Φ¹¹ 60stars Astrology Season Essay Φ¹¹ ” Bring more stimulation into this world ”

60stars  Astrology Season  Essay

English  version

By TOKYO-TANUKI

Φ¹¹　60stars  Astrology Season  Essay Φ¹¹ 

” Bring more stimulation into this world ”

1.  Now, this story is also slightly related  to the “Journey of Fermat Numbers” that Tanu-chan was doing.  

When we say calculation,  
we usually mean the four basic operations (+, −, ÷, ×) plus exponentiation —  
these five are called the basic operations.  

.....Well, these are the rules of calculation.  

Of course, there are people who try to include difficult things  
like symmetry or supersymmetry among these basic operators,  
and others who talk about factorials (!) or mod.  

But, well, let’s calm down for a moment.  

Tanu-chan is from the humanities,  
so complicated things are beyond me.  

...And when I think quietly about it,  
I notice that among the five basic operations,  
“exponentiation” itself already has two patterns.  

.....That is, one way is to multiply by itself (K×K)  
and then keep multiplying by K again and again:  
K ⇒ K² ⇒ K³ ⇒ K⁴ ……  
For example, if K = 2,  
then 2 ⇒ 2² ⇒ 2³ ⇒ 2⁴ ……  

Normally, when we say power or exponentiation, we mean this pattern.  

2. However, there is another kind of exponentiation.  

In this one, we multiply by the new self that is generated each time.  

So it goes like this:  
K ⇒ K² ⇒ (K²)² ⇒ ((K²)²)²  

For example, when K = 2:  
2² = 4, 2³ = 8, 2⁴ = 16 .... no, wait.

Here it becomes  
2² = 4, 4² = 16, 16² = 256,  
256² = 65,536 ……  

....Oh, these are the relatives of the Fermat numbers !  

In short, the above shows the difference between  
additive exponentiation and multiplicative exponentiation.  

Originally, multiplicative exponentiation should be treated as a proper, independent operator.  

However, because additive exponentiation can, to some extent,  represent the same results, people generally do not distinguish between the two, nor are they even aware of it.  

And the reason why the story of Fermat numbers  
attracts so many people is that .....everyone, unconsciously, somehow understands that multiplicative exponentiation is a new operator.  

In other words, it is a revolution!  

Fermat numbers advance along the very edge of the world of arithmetic operations, bringing fresh stimulation to it.  

They blow a new wind into the world of the four operations (+ − ÷ ×) and exponentiation.

  
.......Such a cool kind of number they are.  

Whether they are directly connected to prime numbers or not,  
I am not sure —  ....but it is certainly a new method.  

3. ......However, as "n" increases, the numbers quickly grow huge, and in that sense, this Fermat-style multiplicative exponentiation is more troublesome and less convenient  

than the other operators.  

Also, it’s hard to say what it could be used for...  

.....By the way, there is yet another,  
even greater kind of exponentiation —  exponentiation of exponentiation itself.  

For example, when K = 2:  
2 ⇒ 2^2 ⇒ 2^2^2 ⇒ 2^2^2^2 ⇒ 2^2^2^2^2  
That is,  
2 ⇒ 4 ⇒ 16 ⇒ 65,536 ⇒ 20,035,922,304,068 …  

Well, at 2^2^2^2^2 the number already has about twenty thousand digits,  so it’s not very practical.  

......Anyway, for that reason,  
Tanu-chan will quietly end here the solitary journey of Fermat Numbers.  

As expected of the great master Fermat —  
while standing on the tradition of mathematics, he aimed for a revolution in the world!  

The story of Fermat numbers, rather than being a crack in this world, is an effort to add a new operator, to bring more joy and stimulation into this world.  

Well, for an animal,  
that was a little arrogant of me.  
I repent！

（....to be continued)



Tanu-chan💓　 TOKYO-TANUKI💛