philosophy of math and science

garam_kuta wrote:hahaba... watching epix channel all night, eh?





ps: punctuation reeks of...

not(not(something)) wrote:hi guys.

i wish to discuss philosophy arising out of the following subjects:

- godel's theorems (related cantor, turing, chaitin, uncertainty, theory of everything, bell's theorem, other no-go theorems in physics and those theorems, in different sciences, that are yet to be discovered as a fallout of godel/tarski theorems )
- EPR -- quantum mechanics interpretations (not math)
- random -- algorithmic and chaitin, rational/irrational #s
- all old paradoxes (sorites, causality, zeno, quantum zeno or turing paradox) 
- philosophy of logic (logic vs random, reason vs intuition, epistemology)

i am not interested in discussing numbers and equations because i cannot (i have forgotten calculus and i never liked it) or discrete math or physics equations. i am interested only as a layman in a general or theoretical sense. the reference point of my knowledge, and thus the discussion, i guess, would be wikipedia (wiki is actually technical and frighteningly detailed and accurate). it does not matter if you are wrong -- your interest in the subject, willingness to learn and argue with a layman like me, for kicks, is all that would matter. because i will not be able to get too technical, i am avoiding the stack exchanges. also, the response time there would be slower i think and not in the spirit of a discussion. for learning (as opposed to discussing), wikipedia is more than enough.

not(not(something)) wrote:hi kris.

you are a banker. so, i think, you would be exposed to actuarial sciences. plus you have a good general knowledge; so you would anyway know a bit about all the subjects above. 

ok, choose one subject:

- random sequences and philosophy of logic
- crazy interpretations in quantum mechanics
- thermodynamics, the arrow of time and inductive reasoning

(i would choose the first because it is what i am wrapped up with at the moment but you are free to choose. once you choose, i shall initiate.)

Rashmun wrote:i am interested in the second and third topics, and would like the discussion to begin with the third one (thermodynamics). Specifically, with a discussion about the second law of thermodynamics and how it pertains to evolution, protein folding, and possibly some other subjects. for obvious reasons it would be good if Max participates in this discussion.

not(not(something)) wrote:hi kris.

you are a banker. so, i think, you would be exposed to actuarial sciences. plus you have a good general knowledge; so you would anyway know a bit about all the subjects above. 

ok, choose one subject:

- random sequences and philosophy of logic
- crazy interpretations in quantum mechanics
- thermodynamics, the arrow of time and inductive reasoning

(i would choose the first because it is what i am wrapped up with at the moment but you are free to choose. once you choose, i shall initiate.)

not(not(something)) wrote:

Rashmun wrote:i am interested in the second and third topics, and would like the discussion to begin with the third one (thermodynamics). Specifically, with a discussion about the second law of thermodynamics and how it pertains to evolution, protein folding, and possibly some other subjects. for obvious reasons it would be good if Max participates in this discussion.

good. you are considered as someone hard to convince, so it should be fun discussing these issues with you. 

my ideas would keep converging to the godel incompleteness theorems. so, it might help if you read up on them: incompleteness theorems

having the incompleteness theorems would be a useful reference point because if we disagree, we can hopefully see where or why we are disagreeing by applying the theorem. 

here is the subject which is interesting in thermodynamics:

a) the arrow of time in thermodynamic is created entirely by inductive reasoning (true?). 
b) then time (or spacetime) is irreversible is based on an assumption (inductive reasoning) that could be false (true?). 
c) then travel back in time is a limitation of our assumption (inductive reasoning) and not the physical or observed reality (true?).

note: if you have any difficulty understanding the godel theorems, then we can tackle that first and i would be happy to help you understand them.

