Infinity

Episode #645

June 12, 2021

0, 1, 2, 3, 4, 5…
Keep counting.

Can you count to an infinite number?
You can try.

A person can count the integers by adding the number “1” to each number: 0+1=1, 1+1=2, 2+1=3…
The person could keep counting until their death without reaching infinity.
Let’s make a solar powered computer to count to infinity.
It would count until the Earth or the Sun was destroyed.
Still, it would not have counted to infinity.

Most computer programs, such as operating systems, are designed to run until the program or the computer is turned off.
The following program counts three “zzz”s, then does it again, infinitely.

while :
# by rickiT

:Sleep
For zzz = 1 To 3
Next zzz

GoTo Sleep

There is undying love, but of course there is not.

Infinity comes in different sizes.
There are an infinite number of integers (solid numbers).
Yet, there are infinitely more real numbers (all the fractions) than there are integers.
Is the infinite number of real numbers greater than the infinite number of integers?

It seems that you should not be able to draw a line of infinite length.
A right triangle with two 1 inch sides has a hypotenuse of the length 1.414211356…infinite inches, yet that hypotenuse can be drawn.

The circumference of a circle can be calculated using the formula:
pi times the radius squared.
Since pi is an infinite number, the length of the circumference must also be infinite.
Not surprisingly, there are an infinite number of radii in a circle.

If you were to travel through a möbius tube the journey would be infinite. A möbius tube has no end and no beginning.

Zeno’s paradox:
Traveling along a line to a destination is equally impossible.
To go from a starting point (A) to a destination (B) you must first go half way (point C).
To get from point C to point B you must go half that distance (point D).
To get from point D to point B you also go half that distance.
This progress will repeat infinitely so that you can never arrive at point B.

How can something without a last step be completed?

According to the laws of physics an object approaching the speed of light  is stretched to an infinite length. How long is the object?

In the religion of Scientology there are eight dynamics.
The eighth dynamic is:
“the urge toward existence as INFINITY … It actually embraces the allness of all.”
L. Ron Hubbard must have had his tongue in his cheek when he wrote the eighth dynamic, because the number “8” is the infinity symbol sideways. Really Ron?

I tell my writer’s group that anyone can write a great story.
Take, for example, a monkey hitting random keys on a typewriter for an infinite amount of time. The monkey will almost surely write every text that has ever been written.

How can an infinite process end?

The decimal form of irrational numbers, like pi, go on infinitely, never repeating.
Some calculations approach a solution infinitely.
The Fibonacci sequence approaches the golden ratio, also known as the  Greek letter Phi.
Phi is an irrational number and therefore infinite.

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244970720720418939113748475408807538689175212663386222353693179318006076672635
443338908659593958290563832266131992829026788067520876689250171169620703222104
321626954862629631361443814975870122034080588795445474924618569536486444924104
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705751797883416625624940758906970400028121042762177111777805315317141011704666
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986151437803149974110692608867429622675756052317277752035361393621076738937645
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737880344170093954409627955898678723209512426893557309704509595684401755519881
921802064052905518934947592600734852282101088194644544222318891319294689622002
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836150238913493333122310533923213624319263728910670503399282265263556209029798
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909501680328112194320481964387675863314798571911397815397807476150772211750826…

You can approach the golden ratio, but can never achieve it.

Some infinity is indeterminable.
Ask Siri to divide zero by zero:

The universe seems infinite to us, but maybe it is just immense. 
Buzz Lightyear says: “To infinity and beyond…”
What is beyond infinity?

Time itself may be infinite.
As far as we can see there will be no end to time.

Stand between two mirrors to peer into infinity.
Your eyes and your brain cannot see where your mirrored images end.

Because it cannot be observed or displayed infinity may only exist in the world of ideas.

Keep counting.

… 6, 7, 8, 9, 10…