Georgi Guninski's blog

Math challenge of the day 2018-09-24

For complex $x$ define 

f(x)=exp(x^2)-exp(x)-1

Is it true that f(5 i pi) = 0?

We have strong numerical evidence with precision
100 decimal digits but some meromorphic doubts too ;)

gp/pari session (warning, gp is very buggy):

parisize = 8000000, primelimit = 500000, nbthreads = 2
? \p 100
   realprecision = 115 significant digits (100 digits displayed)
? f(x)=exp(x^2)-exp(x)-1
%1 = (x)->exp(x^2)-exp(x)-1
? f(5*I*Pi)
%2 = 6.952351934431877974 E-108 + 0.E-114*I

Cheers for the day.

On immortality in computer games

When I younger so much younger than today I was playing with computer
games in unorthodoxal way. Instead of playing the game like a user, I
changed the games so the player was immortal. Maybe more precisely the
player had infinite number of lives.

In short the process was: analyze the code and change features you
don't like, like finishing the game because of death. In some sense
this was immortality in the game.

Per rough memory there were several types of immortality

(1) Instant free rebirth, starting from the beginning of the level
(2) No way to die
optionally
(3) Super natural skills like passing thru walls, including exiting
the screen from right and appearing on the screen from the left.

The hardware was Правец 82 (the socialist cloning of Apple II):
8 bit processor 6502, about 64Kb memory, including video memory and
ROM.

My "customers" were the colleagues of my father, engineers and
professors. They reached the end of a patched game and the game told
them: "You are very skilled and win monetary award, call #american
number". They didn't call, partially because the game was pirated.

Similar stuff appears in science fiction. 

Implementing this in Internet Of Things will make great mess, it is
just a matter of time.