://en.wikipedia.org/wiki/Halting_problem

jorgeleo 14y ago
Cool! Thank you for the links, I didn't know that it had a name, mine were just mere observation. To me it stand to logic that different hardware has different capabilities, and if an implementation can use these characteristics then the implementation can have a different O. But my point still remains that as a theorical concept, the O does not depends of the hardware in the sense that it is not a necessary piece of information to make the calculation of O. Also i would like to point that in my original definition the math paint has a purpose of utility for society. To build magic hardware would be like telling Picasso here is infinite canvas and infinite degree of colors, what can you do with them? The magic is not in the resources or the tools, the magic is in thinking independent of those tools, and then using the tools to implement. I understand that people might come from the other end of the spectrum and think that we need to begin with the tools, i just don't share that view, and it has worked for me just fine.