Kris wrote:

not(not(something)) wrote:hi kris.

you are a banker. so, i think, you would be exposed to actuarial sciences. plus you have a good general knowledge; so you would anyway know a bit about all the subjects above. 

ok, choose one subject:

- random sequences and philosophy of logic
- crazy interpretations in quantum mechanics
- thermodynamics, the arrow of time and inductive reasoning

(i would choose the first because it is what i am wrapped up with at the moment but you are free to choose. once you choose, i shall initiate.)

>>>Sorry about the late response. I will choose the first.

Kris wrote:

>>>Sorry about the late response. I will choose the first.

Rashmun wrote:

before discussing the applications of thermodynamics, can we get some clarity on what is meant by "order" and "disorder" (denoted by the word "entropy") with respect to the second law of thermodynamics.

not(not(something)) wrote:

Kris wrote:

>>>Sorry about the late response. I will choose the first.

our replies might take time because we both lead busy lives -- so no need to apologize. we may also lose interest or get stuck. but, for as long as the discussion sustains, i feel it will be worth it.

ok, i guess i will first test if you understand the laws of probability:

have you ever wondered how an infinite sequence of a fair coin tosses, or n number of events in a sequence (provided n is sufficiently large), reveals a normal pattern? let us represent the tosses as an infinite sequence of 0s and 1s where 1 = heads of a fair coin and 0 = tails of it. so as per probability laws, an infinite sequence of these tosses, represented as an infinite sequence of a binary number, will be perfectly "normal." normal means that the n events will have roughly the same numbers of 0s and 1s. an infinite sequence will go further: it will have the same number of any sequence present in that sequence.

but how does a coin, hypothetically tossing on a table, know that it has to normalize after a sufficiently large number of events? where does the coin store the data it needs to continually refer to to normalize?

kris wrote: I guess I am grappling with the idea here that randomness, itself, paradoxically acquires a  pattern over the long run.

not(not(something)) wrote:

kris wrote: I guess I am grappling with the idea here that randomness, itself, paradoxically acquires a  pattern over the long run.

yes, you are absolutely right. the formal definition of randomness contains a paradox. yet, this is nothing surprising for science has plentiful such paradoxical definitions and whenever we struggle with one, we are warned that the theorem/axiom might seem "counterintuitive." 

i will return to this later in the day. it might be worth investigating why we had to define it this way. 

hopefully, as we go through this, you might have some insights to offer that would be equally worth investigating (my purpose of discussing this issue). so, it is all just for fun.

what was your confusion about bell curves? did you get a satisfactory answer?

Idéfix wrote:The nature of truth and reality is an interesting topic for these times. 


Is this the new normal, or will we get back to some degree of shared understanding of facts?

Kris wrote:
 On the bell curve, I was intrigued by the idea of distributions from disparate areas of life all falling into a certain (bell) pattern, where you would expect randomness. The guy who taught the class was the one who initially pointed this out, but we later explored other types of distributions as well. 

• [randomness] the Financial crisis of 2007–2010, and four years before the Flash crash of May 2010, during which the Dow Jones Industrial Averagehad a 1,000 point intraday swing within minutes,[8] Mandelbrot and Nassim Taleb published an article in the Financial Times arguing that the traditional "bell curves" that have been in use for over a century are inadequate for measuring risk in financial markets, given that such curves disregard the possibility of sharp jumps or discontinuities. Contrasting this approach with the traditional approaches based on random walks, they stated:[9] We live in a world primarily driven by random jumps, and tools designed for random walks address the wrong problem. Mandelbrot and Taleb pointed out that although one can assume that the odds of finding a person who is several miles tall are extremely low, similar excessive observations can not be excluded in other areas of application. They argued that while traditional bell curves may provide a satisfactory representation of height and weight in the population, they do not provide a suitable modeling mechanism for market risks or returns, where just ten trading days represent 63 per cent of the returns of the past 50 years.
  
  

not(not(something)) wrote:

Kris wrote:
 On the bell curve, I was intrigued by the idea of distributions from disparate areas of life all falling into a certain (bell) pattern, where you would expect randomness. The guy who taught the class was the one who initially pointed this out, but we later explored other types of distributions as well. 

