Dave Keirsey.com Blog#11 A Brilliant Mistake

[keirsey]

Issac Newton, a Mastermind Rational

A Brilliant Mistake

[shytiger]

One thing you might mention is that Newton more or less got the idea of continuous motion from the Greeks. Philosophers like Zeno objected to the idea. Also, a precise definition of continuity was not developed till the 18th century, so Newton was basically dealing with infinitesimals (and had a nasty, non-rigorous way of calculating with them).

Loop quantum gravity is an interesting attempt to do away with continuous background spacetime. I'm in the Newton camp on this. I personally find the whole idea of developing a theory from philosophical notions to be backwards. Give me data!

[keirsey]

Loop quantum gravity is an interesting attempt to do away with continuous background spacetime. I'm in the Newton camp on this. I personally find the whole idea of developing a theory from philosophical notions to be backwards. Give me data!

I guess I am straddling the fence here. I see it important to "work it" from both ends. Give me data! and let me think about it.... Both sides have their strengths and weaknesses. Clearly the "wave" and "particle" metaphors do not suffice. I am of the camp (probably by myself) that concepts such as "mass," "energy," "space," "time," "spacetime," "in," "out," "large," "small," "finite," "infinite" are too ambiguous and simple, even in equation form.

The mathematicians have many fundamentally different (at least 20) definitions of "space" and many different notions of "equivalent" -- this is a mess -- and we have no systemic way of attaching them to physics, other than "philosophy"(random models) -- which I agree is not very scientific.

[shytiger]

Loop quantum gravity is an interesting attempt to do away with continuous background spacetime. I'm in the Newton camp on this. I personally find the whole idea of developing a theory from philosophical notions to be backwards. Give me data!

I guess I am straddling the fence here. I see it important to "work it" from both ends. Give me data! and let me think about it.... Both sides have their strengths and weaknesses. Clearly the "wave" and "particle" metaphors do not suffice. I am of the camp (probably by myself) that concepts such as "mass," "energy," "space," "time," "spacetime," "in," "out," "large," "small," "finite," "infinite" are too ambiguous and simple, even in equation form.

The mathematicians have many fundamentally different (at least 20) definitions of "space" and many different notions of "equivalent" -- this is a mess -- and we have no systemic way of attaching them to physics, other than "philosophy"(random models) -- which I agree is not very scientific.

I do think very intensely, when starting on a project, about what things are.

For example, take prime numbers. What ARE they? I am still trying to figure this out. The standard definition is that they are numbers divisible by only one and themselves, but that doesn't explain why one number is prime and another number is not prime. One interpretation is that they are the atoms of numbers. But why is 7 prime and 9 not? I guess you could ask why oxygen is an element and water is not. Is there a deep reason for it? I guess my goal here is not to come up with THE answer but just to find an interpretation that is more useful than the standard dogma. So in thinking about those concepts like spacetime my goal is to understand it from enough points of view that I can safely break the rules or find a path that hasn't been thought of.

[keirsey]

For example, take prime numbers. What ARE they? I am still trying to figure this out.

Same here.

One of approaches I am taking is to look at the Monster Group (and the six pariahs). Particularly there is something interesting about the prime factors of the Monster Group, they -- the 15 -- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 and if you include one of either 1 or 0, that adds up to 16, which is the same number of boolean binary operators. Given that those 15 are supersingular primes (their genus is 0), I am wondering if there is a casual and more specifically what is the precise (logical) connection to the boolean binary operators. So, I am been looking at WHAT KINDS OF PRIMES are there. The physics connection is along the lines of Monstrous Moonshine.

Understanding the coding and decoding of the various primes (such as Mersenne primes, irregular primes, regular primes, twin primes, Chern primes, factorial primes, ...) and of course, understanding prime ideals and prime elements are important. I would like to have a program that given a prime it gives me the genus of that prime -- that would be very interesting to see. I suspect various forms of "time" (as a lifetime of an physical entity -- or path) serve as these prime "times."

[Sagathiest]

clearly there are some very basic connections between logic and mathematics. What I find is that often as I begin analysing things I have a set of general propositions which as deductions are drawn seem to lead more and more into mathematical terminology. So that very often I feel as if I'm close to defining variables and preceding into some of sort of quantifiable analysis. The problem being that there are a great many things which we have some knowledge of and are well described by the language of maths, but lack any observable identity and thus cannot be quantified.

