8/9/13, 2:21 AM

Ken Wais

Age, Half-Life and Immortality

Here is an interesting idea concerning two sets of numbers.  One we will call: YourAge.  YourAge is just how old you are, expressed in integer numbers like 1, 2, 3, etc.  The other set we will call: YourHalfLife.  This set will be a set of rational diminishing numbers that is also a convergent set. Unlike the YourAge set which is divergent.  They can be shown as follow:

YourHalfLife

1, ½,1/4,1/8, 1/16,1/32,1/64….→0

This half-life set decreases by ½ of the original number with every member added. But let’s go back to the YourAge set. It increases by integer values so to show it we have:

YourAge

1,2,3,4,5,6,7,8….→∞

Now, let’s say at some point in the 2nd set, how ‘bout 25, which is your real age in time, we could map the first set to the second?  But, I want to go further.  Let us also define that the YourAge set is your real physical age with all the medical-biological implications that coinage means.  The second set, YourHalfLife, is a measure of how much the first set extends.  Here we have an exquisite mapping of sets.  As you age in life from say an arbitrary number, 25 in YourAge set, the second set YourHalfLife is mapped to it.  Here is an example of it.

25→25, 26→1/2, 27→1/4, 28→1/8, 29→1/16….∞

When you are 25 you are 25.  This is your base year.  But as years continue your age decreases by a fraction of that base year. So, when you are 26 you increase in age ½ your age at 25, at 27 you increase ¼ your age at 25, when you are 28 you increase 1/8 your age at 25, at 29, you increase 1/16 your age at 25.

Thus, as you age in real time you actual age would decrease, or should I say your half-life would decrease?

Here we are making what algebraic mathematicians call a surjective map from one set to another.  That is, we are putting numbers from one set to another but not the other way around.  Both these sets have properties.  The set YourAge is an infinitely increasing set.  The set YourHalfLife is an infinitely decreasing set.  But YourHalfLife is decreasing to a value.  Its value converges to 0.  But, that value is 0, and it applies to only part of this set.  Since YourHalfLife is a rational number.  The integer part, 25 stays constant only the decimal is converging to the value of 0.  Which means, the set value YourHalfLife is converging to 25.  Let us show this in a diagram.

 

YourAge

25

26

27

28

29

30

31

32

 

 

 

 

 

 

 

 

 

YourHalfLife

25

25.5

25.25

25.125

25.0625

25.03125

25.015625

25.0078125

 

You can see that as your real age increases, your half-life age will never go beyond 25.  In fact it will keep getting closer and closer to your original age of 25.  Notice also, though YourHalfLife does converge to 0, it does it infinitely.  It never actually reaches 0, it just tends toward 0. Of course, this means with such a set mapping you will live infinitely at the age 25.  This could be called immortality I guess, except no one has figured out how to map such age-sets. And man o man, I wish some biologist-geneticist-wizard-scientist-booger would! 

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