-------------------------------

• ------ Mandelbrot and Taleb pointed out that although one can assume that the odds of finding a person who is several miles tall are extremely low, similar excessive observations can not be excluded in other areas of application. .....
  
  >>>>>This was the gist of my problem when I was first exposed to Bell curves. 
  
  

We are familiar with only that randomness that is computable like the decimal expansions of algebraic irrationals, pi, log normals. so, in a sense, there is nothing random about randomness (or random sequences in arithmetic). if we move from this point in the informal definition of randomness to the other end, i.e. uncomputable or pure randomness, then everything is random about those random sequences, but, they are absolutely impossible to generate (to the extent that one can wonder if the existence of such randomness is at all a valid premise... constructivists think not).normal (except in retrospect on n digits of the number sequence). 

>>>>> I am having trouble with the first idea of randomness above. The latter (bolded section above) seems to be the appropriate definition of randomness. I will read up more and come back to this and come back to this in a day or tow. I am in India now and am in the midst of refinancing of a property and neck deep in procedures, much of which does  not seem to make any sense (speaking of randomness:)

Kris wrote:

>>>>> I am having trouble with the first idea of randomness above. The latter (bolded section above) seems to be the appropriate definition of randomness. 

I will read up more and come back to this and come back to this in a day or tow. I am in India now and am in the midst of refinancing of a property and neck deep in procedures, much of which does  not seem to make any sense (speaking of randomness:)

MaxEntropy_Man wrote:since you mentioned you want to discuss something interesting in another thread, and posted a long list most of which i am not that deeply familiar. but two on the list is something i can discuss:

a) time's arrow as evidenced by the second law of thermodynamics. my question -- why did you say the proof was inductive?
b) uncertainty (or fluctuations) in QM.  my question to you is whether you know that this uncertainty is fundamental and intrinsic to nature itself and is not attributed to some measuring error.

MaxEntropy_Man wrote:since you mentioned you want to discuss something interesting in another thread, and posted a long list most of which i am not that deeply familiar. but two on the list is something i can discuss:

a) time's arrow as evidenced by the second law of thermodynamics. my question -- why did you say the proof was inductive?
b) uncertainty (or fluctuations) in QM.  my question to you is whether you know that this uncertainty is fundamental and intrinsic to nature itself and is not attributed to some measuring error.

https://www.quora.com/Does-the-Godel-incompleteness-theorem-explain-the-Heisenberg-uncertainty-principle wrote:
Karl Svozil reports in his book, Randomness and Undecidability in Physics, p. 112, that Gregory Chaitin asked John Wheeler about the relationship between Gödel’s Theorem and Heisenberg’s Uncertainty Principle. According to Svozil, Chaitin recalls:

[[In 1979]] I went up to [[John Archibald]] Wheeler and I asked him, “Prof. Wheeler, do you think there's a connection between Godel's incompleteness theorem and the Heisenberg uncertainty principle?” Actually, I'dheard that he did, so I asked him, "What connection do you think there is between Godel's incompleteness theorem andHeisenberg's uncertainty principle?" This is what Wheeler answered.
He said, "Well, one day I was at the Institute for Advanced Study, and I went to Gödel’s office, and there was Gödel ...” I think Wheeler said that it was winter and Gödel had an electric heater and had his legs wrapped in a blanket. Wheeler said, “I went to Gödel, and I asked him, ‘Prof. Gödel, what connection do you see between your incompleteness theorem and Heisenberg’s uncertainty principle?’ ” I believe that Wheeler exaggerated a little bit now. He said,"And Gödel got angry and threw me out of his office!” Wheeler blamed Einstein for this. He said that Einstein had brain-washed Gödel against quantum mechanics and against Heisenberg’s uncertainty principle!

