The Limitations of Science
Lead: Steve Pirnie & Kyle LaFountain

4/24/2006

Summary by Marty Rowley

Prelude

Steve and Kyle were responsible for presenting on the limitations of science’s ability to disseminate all the mysteries of the universe such that we as observers may know every empirical fact about reality. They focused their efforts throughout the presentation primarily on Kurt Gödel’s inconsistency theorem, which roughly states that no system can be wholly true and consistent. Using this theory, they argued that because so much of science is based on, or heavily relies upon mathematics (physics being the prime example of this) Gödel’s theorem is damning proof of the limitations of science to give us access to all knowledge.

Mathematical Limitations

Kurt Gödel
Summarization of Gödel’s Theory- Science is based on Mathematics; Mathematics cannot discover all truths; therefore science cannot discover all truths. Is this logical?

Pessimistic and Optimistic Views of Gödel’s Theory-

• Stanley Jaki (Pessimistic) - The human mind cannot know all (or perhaps even most) of the secrets of nature
• Freeman Dyson (Optimistic) – The human pursuit of information that would be disrupted if science were “completed.”

The Mathematical Dilemma:
The following (I presume) is an example for such a dilemma.

   1+2+3+4+5…..= ∞
But:
   1 + 1/9 + 1/25 + 1/36 + 1/49 +…..= pi2/8= 1.2337005….
Therefore:
   1-1+1-1+1-1+1-…..=?????
If you divide these equations into pairs:
   (1-1)= (1-1) +…..=0+0+0=0 but
If you divide the numbers like this:
   1-{(1-1) + (1-1) +…..} it looks like 1-{0} = 1 proving that
     0=1

Limits of Science Large and Small

As has been discussed before, there are limits on our observations of the universe; namely that space is expanding faster than the speed of light, and we are “losing parts of the universe beyond this “universal curtain.” On the other end of the spectrum, we have talked about quantum physics, and the possibility of an indeterminate state. Does the Heisenberg uncertainty principle limit the amount of information that we can know about elementary particles?

The following are three questions the presenter’s asked on their handout dubbed “talking points” to serve as discussion prompts. The first questions the ability of science to prove or refute the existence of God, and (presumably, though it could also simply express skepticism of such an attempt) addresses the ethical implications of its attempting to do so. The second talking point questions the role of mathematics, and the third is unclear…

Other Talking Points

1. Can science prove the existence or non-existence of God? Should it try to?
2. Mathematics is used to describe observable reality, but it is also more expansive than that. Can mathematics be suited to describe things which we have not been able to observe?
3. Do the patterns which are inherent to nature necessarily limit the possible states of the universe?

Summary of Conversation:

Professor Moebius objects to some of the points made by the presenters concerning Gödel’s theorem.

Professor Moebius (PM): This is an example of a series that doesn’t converge, but jumps between two values. Take every odd number, and it will always be one, and every even number will always be 0. Even though this may at first appear counterintuitive, math can describe things. The question is: can you construct the right logical proofs for every step? According to Gödel, a system must be at least as rich as the mathematical system, as this lets you make more encompassing systems.

Steve Pirnie: Can you get to an all encompassing theory?

DM: No, no system is both consistent and complete.

Professor deVries (P deVries): What you mean by a system must be a finite set of axioms.

Sam Schweitzer at this point changes the topic by asking about the third “talking point” question on the presenter’s sheet.

Sam Schweitzer: What do you mean by the third talking point “do the patterns which are inherent to nature necessarily limit the possible states of the universe?”