Mathematics, Shaken but not Stirred by Kevin H Knuth

Greetings Professor Knuth,

I have downloaded and begun to read your essay. Looks interesting. In my essay; I take almost the polar opposite tack. Recently; Giulio Tiozzo proved some very broad connections between the Mandelbrot Set and entropy, completing some of the last work of Thurston (with whom he collaborated). I have been exploring some specific connections of M to Physics for more than 30 years now, and the location I focus on in my essay has relevance for entropic theories of gravity.

I'd appreciate your comments on my essay. I will be back once I have read your paper in its entirety.

Warm Regards,

Jonathan

Thsnks Kevin,

Tiozzo was a PhD student of C.T. McMullen at Harvard...

He was set to work on a problem by Tan Lei, to make general a result involving local symmetry at Misiurewicz points against global asymmetry, which I think applies broadly to Physics. This led to his work with Thurston beofre Bill's demise.

More later,

Jonathan

This essay is beautiful work Kevin...

I am not in full agreement however. Some statements are only absolutely true if you rule out the possibility of hyper-dimensional super-determinism - an avenue I have been exploring of late. I have a paper in peer-review on "Painting, Baking, and non-Associative Algebra" that talks about forced ordering in higher-order Maths. Things must be done in proper order and sequence to work. The epic statement by Connes "noncommutative measure spaces evolve with time!" is amplified in non-associative geometry. But I digress.

I loved what you wrote about counting and the 'why?' of addition. Children are seldom taught the profound difference between none and one of something. Then it naturally follows that as you add more units of the same item, the additive rule comes into play. That worked since ancient times, but has been forgotten. The result of Turing was also well-known for years in indigenous cultures, as documented by my friend Evan Pritchard in "No Word for Time." So I regard the halting problem and its generalizations as established fact. But I think perhaps Gödel's work is a near-miss.

Still; I think it is remarkable that you reproduce some things that would be true even in a hyper-d super-d generalization, in what I see as a flattened form. This reminds me of comments in a lecture by John Klauder where he talked about QM as a projection from infinite-d Hilbert space onto a specific 2-d surface, and the possibility to lift the target space. So a lot of the evolutive properties from higher-d would automatically carry over as rules of inference in lower-d projections. So your paper is a tremendously fun read, when I put on my "Griff" cap (see MIB 3). I am wearing it now.

For the record; I loved the idea on softening logical statements by Jaynes, and how you worked that in. I also greatly love the works by Polya which spell out a wonderful roadmap for learning about most anything. But I'll have to return with additional comments.

More later,

Jonathan

Dear Prof. Kevin Knuth

Hope you will read and rate my essay after getting your comments cleared by me soon....

Let me also reciprocate later...

best regards

=snp

Dear Prof Kevin H Knuth

This post is a discussion post after well knowledged reply given on May. 4, 2020 @ 07:55 GMT above ... Your nice words.........

Godel's theorem is generally applicable to mathematics. Whether there are implications for cosmology really comes down to whether the cosmological questions, that one wishes to prove, rely on mathematics that is undecidable.

............... Well said!

Your nice words.........

In science, we only entertain testable hypotheses. These are hypotheses that make predictions. And it is by making predictions, using our theories, that allow us to test them against experimental data by applying the weakest of the logical syllogisms listed in my essay. This is the process of inductive inference, also known as Bayesian inference. And it is possible that one can get around Godel's theorem in a way by assigning probabilities to hypotheses rather than truth values. Of course, nothing will be known with certainty. But this is the situation that we are very familiar with in the physical sciences.......................

This process is different in Dynamic Universe Model, there Linear tensors are used, no differential and integral equations,.....

Your nice words.........

My essay claims that mathematicians threw up their hands and gave up, whereas they (especially now) could re-visit these issues and consider applying inductive inference rather than deduction.

As an amusing aside, I was watching the TV show, Sherlock, about the famous fictional detective Sherlock Holmes, and in the show, Sherlock claims that he arrived at his conclusions via deduction. However, this is not the case. Sherlock routinely uses inductive inference rather than logical deduction.

.........................

Wow very good, How to apply inductive inference..???

Your nice words.........

I think that mathematicians should give it a go and try it too!

.................

You can get the mathematics of my Model, in my blog

" https://vaksdynamicuniversemodel.blogspot.com/ "

You can have a general outlook of this model at my essay....

" https://fqxi.org/community/forum/topic/3416 "

Best Regards

=snp

Dear Professor Kevin Knuth,

Your essay was a joy to read your essay!

Your focus on addivity and expounding on its centrality to the sciences made for a nuanced and intelligent argument. My submission (co-authored) has a similar focus, where we interpret mathematics as the exclusive language of natural science and try to work out the implications it has and how the 3 un's become relevant. We view science as a function mapping observations to numbers, which I think is consistent to your statement:

"In science, we quantify things so that we can rank them: quantity, mass, volume, voltage, probability.

To maintain such rankings, quantities must be assigned consistently, especially in situations in which

things are combined or partitioned to form other numbers of things."

And, thus, like you conclude ( though nowhere as rigorously as both authors are undergrad level students) that we will have statements that are undecidable.

Whereas we differ in our work , is that we do not think observation and its interpretation through probability theory can rescue us, and found your arguments very convincing!

Raiyan Reza

(PS: I have you find time to read our work : https://fqxi.org/community/forum/topic/3563 )

Dear Prof,

Hope you will visit my essay, before time expires...

Best

=snp

Nice essay Kevin. Perhaps not surprisingly, I am one of those people who actually has wondered about addition. Bertrand Russell actually talks a little bit about this in the Introduction to Mathematical Philosophy, but what I find most intriguing is how this becomes known to sentient beings. I use the term "sentient beings" simply because it is known that many species can actually perform simple addition. Strangely, there is a point at which children (when they are very young), confuse strict addition with spatial extent. That is, for a certain period of time as they develop their understanding of space (usually during the toddler years), they often will mistakenly think that fewer objects spread out over a greater extent, are greater than a larger number of objects packed close together. There was some pioneering work done on this in the late 60s. Anyway, interesting stuff and, as I said when you commented on my essay, we need to have a beer when this whole pandemic is over.

Dear Professor Kevin Knuth,

Just now I gave the best rating for your wonderful essay, Earlier yours is 6.3 ( 16 ratings) now 6.5. Congratulations!!!

Hope you will get some time to look at mt essay TODAY and rate it. Tomorrow contest is closing is closing!!!

Best wishes to your essay!

=snp

Hello again Kevin,

I am curious what you will think if you read my essay. I hope you get the chance, while there is still time for ratings to count, because I have the sense you reward good scholarship. Even though we have near-opposite approaches in some areas, I think you will be rewarded for taking the time.

All the Best,

Jonathan

Hi Kevin,

Pleased I got to your essay. As high quality in content and well written as usual.I loved your identification that; "The effectiveness of mathematics is reasonable because mathematics is designed to work. Yet it still has it's limits in approximating nature itself! Good score coming. I'm sure you'll also like mine, challenging some foundations to good effect, and hope you get to it.

Very best

Peter

Perhaps after the ratings wars have concluded...

I can contact you about an Entropy submission. I was invited to write a paper for a special issue once, but then the market crashed and I could not cover the publication fees, so I had to pull it. That work was on a common basis for non-locality and entropy, which I presented on at FFP10. But my current research is in a different direction. My essay will provide insights.

Regards,

Jonathan