As Svozil points out, “several attempts have been made to translate mathematical undecidability into a physical context”. See his book chapter 9.
Cristian Calude and Michael Stay wrote a paper “From Heisenberg to Gödel via Chaitin.” So, there is a good reason to dig for the relationship between these two deep and fundamental results.

https://www.quora.com/Does-the-Godel-incompleteness-theorem-explain-the-Heisenberg-uncertainty-principle wrote:
Karl Svozil reports in his book, Randomness and Undecidability in Physics, p. 112, that Gregory Chaitin asked John Wheeler about the relationship between Gödel’s Theorem and Heisenberg’s Uncertainty Principle. According to Svozil, Chaitin recalls:

[[In 1979]] I went up to [[John Archibald]] Wheeler and I asked him, “Prof. Wheeler, do you think there's a connection between Godel's incompleteness theorem and the Heisenberg uncertainty principle?” Actually, I'dheard that he did, so I asked him, "What connection do you think there is between Godel's incompleteness theorem andHeisenberg's uncertainty principle?" This is what Wheeler answered.
He said, "Well, one day I was at the Institute for Advanced Study, and I went to Gödel’s office, and there was Gödel ...” I think Wheeler said that it was winter and Gödel had an electric heater and had his legs wrapped in a blanket. Wheeler said, “I went to Gödel, and I asked him, ‘Prof. Gödel, what connection do you see between your incompleteness theorem and Heisenberg’s uncertainty principle?’ ” I believe that Wheeler exaggerated a little bit now. He said,"And Gödel got angry and threw me out of his office!” Wheeler blamed Einstein for this. He said that Einstein had brain-washed Gödel against quantum mechanics and against Heisenberg’s uncertainty principle!

MaxEntropy_Man wrote:to understand very basic issues in quantum mechanics and the nature of uncertainty i could do no better than recommend watching the first lecture of prof balakrishnan's quantum physics lecture series which IIT-M has posted on youtube. the first lecture is for a lay audience. no great grasp of advanced mathematics necessary.

not(not(something)) wrote:

Kris wrote:

>>>>> I am having trouble with the first idea of randomness above. The latter (bolded section above) seems to be the appropriate definition of randomness. 

I found it easier to understand which-way-is-up with the help of real numbers but that doesn’t mean it is the only way. 

I will read up more and come back to this and come back to this in a day or tow. I am in India now and am in the midst of refinancing of a property and neck deep in procedures, much of which does  not seem to make any sense (speaking of randomness:)

I hope refinance means lower rates. I think current rates are not going to be lowered for some time. Our method of calculating inflation changed last year and from only-commodities, it has partly moved to cost of services like education, medicine and housing. The latter relentlessly keep getting costlier. I find Kotak the best bank locally. I am a big fan of Uday Kotak. Vijay Sharma, of Paytm, is next. With Softbank and Alibaba behind him, he has infinite source of funds and intends to take over banking and credit cards. But then close on his heels is blockchain banking. Of course, Uday Kotak could adopt blockchain and thus beat both. So, the future is always unpredictable.

Kris wrote:

>>>>Unfortunately, I have not been able to do much comparison shopping, due to time constraints. My loan now is with ICICI which the builder cajoled me into 4 years ago. In fairness, I went along with it, because I knew some people there and had to wrap it up within a couple of weeks. Due to the short tenure and the high int rate, my game plan as of last month was to do some cash out on a refinance on my rental property in the US and pay this loan off. The US $ is substantially cheaper in the near term. Since I am hoping to sell this India rental and repatriate the funds within 2 to 3,maybe 4, years, I don't think a rupee slide, as a worst case scenario, will still make the US option a less viable option. Still, I am going to grin and bear it with the refi locally in India, because of the logistics involved with the  US $ option, which I will be required to orchestrate. The process is laborious as it is. I need to read up more on random numbers. As I mentioned previously, my knowledge is at best at a layman's  level. Happy new year to you and your family.

 pure randomness is only a "good idea." -- it does not exist.