Nothing!!

Speaking of Nothing, once there was a factory that invited an industrial engineer to see whether things can be made more efficient and streamlined, and whether it would be possible to eliminate some jobs due to duplications. So the engineer sees a worker who seems to be idle, and asks him: “what are you doing all day?”, “Nothing”, he replied. The engineer says “thank you” and goes on. A while later, the engineer sees another worker who seems to be idle, and asks him the same question, and gets the same answer, “Nothing”. The engineer then recommends to the manager to fire that other guy. “But that’s unfair, exclaimed the worker, that first guy is also doing nothing, and you didn’t fire him!”. The engineer replied: “That’s exactly my point, we don’t need two different people doing the same thing!”

So Nothing is really something, but only one thing.


Let me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible.

The Empty Set In the 19th century, Leopold Kronecker famously said that “God created the integers, all the rest is man-made”. A bit later, about a hundred years ago, mathematicians and logicians thought that even integers are too complex to be really fundamental, and they tried to reduce everything, in particular integers, to sets. So the great computer pioneer, John von Neumann, when he was still rather young, came with a brilliant way to define integers in terms of sets, and all he really needed was a starting point: the empty set.

So according to von Neumann:
0 := ∅ .
Now we have one object at our disposal, so let us form the set consisting of what we have so far:
1 := {∅} .
Now, at the second day, let’s gather what we had so far, and make them into a set
2 := {∅, {∅}} ,
and at the third day, let’s define
3 := {∅, {∅}, {∅, {∅}}} ,
and, in general
n := (n − 1) ∪ {n − 1} ,
ad infinitum.


But von Neumann’s construction can only handle integers, starting with the empty set. What about other kinds of numbers? About thirty-five years ago, John Horton Conway realized something revolutionary. All numbers are games! Now there are many games that are not numbers, so game is a more fundamental object than number. According to his own account, he felt a bit guilty that during the research slump that hit him after discovering the Conway groups, he hardly did any mathematics, but spent most of the day playing games at the common room of his Cambridge college. Only later did he realize that playing games is research, and furthermore, more interesting and significant than the vast majority of his colleagues’ research, since it lead him to the great idea that numbers are games.

That is one astonishing theory!!!! but out of the scope of this discussion !
This blog is al ready painfully large . I must end it now. Before finishing I prove a Theorem that proves the power of nothing!!! so that reader doesn't under estimate nothing

Nothing .

Theorem: (anon.) A ham sandwich is better than good sex.

Proof: (anon.) The following two assertions are obvious.

1. A ham sandwich is better than Nothing .
[Indeed!! Though I am Muslim and don't have ham, if I were stuck on a desert island, and had nothing to eat for five days, I admit that I would eat it, and it is better than having nothing.]

2. Nothing is better than Good Sex .
[Actually I cannot say it exactly, because I didn't have sex yet (very sad indeed!!). But existing data indicates that for sure!!! :p]

The theorem follows by the transitivity of the is better relation.

[Q.E.D]


Acknoledgement .

Doron ZEILBERGER for his nice talk on nothing.

Maxwell

"To anyone who is motivated by anything beyond the most narrowly practical, it is worth while to understand Maxwell's equations simply for the good of his soul."
-J. R. Pierce