Correct me if i'm off base but it seems to me that the first and most necessary step to precede with an applied mathematical analysis is too have an identifiable set of things, which can be measured and thus quantified. When this is done its easy to establish a relationship amongst the data which has been collected its simply a matter of time spent piecing it together. But from the philosophical end what seems to happen is that a hypothetical relationship has already been established by speculative logical deduction. The process of which involves identifying entities, thinking through the possible ways they interact and developing a hypothetical relationship/model.

so anyway the way I understand the process of experimental natural philosophy/science is too

observe--Identify--logical speculation--hypothesis---quantify/measure/collect data--establish relationship--logical speculation/analysis--new hypothesis...etc.

clearly you can retool this in a few ways. Now its important to think about this both at an individual level and at a specialised societal level.

so the role of philosophical deduction in the process of science is simply to establish a likely hypothesis, correct for weaknesses in data, alternative explanations, which leads to improvement in models etc.

I quite enjoyed reading Alfred North White heads book called the Adventure of Ideas,(co-author with Bertrand Russell Principia mathematica) which argued that speculation and observation were the two most important processes in the development of the human intellect across time.

[Sagathiest]

I suspect various forms of "time" (as a lifetime of an physical entity -- or path) serve as these prime "times."

Just an example of deductive speculation.

[keirsey]

I suspect various forms of "time" (as a lifetime of an physical entity -- or path) serve as these prime "times."

Just an example of deductive speculation.

Yes.

Although I do think I have a hint of a systemic method of analysis, synthesis, and observation -- that is what my "Formatics" (Relational Science, Comparative Complexity) is all about. Unfortunately I am not able to explain it coherently enough at this time, but hope to in the next decade. The key is combining structural reasoning (such as I am doing above) and a more functional approach, more like Rosen, but still different. Keirsey's game is one attempt to start at the purely functional end. I want to do something similar except maybe start with some forms of "time" "space" "energy" and "mass" as my four functional Hegelian-Keirsey concepts,

[Sagathiest]

I suspect various forms of "time" (as a lifetime of an physical entity -- or path) serve as these prime "times."

Just an example of deductive speculation.

Yes.

Although I do think I have a hint of a systemic method of analysis, synthesis, and observation -- that is what my "Formatics" (Relational Science, Comparative Complexity) is all about. Unfortunately I am not able to explain it coherently enough at this time, but hope to in the next decade. The key is combining structural reasoning (such as I am doing above) and a more functional approach, more like Rosen, but still different. Keirsey's game is one attempt to start at the purely functional end. I want to do something similar except maybe start with some forms of "time" "space" "energy" and "mass" as my four functional Hegelian-Keirsey concepts,

Cool.

I think its very possible to do some incredibly interesting stuff with completely abstract concepts. Spinoza's Ethics are very abstract and follow a completely deductive axiomatic method. Some people would reject him simply on the basis that his axioms are not empirical, but when you see what he achieved it is very difficult as a rational not to appreciate and stand in awe of such a system. I think it would be foolish to say that there were no truths present in his conclusions.

The idea of something which is a synthesis between that and observation/experimentation is very appealing to me. In short i would love to take the strengths of all forms of reasoning and investigation and concentrate them into a balanced systematic method-formula. Now whether balance between each form or specialisation is superior is a question that would be fun to address. personally I have always favoured diversification over specialisation as a means to reaching a certain pinnacle of knowledge although I think that the different peaks all have there unique perspectives, but eventually converge upon one another given sufficient time.

[shytiger]

For example, take prime numbers. What ARE they? I am still trying to figure this out.

Same here.

One of approaches I am taking is to look at the Monster Group (and the six pariahs). Particularly there is something interesting about the prime factors of the Monster Group, they -- the 15 -- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 and if you include one of either 1 or 0, that adds up to 16, which is the same number of boolean binary operators. Given that those 15 are supersingular primes (their genus is 0), I am wondering if there is a casual and more specifically what is the precise (logical) connection to the boolean binary operators. So, I am been looking at WHAT KINDS OF PRIMES are there. The physics connection is along the lines of Monstrous Moonshine.

Interesting. This is an example of one of the many patterns math. As one of my profs used to say, "math is man-made" so it all depends on what you can do with it.

My current approach to the primes is algorithmic. I see the Sieve of Eratosthenes as being a recursive algorithm acting on the natural numbers. Because it is recursive, i.e. when you remove multiples of 2 you also remove multiples of 2 and 3 like 6, 12, 18, so when you get to removing multiples of 3 you have to "skip" those (at least in my approach to the algorithm which is more theoretical than practical). You have to "know" that you removed those multiples of 2 already so there is information communicated from one step to the next. The complexity of the primes comes precisely from the recursive nature of the sieve. Thus, one might understand a great deal about the natural numbers by studying various recursive algorithms for removing them.