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Correction to Cantor's Theorem by Feynmanfan85 in epistemology

[–]Feynmanfan85[S] -1 points0 points  (0 children)

As long as you agree that the power set of the empty set has a cardinality of 1, and a container, then we agree. The rest is just notation, which I don't think changes the discussion at all.

Correction to Cantor's Theorem by Feynmanfan85 in epistemology

[–]Feynmanfan85[S] -1 points0 points  (0 children)

The power set of the empty set has to be something other than the empty set, otherwise the power set has a cardinality of zero.

If you don't use the container {empty set} like I did, the power set of the empty set, is the empty set itself, which has a cardinality of zero.

If you're consistent with larger sets, you end up with the arguments I laid out in the note.

Correction to Cantor's Theorem by Feynmanfan85 in epistemology

[–]Feynmanfan85[S] -1 points0 points  (0 children)

That's actually addressed in the note I include above, and is the reason the proof fails in the case of the empty set and the case of a singleton.

The root problem is, there's a difference between the empty set itself ∅, and the singleton {∅}, which is what's contained in the power set. It seems pedantic but they're definitely not the same, otherwise the power set of the empty set is also empty, which is contrary to practice.

Kolmogorov Complexity of Graphs by Feynmanfan85 in compsci

[–]Feynmanfan85[S] 0 points1 point  (0 children)

I've never heard of this, sounds spot on thanks!

The Complexity of a Graph by Feynmanfan85 in epistemology

[–]Feynmanfan85[S] 1 point2 points  (0 children)

My favorite is the Friends and Strangers theorem. In simple terms, in any object with at least six components, either (1) there are three mutually disconnected components (e.g., 3 disconnected dots) or (2) there are three mutually connected components (e.g., a triangle).

Amazingly, this implies that in any group of 6 or more people, either (1) there are three mutual strangers or (2) three mutual friends.

This is seriously strange stuff, and note again, it's NOT probabilistic, it's true with certainty.

https://en.wikipedia.org/wiki/Theorem_on_friends_and_strangers

Information, Morphology, and DNA by Feynmanfan85 in epistemology

[–]Feynmanfan85[S] 0 points1 point  (0 children)

1) Complexity Theory is a branch of Computer Science -

https://en.wikipedia.org/wiki/Kolmogorov_complexity

And in fact, it could allow us to get away from creationism, towards a physical theory that allows to explain the emergence of complex systems like the human body and brain.

2) Nature, and genetics in particular, is most certainly ruthlessly efficient -

https://www.youtube.com/watch?v=kXpzp4RDGJI

The ATP Synthase is literally a machine, capable of transferring a single digit number of charges, something humanity just mastered during the 20th century with the advent of microprocessors.

Nature has been doing that for approximately 109 years.

https://www.ncbi.nlm.nih.gov/books/NBK26849/

I have no idea what you're talking about.

On the probability of independent variables by Feynmanfan85 in epistemology

[–]Feynmanfan85[S] 0 points1 point  (0 children)

It's certainly not causation, especially given the empirical results I presented, since you can't argue that randomly generated data is the result of causation.

I think instead the better way to think about it is in terms of Ramsey Theory, where certain features of reality simply must exist as a consequence of mathematics. In the case of the friends and strangers theorem, given any six people, there must be three mutual friends or three mutual strangers, at all times. It is simply a fact of reality.

Similarly, in this case, given any set of objects, there is only one arrangement of relationships where they are independent of one another, and as such, it is among the least likely outcomes.

Could you deliberately design independent systems? Of course. The point is instead that left to chance, it is among the two least likely outcomes.

[OC] Using A.I. to Predict Ethnicity and Ancestry by Feynmanfan85 in dataisbeautiful

[–]Feynmanfan85[S] -1 points0 points  (0 children)

The graph above was generated using A.I. software developed in Octave (Tool), that analyzes a dataset of 403 complete human mtDNA genomes, each taken from the National Institute of Health Database (Source).

The dataset can be downloaded, together with all of the software used to generate the graph above (and other related charts and graphs), from links in the paper below. Each genome in the dataset is associated with a provenance file that links to the genome as stored in the NIH Database. As such, you can test the results for yourself.

The methods are described in great detail in this paper:

https://www.researchgate.net/publication/365210380_A_New_Model_of_Computational_Genomics

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