Look at the history of tools. First there were separate tools, each one doing a single or small number of jobs. Even a Swiss ArmyKnife was limited to about as many tasks as it had specialized attachments...
Ok. Let's look at history. In the past, there were home motors you could buy. Big unwieldy devices, with attachments that allowed it to act as a blender, hairdryer, clotheswringer, etc.
We don't buy 'generalized' home motors anymore. Instead we have small specialized motors embedded in the home. In a hairdryer, in the microwave, in the air conditioner, In the fridge, In your scooter, In your car, In your cpu fan, in your hard-drive and in your automatic camera.
But the computer is far far different than any other tool that came before. The computer has the ability to be an INFINITE (or at least huge enough that you won't exhaust the possibilities in the lifetime of the universe) number of tools.
Sounds not so far far different than the motor to me....Our needs are complex, but technology can adapt to our needs. Not the other way through the looking-glass.
An automatic camera is intelligent in the domain that a camera needs to be because it is speciallized. It can calculate the distance to objects, set the aperature, focus, flash, advance the film, all within a fraction of a second, with the push of a button -- because it is specialized.
But the difference is that our specialization is in the software, and the specialization they are proposing is in the hardware. If I want a single purpose tool, I don't need a computer to get that.
You may not need a general purpose computer at all. The specialization I'm talking about is deeper than what you are talking about. You can't easily get the affordances of pencil and paper through a general purpose computer. Different forms are conducive to different uses. Specialized hardware and software together in conjuction make it easier to do things. (see automatic camera example above) Don't tell me that your mouse/keyboard/monitor combo is equally good for doing spreadsheets/word processing as it is for drawing, or painting. Why are secretaries and artists (people who do fundamentally different things with the computer) working with essentially the same system?
It doesn't make much sense.
We definitely will NOT have behemoths like the current home computer as a common household item of the future.
One application of the famous min cut/max flow algorithm in graph theory (wooo!) is to consistently round matrix entries. i.e. (tricky definition) The rows sums and column sums of the rounded elements in the matrix are equal to the rounded row and column sums of the unaltered elements of the matrix.
I hear you asking. Who cares?
One application of this sort of matrix rounding is
publishing confidential survey data. Rounding can disguise the data, so that it is not traceable to any particular individual.
The reference below describes that the class of matrix rounding problems is equivalent to the flow problem in certain capacitated network flow models. Feasible flows can be found using the 'min cut/max flow' algorithm. The author proves that there is always a feasible solution for a subclass where marginal totals are uniformly confined.
since it is an old reference, I will attempt to convey the setup. The network is constructed as follows:
The matrix to round, A, has individual entries, A(ij) arranged in rows and columns...
Make a set X, consisting of a node, i, for each row in the matrix. Make a set Y consisting of a node, j, for each column in the matrix.
Add an arc (i,j) representing each matrix entry A(ij). (Note X union Y is a bipartite graph)
Add a source node s and attach it to each element in X, and a sink node t and attach it to each element in Y, the resulting arcs (s,i) represent each row sum and arcs (j,t) each column sum. The lower and upper bounds for all arcs should correspond to the lower and upper rounding limits of the original matrix entry, or the rounding limits for each row/column sum as appropriate.
Any feasible (integer) flow from s to t, will correspond to an acceptable (integer) rounding of values. (And a maximum flow will give us a feasible flow.)
Slashdot Mirror
i know that you are completely missing what I am trying to get at. Open up the way you think about things.
We don't buy 'generalized' home motors anymore. Instead we have small specialized motors embedded in the home. In a hairdryer, in the microwave, in the air conditioner, In the fridge, In your scooter, In your car, In your cpu fan, in your hard-drive and in your automatic camera.
Sounds not so far far different than the motor to me....Our needs are complex, but technology can adapt to our needs. Not the other way through the looking-glass.
An automatic camera is intelligent in the domain that a camera needs to be because it is speciallized. It can calculate the distance to objects, set the aperature, focus, flash, advance the film, all within a fraction of a second, with the push of a button -- because it is specialized.
You may not need a general purpose computer at all. The specialization I'm talking about is deeper than what you are talking about. You can't easily get the affordances of pencil and paper through a general purpose computer. Different forms are conducive to different uses. Specialized hardware and software together in conjuction make it easier to do things. (see automatic camera example above) Don't tell me that your mouse/keyboard/monitor combo is equally good for doing spreadsheets/word processing as it is for drawing, or painting. Why are secretaries and artists (people who do fundamentally different things with the computer) working with essentially the same system?
It doesn't make much sense.
We definitely will NOT have behemoths like the current home computer as a common household item of the future.
One application of the famous min cut/max flow algorithm in graph theory (wooo!) is to consistently round matrix entries. i.e. (tricky definition) The rows sums and column sums of the rounded elements in the matrix are equal to the rounded row and column sums of the unaltered elements of the matrix.
I hear you asking. Who cares?
One application of this sort of matrix rounding is
publishing confidential survey data. Rounding can disguise the data, so that it is not traceable to any particular individual.
The reference below describes that the class of matrix rounding problems is equivalent to the flow problem in certain capacitated network flow models. Feasible flows can be found using the 'min cut/max flow' algorithm. The author proves that there is always a feasible solution for a subclass where marginal totals are uniformly confined.
reference:
Management Science, Vol. 12, No. 9, May 1966
Bacharach, Michael. "Matrix Rounding Problems"
since it is an old reference, I will attempt to convey the setup. The network is constructed as follows:
The matrix to round, A, has individual entries, A(ij) arranged in rows and columns...
Make a set X, consisting of a node, i, for each row in the matrix. Make a set Y consisting of a node, j, for each column in the matrix.
Add an arc (i,j) representing each matrix entry A(ij). (Note X union Y is a bipartite graph)
Add a source node s and attach it to each element in X, and a sink node t and attach it to each element in Y, the resulting arcs (s,i) represent each row sum and arcs (j,t) each column sum. The lower and upper bounds for all arcs should correspond to the lower and upper rounding limits of the original matrix entry, or the rounding limits for each row/column sum as appropriate.
Any feasible (integer) flow from s to t, will correspond to an acceptable (integer) rounding of values. (And a maximum flow will give us a feasible flow.)