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Infinity

  • Surely goodness and love will follow me all the days of my life, and I will dwell in the house of the LORD forever. Psalm 23:6
  • Glorious and majestic are his deeds, and his righteousness endures forever. Psalm 111:3
  • Do you not know? Have you not heard? The LORD is the everlasting God, the Creator of the ends of the earth. He will not grow tired or weary, and his understanding no one can fathom. Isaiah 40:28
  • How precious to me are your thoughts, O God! How vast is the sum of them! Psalm 139:17
  • See if there is any offensive way in me, and lead me in the way everlasting. Psalm 139:24
  • But who is able to build a temple for him, since the heavens, even the highest heavens, cannot contain him? 2 Chronicles 2:6a

I have been exploring the concept of infinity. How big is infinity really? Is there a way to grasp this? After all infinity will always be bigger than the biggest number anyone can think of.

I know how long a meter is - I can see a millimeter on a ruler - one thousandth of a meter (or 10E-3 in math exponential notation). I can drive 1 kilometer (1 km - 10E3 meters) and even 1,000 kilometers (10E6 meters). The earth has a circumference of about 40km, and the distance from the earth to the moon is 384km (384x10E6 meters) and from the earth to the sun is 149,600,000km (1.496 x10E11 meters).

Infinity is of course bigger than this.

A light year is the time it takes light to travel in a year. Given light travels at about 300,000,000 (3x10E8) meters a second, a light year is a big distance: 9,460,000,000,000,000 (9.46 x10E15) meters. The nearest star is estimated to be 4.3 light years away - i.e. about 4x10E16 meters away.

Here's a number that's 10 times bigger - if one accepts that the age of the universe is 14 billion years old, then this translates to about 4x10E17 seconds.

It is estimated that the galaxy we're in is about 1,000,000,000,000,000,000,000 meters wide. (10E21)

The latest estimate for the size of the observable universe is 1,000,000,000,000,000,000,000,000,000 meters across (10E27)

Infinity is bigger.

In fact a slightly bigger number than the size of the observable universe in meters is the number of atoms in a human body - about 7x10E27 (this for a person who is about 70 kg or about 150lbs).

The number of atoms in the world is estimated to be 10E50: 100,000, 000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000.

The number of atoms in the observable universe is estimated to be 10E80: (I'll stop writing 0's now. 10E80 a 1 followed by 80 0's.)

Infinity is bigger.

In 1920, Milton Sirotta was 9 years old when he was asked by his uncle what he would call the biggest number he could think of. His uncle was the American mathematician Edward Kasner who used his answer in his book "Mathematics and the Imagination" and the term stuck. The name he thought up was 'Googol'. A Googol is a 1 followed by 100 0's - or 10E100. This number is bigger than the estimated number of atoms in the observable universe.

How to imagine this number? Consider 70 people sitting on 70 chairs. How many ways could they be ordered? How many seating arrangements are there? It turns out about a Googol!

This means there are very big numbers associated with the possible order of things. For example how many possible games of chess are there? The answer is estimated to be one googol times ten billion times ten billion (10E120).

Infinity is bigger.

A googolplex is 10 to the power of a googol (10EGoogol) - or a 1 followed by a googol 0's. It's impossible to write this number down in long hand since there are not considered to be enough atoms in the observable universe to do so.

In fact if one could freeze time, and in that instant allow any number of atoms to swap positions in the whole of the observable universe, the number of possible combinations and permutations is less than a googolplex. (Mathematically 10E80! < 10EGoogol.)

Infinity is bigger.

So far I've been talking about numbers in just the 3 dimensions of space and the one of time. Theoretical mathematicians explore problems with multidimensional space. So numbers can get really very much bigger. But I can't get my head around abstract theoretical space involving 100s of dimensions. So I'll stop here, knowing infinity is bigger than the biggest number someone in the world is using on a problem that only a few people will ever understand.

In conclusion everlasting and forever are immeasurable and can never be really comprehended. But it was fun trying.

With this in mind, what should our priorities be?

  • I tell you the truth, he who believes has everlasting life. I am the bread of life. Your forefathers ate the manna in the desert, yet they died. But here is the bread that comes down from heaven, which a man may eat and not die. I am the living bread that came down from heaven. If anyone eats of this bread, he will live forever. This bread is my flesh, which I will give for the life of the world. John 6:47-51.

John Bell
August 26th 2006
Irvine, California, USA.

 

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