An idea? Okay: Setup a software as a service Web site to solve quickly all traveling salesman problems with fewer than, say, 1 million cities, and everything equivalent in computational complexity to them.
First difficulty: To write the server side software, basically are asking for an algorithm that shows that P = NP, and now we have had some decades to conclude that so far no one knows how to do that (with a von Neumann computer, but maybe could get a solution using a quantum computer).
Well, for positive integer n <= 1 million, consider the traveling salesman problem on n cities. Without loss of generality, assume that n is a prime number (with factors only 1 and n). Then embed this problem in ..., and notice that ..., and then apply ..., exploiting special case ...! Right!!!
Lesson 1: This idea was super easy to find!
Lesson 2: What it takes to make this idea work is something new, and, if we get a solution, that would contradict the observation that there are no good new ideas because all the good ideas were thought of long ago.
Lesson 3: Finding an algorithm that shows that P = NP is challenging, but with that algorithm would have one heck of a strong technological barrier to entry and a contradiction to the claim that it is easy to copy a startup!
My real point: Have two lists. List A has the problems that plenty of people would pay big bucks to have solved. List B has the tools for solving problems. Pick a pair from lists A and B where the tool from B solves the problem from A.
Next, if there is no suitable tool in list B, then do some research and find one. If can't find a tool for the problem from A, then pick another problem from A and try again to do the research to find the needed tool.
The research need not be as challenging as proving that P = NP. But broadly one way to find "good ideas" is do some research that yields a tool that enables solving a problem from list A that has been sitting there for a long time unsolved due to the lack of a suitable tool from list B.
That is, one way to find a "good idea" is to do some research.
If we are restricting to having von Neumann computers do the data manipulations, then we can notice that the manipulations are necessarily mathematically something so that an enabling tool and the research are about forced to be in applied math.
It might also be sufficient to use some of the math on the shelves of the research libraries, math that so far has been neglected by the information startup culture.
Possible psychological issue: It may be that we frequently see good problems to solve but right away, within a few seconds, implicitly, maybe even unconsciously, reject solving the problem as a startup idea because we don't see a suitable tool for a solution. Well, then, slow down a little on the rejection step and consider some research or just what is already in the research libraries. Uh, there's a lot in the research libraries!
An idea? Okay: Setup a software as a service Web site to solve quickly all traveling salesman problems with fewer than, say, 1 million cities, and everything equivalent in computational complexity to them.
First difficulty: To write the server side software, basically are asking for an algorithm that shows that P = NP, and now we have had some decades to conclude that so far no one knows how to do that (with a von Neumann computer, but maybe could get a solution using a quantum computer).
Well, for positive integer n <= 1 million, consider the traveling salesman problem on n cities. Without loss of generality, assume that n is a prime number (with factors only 1 and n). Then embed this problem in ..., and notice that ..., and then apply ..., exploiting special case ...! Right!!!
Lesson 1: This idea was super easy to find!
Lesson 2: What it takes to make this idea work is something new, and, if we get a solution, that would contradict the observation that there are no good new ideas because all the good ideas were thought of long ago.
Lesson 3: Finding an algorithm that shows that P = NP is challenging, but with that algorithm would have one heck of a strong technological barrier to entry and a contradiction to the claim that it is easy to copy a startup!
My real point: Have two lists. List A has the problems that plenty of people would pay big bucks to have solved. List B has the tools for solving problems. Pick a pair from lists A and B where the tool from B solves the problem from A.
Next, if there is no suitable tool in list B, then do some research and find one. If can't find a tool for the problem from A, then pick another problem from A and try again to do the research to find the needed tool.
The research need not be as challenging as proving that P = NP. But broadly one way to find "good ideas" is do some research that yields a tool that enables solving a problem from list A that has been sitting there for a long time unsolved due to the lack of a suitable tool from list B.
That is, one way to find a "good idea" is to do some research.
If we are restricting to having von Neumann computers do the data manipulations, then we can notice that the manipulations are necessarily mathematically something so that an enabling tool and the research are about forced to be in applied math.
It might also be sufficient to use some of the math on the shelves of the research libraries, math that so far has been neglected by the information startup culture.
Possible psychological issue: It may be that we frequently see good problems to solve but right away, within a few seconds, implicitly, maybe even unconsciously, reject solving the problem as a startup idea because we don't see a suitable tool for a solution. Well, then, slow down a little on the rejection step and consider some research or just what is already in the research libraries. Uh, there's a lot in the research libraries!