文档介绍：THE UNKNO W ABLE
G
J
Chaitin
IBM Researc h Division
T
J
W atson Researc hCen ter
Ha wthorne
New Y ork
Jan uary
Preface
Ha ving published four b o oks on this sub ject
wh y a
fth
Because
there
s something new
pare and con trast G
odel
s
T uring
s and
m yw ork in a v ery simple and straigh t
forw ard manner using LISP
Up to no wInev er w an ted to examine G
odel
s and T uring
s w ork
to o closely
I w an ted to dev elop m yo wn viewp oin t
But there is no
longer an y danger
So I set out to explain the mathematical essence of
three v ery di
eren tw a ys to exhibit limits to mathematical reasoning
the w a yG
odel and T uring did it in the
s
and m yw a y that I
v e
been w orking on since the
s
Inan utshell
G
odel disco v ered pleteness
T uring disco v ered
putabilit y
and I disco v ered randomness
that
s the amazing fact
that some mathematical statemen ts are true for no reason
they
re true
b y acciden t
There can b e no
theory of ev erything
at least not in
mathematics
Ma yb e in ph ysics
I didn
t w an t to write a
journalistic
b o ok
Iw an ted to explain
the fundamen tal mathematical ideas understandably
And I think that
I
v e found a w a y to do it
and that I understand m y predecessors
w ork
b etter than I did b efore
The essence of this b o ok is w ords
explaining
mathematical ideas
but readers who feel so inclined can follo wmeall
the w a y to LISP programs that prett ym uc hsho wG
odel
s
T uring
s
and m y pro ofs w
orking on puter
And if y ou w an ttopla y with
this soft w are
y ou can do wnload it from m yw eb site
This b o ok is also a
prequel
to m y Springer b o ok The Limits of
Mathematics
It
s an easier in tro duction to m y ideas
and uses the same
v ersion of LISP that I use in m y Springer v olume
Hop efully it
ll b e a
stepping stone for those for whom The Limits of Mathematics is to o
in timidating
This b o ok b egan as a lecture on
A h und