Mathematics has no Future?
Jack May
him that math is not powerful enough to solve difficult problems.
Below it the start of a New Scientist article which says that the systems we
are building are becoming so complex that there is no way to do any analysis
of why the work or how to solve their problems. Instead we have to develop
systems that figure out their own solutions.
Does this mean the future is going to be more evolution of technology to
find the things that survive in our increasingly complex world created by
people?
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Why complex systems do better without us
* 06 August 2008
* From New Scientist Print Edition.
* Mark Buchanan
WE HUMANS prefer the tidy to the untidy, the ordered to the disordered. We
like pristine geometrical regularity, and eschew what is erratic and
irregular. We want predictability and, more than anything, we want control.
In these confusing times, it might seem as if we have little power over
anything. Instead of letting it get us down, though, perhaps we should take
comfort from the work of Dirk Helbing, a physicist at the Swiss Federal
Institute of Technology (ETH) in Zurich. Helbing has been studying the
movement of tens of thousands of cars on road networks; the workings of vast
webs of interacting machines on factory floors; and other systems, where the
complexity of what happens and why routinely defeats the human mind.
What Helbing and others are finding is that our penchant for regularity and
control is seriously misguided. In many situations they are discovering that
it is better to give up some of our control and let systems find their own
solutions. Often the answers turn out to be unlike anything our minds would
imagine, yet the outcomes are far more efficient.
The findings come as something of a relief to today's engineers, who are
increasingly dealing with problems too complicated for them to solve. Take
one of the earliest successes chalked up by machines allowed to take
control.
Back in 1992, General Motors were having trouble managing the automated
painting of trucks at an assembly plant in Fort Wayne, Indiana. Machines in
10 different paint booths could paint trucks as they came off the line, but
because the trucks came off in an unpredictable order and the painting
machines needed sporadic maintenance and repair, finding an efficient
assignment of trucks to booths seemed impossible.
General Motors' visionary engineer Dick Morley suggested letting the
painting machines find a schedule themselves. He set out some simple rules
by which the various machines would "bid" for newly available paint jobs,
trying their best to stay busy while taking account of the need for
maintenance and so on. The results were remarkable, if a little weird. The
system saved General Motors more than $1 million each year in paint alone.
Yet the line ran to a schedule that no one could predict, made up on the fly
by the machines themselves as they responded to emerging needs.
"The production line ran on a schedule that no one could predict, yet saved
$1 million a year"
Production processes generally depend on so many inputs, parameters and
factors that even small changes in the set-up can lead to wildly different
and unpredictable consequences. That is why it is almost impossible to
predict what will happen in a new production line based on previous
experience. "Managers sometimes take performance in past set-ups and try to
estimate what will happen in a new setting by interpolation," says Helbing.
"This often gives very bad results."
eatfastnoodle
some sci-fi novels I read a few years ago postulated a human society
managed by a hugely complex system which is too complex to be
understood by any single or a group of individuals, however smart they
might be. People can only make limited modification, perform some day
to day maintenance, but human as a species are unable to change the
system in any significant way without entailing disruptive
consequences to human civilization. In essence, advance in science and
technology, social progress, even evolution stop due to inability to
change the system we human being rely upon.
PHPBABY3
> PHPBABY3 posted speculation on the future of mathematics. I explained to
> him that math is not powerful enough to solve difficult problems.
What does the scope of Mathematics have to do with examining how it
has been developed in the past and continuing that process to
anticipate the future? Nothing. Whether we are talking about Biology
or Physics or Mathematics - whatever domain of problems we wish to
discuss - we can examine how that branch of knowledge has been
developed and continue the process to create more of that knowledge,
regardless of the size or nature of the problems solved.
It is the process of developing Mathematics that I am talking about,
not what problems the principles of Mathematics solve.
You need to stop talking about what Mathematics is or is not good for,
and examine the issue that I am addressing: How is Mathematics
developed and how can we automate this process? Does my algorithm in
fact develop the Mathematics of the past and present? That is the
question.
You will need to address the algorithm that I propose in order to
answer that question, something that you have not done.
Charlie-Boo
PHPBABY3
Complex system are almost always simplified by structuring them into a
hierarchy where each level represents the lower levels without all of
the details, but with reference to the parts that are not given at
that level. Thus we can all say (and understand) "Godel proved that
there are Mathematical statements that are true but not provable."
while there are a thousand times as many words needed to describe the
lowest level of details many levels below.
Software development in particular is often done by multiple people,
each handling some part of the job. We can discuss and understand any
amount of detail we want. After all, each part has to be understood
to have been developed.
> People can only make limited modification, perform some day
> to day maintenance, but human as a species are unable to change the
> system in any significant way without entailing disruptive
> consequences to human civilization. In essence, advance in science and
> technology, social progress, even evolution stop due to inability to
> change the system we human being rely upon.- Hide quoted text -
>
> - Show quoted text -
eatfastnoodle
not necessarily, software development still a very messy enterprise, a
lot still relies on human management of humans, still there is no
guarantee that 30 years from now, the code we write today can be
understood and maintained by future programmers. It took longer and
longer for Microsoft to develop new OS mainly because some of the
underlying codes in today's windows were written more than 20 years
ago. It's extremely hard to figure out how to replace it. Divide and
conquer is ok, but as the size of the task grows, the complexity of
dividing the task and, making sure subtask communicate and cooperate
with each other, etc also grows exponentially.