Mathematics, Shaken but not Stirred by Kevin H Knuth

Hope I didn't gush too much Kevin...

But I really like that your more down to Earth approach yields similar answers as a more wildly open-ended version of reality might. I think I'll probably read this essay again for detail, even though I've already given my rating. Good luck in the contest.

Best,

JJD

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

Kevin. Thanks for your post on mine. I copy me response below;

Kevin,

Thanks, but it clearly DOES "apply to objects"! Galaxies down to snowflakes, grains of sand & atoms, so not so easily dismissed! You must keep Booleing at higher orders! I also agree the 2nd 'Born rule' case, and please now sit down and prepare to be shocked; describe a physical interaction sequence that produces BOTH complex amplitudes!!. You can't dismiss that either (though most run away) as it's entirely self apparent, just a bit complex to first follow! You just have to try. (the 'fast & furious' solutions are just derivatives of this!); I'll outline it now;

Consider absorption/re-emission by polariser and photomultiplier electrons as momentum exchange at some tangent point on a sphere with and angle of 'Latitude' (0-90 degrees) from a pole. 'Entanglement' is just a common spin axis orientation to each PAIR.

Now look at electron (etc) OAM for 'exchange' (on absorption/re-emission); it has TWO momenta sets!;; Polar CURL, 0 at the equator, and LINEAR, 0 at the poles. What's more these change non linearly, AND INVERSELY! by the cosine of the tan point latitude angle.

So the RE-EMISSION POLARITY and 'ELLIPTICITY' are changed at the polariser, by CosTheta. Now we have the Photomultiplier electrons to interact with. (if the hairs on the back of your neck aren't starting to stand up read the above gain!)

The cos value amplitude is then changed by the LOCAL cos value 'vector addition' again, giving Malus' Law, or the 'Born rule'!! In the 2 channel/magnet case best think of it as elliptical polarity, where only the major axis amplitude can trip the *click* counter.

Now all that was in my essay last year but your brain rejected it (as most, due to cognitive dissonance.). It's been independently verified as violating Bells inequalities by computer code & plot I refer to. And it does NOT REQUIRE 'NON-LOCALITY'! Bob changes only his own state by rotating his dial (electrons).

You may need to read & visualise that 'DFM' sequence carefully 3-5 times before it displaces the old embedded nonsense beliefs about QM.

Nature Physics have been wrestling with the shock and a decision on a joint paper for a few weeks. I expect it to be among the 99.9% they reject, but it may need a professor who can understand it to join the collaboration. Will you be the first?!

My Email is pj.ukc.edu@physics.org

Very best

Peter

p.s. Great to see your essay seems to have sneaked in as one of the 40 finalists. It was up to 6.4 after my score. I see it slipped again, but just, deservedly, hung on. Something really must be done about the trolling with 1's. I didn't give out any but seemed to get around 6!

It looks like we both made it by a hair...

But either way, I'm glad we got a chance to interact this round, professor Knuth. I'd be pleased if we can continue the conversation. I'm tempted to give a brief explanation of the entropy and non-locality connection now. But I'd better leave off here. I get up to Albany from time to time, if you would care to meet in person at some point.

All the Best,

Jonathan