Existing Unknowable II

The ideas from the previous post can still be expanded.  Chaitin’s constant illustrates that science as a whole is quite limited.  Scientism in itself pictures all of reality as a knowable landscape, say a plane.  However the existence of unknowable quantities illustrate that this landscape is not smooth.  In other words if you were a bug crawling on its surface you may fall through the numerous holes littered throughout!

Consider taking a sheet of paper.  This is the “knowledge plane”.  It represents the total knowledge of knowable and unknowable quantities.  Now take a finite collection of coins, say 10.  Each coin represents what is knowable through an exhaustive collection of tools.  As the coins land and settle they represent an area of the knowledge landscape that is known, or at least can be known.  In order to make leaps in our knowledge means jumping between separate coins requiring tremendous intuition, luck, and perspiration.  This example illustrates why a certain area of science may never “bridge the gap” between areas, albeit how close they actually are.  Science is not exhaustive, rather limited, and nonetheless full of interesting discoveries that await.  However, my fear is that too many people are waiting for the discovery of the unknowable, in that they require exhaustive knowledge to make a definitive decision rather than looking at suggestive evidence pointing toward a certain direction.  This is ever apparent in the existence of God and in his precious son Jesus.  God has the ability to reveal himself and lead us toward him as much or as little as He sees fit.   Indeed, in Jesus, He has.

What evidence is required to trust that Jesus is that very revelation?  This is not an issue of ‘time’, evidence is evidence regardless of its age.   Like a juror in a trial, you must make a decision.  It will not be an unreasoned decision, however the decision will be made on faith.  It is a reasonable faith.  Such as casting a guilty or not-guilty verdict, after all a juror in a trial will not have been present at the events in question!  Even Jesus’ followers during His ministry were faced with a similar predicament (John 20:29).  Consequently, after His resurrection and ascension, His followers were also faced with similar issues, such as when Paul was preaching in Rome (Acts 28:24-28).

This leads to a natural question: what evidence is so profound that leads a person to trust that Jesus Christ is who He says He is and to put your life into His hands?  The answer?  The resurrection of Jesus Christ.  In fact, the entire faith rests on that very fact.  If Jesus Christ did not raise from the dead our faith is futile, we are still unreconciled to God, and dead to our sins (1 Cor 15:12-58).  It seems that this precarious thread must be, in fact, quite strong.  In the following post afford me the opportunity to explore this even further.

Existing Unknowable

Mathematics.  A large bag of tools used to discover many of the greatest kept secrets our world has to offer.  Some secrets can be mined using our applicable tools, while others are unknowable even when exposed to an exhaustive collection of tools. Yes, there are unknowable ‘things’, if that is even the right word for them, yet we can prove their existence.  What?!  In other words, there are concrete limitations to science as a whole.

Consider Chaitin’s constant as a simple example. This is a number that is known to exist but can be shown that not a single bit of it can be computed.  Sounds like trying to pin down an eggshell in water!  However, if this number was known or be found it then could be used to prove a slew of theorems most notably the Riemann hypothesis, arguably the most famous unsolved problems of all mathematics!

How could this be?  What is so special about this number?  Let us consider the following.  Suppose you have an oracle, call the Oracle Bec.  The oracle tells you if something is true or not.  You ask Bec, “Hey is the Riemann hypothesis true or not?” She nods her head yes.  Proven. You also now inherit the million dollar award for solving this problem.  Thank you Mrs. Oracle!

This is because Chaitin’s constant is connected to a certain type of computer program.  This program can review any other program and see if that program will stop or not.  For instance suppose we have the following program:

count=1; flag=0; while(flag==0), count=count+1; end;

This is a bad program.  It continues to add one to count indefinitely, never-ending.  You take your algorithm and ask Mrs. Oracle if the program will stop.  She states you have a probability of zero, that is, it will not stop.

Now assume you have a program that tests a certain hypothesis of a theorem.  You could then ask the Oracle if it will stop.  Hence the theorem is proven or disproven.  Gee, you could disprove a theorem without even constructing the counter-example, as you’ll know that one exists!

The future of science is quite mysterious, the hope of having a continuum of scientific knowledge oozing between different fields is a mere fantasy.  At best our complete knowledge will still have holes for which are unknowable.  They exist.  And no amount of passing, fleeting time will ever encapsulate that.