“Every mathematical system will have some statements that can never be proved.”
Mathematics
Appreciating Design and Designer – Vern Poythress
Cunningham: Rev. Dr. Vern Poythress (PhD, Harvard; DTh, Stellenbosch) is distinguished professor of New Testament, biblical interpretation, and systematic theology at Westminster Theological Seminary. His books include Redeeming Science, Redeeming Mathematics, and Redeeming Philosophy, or Chance and the Sovereignty of God.
Distribution of tossed coins, a reminder
We see the binomial distribution of coin-flipping possibilities, here based on 10,000 actual tosses iterated 100,000 times, also indicating just how tight the peak is, mostly being between 4,850 and 5,150 H: Thus we see the roots of discussions on fluctuations: Note, not coincidentally, sqrt (10^4) = 10^2, or 100. (Compare the bulk of the Read More…
Michael Egnor: Mathematics can prove the existence of God
Egnor: Because mathematics can show infinity, eternity, and omnipotence, it can only have proceeded from a mind with those characteristics. That’s God.
At Mind Matters News: Recent research: Imaginary numbers are part of the real world
Takehome: Perhaps the universe is bound to seem mysterious, in part because it is not wholly material. It keeps the rules but the rules are not always what we expect.
Robert J. Marks: Some infinities are bigger than others but there’s no biggest one
In Marks’s view, infinity is a beautiful — and provable — theory in math that can’t exist in reality without ludicrous consequences. (Thus the immaterial human mind is capable of creating things that don’t exist in material reality.)
Robert J. Marks: 4. How Almost All Numbers Can Encode the Library of Congress
Re math: Almost every number between zero and one, randomly chosen by coin flipping, will at some point contain the binary encoding of the Library of Congress. That’s why infinity is a concept in math but not in the real world. Note: You should ask, how do we come to have concepts that are not part of the real world?
At Mind Matters News: 2. Infinity illustrates that the universe has a beginning
The absurdities that an infinite past time would create, while not a definitive mathematical proof, are solid evidence that our universe had a beginning.
At Mind Matters News: 1. Why Infinity Does Not Exist in Reality
Robert J. Marks: In a series of five posts, I explain the difference between what infinity means — and doesn’t mean — as a concept.
At Mind Matters News: Claim: Honeybees, “like humans” can tell odd vs. even numbers
Bees are not six-legged humans. They are incorporating the mathematical structure of the universe into their survival strategies. The researchers mainly demonstrated that we can use operant conditioning on bees.
At Mind Matters News: No, civilization has NOT won the war on math. Not yet anyway…
Maybe it comes down to how much accurate ideas actually matter, as opposed to politics some people can force other people to pay for.
At Mind Matters News: Unexplained — maybe unexplainable — numbers control the universe
Nobelist Wolfgang Pauli (1945) is said to have remarked, “When I die, my first question to the devil will be: What is the meaning of the fine structure constant?” At any rate, he thought about it a great deal during his life.
At Mind Matters News: Single neurons perform complex math — even in fruit flies
The fly’s specialized neurons either multiply or divide incoming signals in order to pinpoint the location of a sound or the direction of movement. How likely is this to happen without any intelligence behind nature at all?
At Mind Matters News: Why would a purely physical universe need imaginary numbers?
The most reasonable explanation is that the universe, while physical, is also an idea, one that cannot be reduced to its physical features alone.
L&FP, 49: Debating the validity (and objectivity) of infinity
Steve Patterson, among many points of objection, is doubtful on the modern concept of infinity (or more strictly the transfinite): The foundations of modern mathematics are flawed. A logical contradiction is nestled at the very core, and it’s been there for a century. Of all the controversial ideas I hold, this is the most radical. Read More…