The problem of Self-Referential systems

[Sherlock Holmes]

Yes, I totally agree with that. I am not saying that simple is better than complex. I am saying that simple is more fundamental than complex.

You're wandering around in the dark, tell me, what does "complex" or "simple" mean to you and what does "more fundamental" mean? why is it "better"?

 

[Write4U]

You're wandering around in the dark, tell me, what does "complex" or "simple" mean to you, and what does "more fundamental" mean? why is it "better"?

Did you read post #59 ?

With the terms I used, I meant the exact meaning as defined in dictionaries. No hidden implications intended.

 

[phyti]

Write4U;

Pi refers to something that does not physically exist in nature.

If nature includes human life forms, then pi is an abstract concept in the brain, which refers to the ratio of circumference to diameter, other abstract concepts in the brain.
That is all human knowledge can be, abstract concepts representing the physical reality outside the brain. The brain and its neural network is physical. The world as it exists in the mind is perception, which may or may not agree with the world outside.
If nature excludes human life forms, then what purpose would pi serve?

Therefore, according to Occam's Razor, the least complex valid explanation should be the preferred perspective.

Most human thought prefers the simplest explanation as a first approximation, to get initial understanding, then make refinement as needed. How many times in history we hear, "it's more complicated than we originally thought'.

Perhaps the fault of clarity is mine.

When you say 'time', I'm not aware you have a definition different from clock time.

We now know that the simple egg (single-celled organism) came before the complex chicken.

Who is 'we'?
In the case of reproduction via male and female, both contribute. The development of embryos requires genetic code from both.
For most animal species and humans, the parent body produces eggs, which develop within the body until birth. For birds, the egg is expelled to complete development outside the body. It is still a life form producing a copy of itself, with the egg an intermediate state.
A process more complex than the egg.
An additional question.
What is the source of DNA or genetic code?

 

[Sherlock Holmes]

Did you read post #59 ?

With the terms I used, I meant the exact meaning as defined in dictionaries. No hidden implications intended.

Which dictionary? My question is your opportunity to elaborate, explain in more detail, that's what I'm asking you to do, explain in more detail.

 

[phyti]

Write-4U;

Alternate theory to big bang.

The universe began as an astronomically large field of dormant elements.
The field was exposed to a source of energy, resulting in composition of more complex elements and random outward motions.
This scenario doesn't require an initial super-fast expansion from a point and leaves a small residual expansion.

 

[Write4U]

Which dictionary? My question is your opportunity to elaborate, explain in more detail, that's what I'm asking you to do, explain in more detail.

Do you want an explanation of the "the whole is greater than the sum of its parts"? Read Aristotle.

Would you agree that a molecule is more complex than an atom? And how is it that when you assemble a large collection of H2O molecules the pattern acquires a character of "wetness", an emergent property.

What is water, or ice ? Collections of H and O atoms in a pattern that is liquid or solid depending on temperature, no? H2O molecules are not wet!

 

[Write4U]

Write-4U;

Alternate theory to big bang.

The universe began as an astronomically large field of dormant elements.
The field was exposed to a source of energy, resulting in composition of more complex elements and random outward motions.
This scenario doesn't require an initial super-fast expansion from a point and leaves a small residual expansion.

Yes, but it has been established that there was a super-fast expansion from a singularity. It has been named the "Inflationary Epoch" and the echoes of this event are still measurable.

While things could have happened the way you speculate, there is no evidence for that, and by Occan's Razor, etc........

 

[Write4U]

If you win the lottery it's just a coincidence.
....
The reality is, they don't and can't know, and make it up as they go.
Truth will never be decided by an opinion poll

"Discovery " is not opinion or making-it-up. It is somewhat like winning the lottery.
But instead of money the result of discovery is gain in "knowledge". The exact opposite of speculation.

It is by utilizing mathematics that we discover how the universe works and can test hypotheses, which reduces the uncertainty in the findings considerably.

Mathematics is self-referential (equations)!

Name me one axiomatic natural phenomenon or artificial pattern that does NOT involve a generic (algebraic) mathematical equation that can be symbolized with human maths.

At some point you must admit that unless you invent a mysterious unknowable force, we have this universe pretty well figured out, granting that there are still gaps in our knowledge. But those gaps are due to our current inability to measure things that are too large (event horizon) or too small (quantum). But even that territory is already being explored. The discovery of the Higgs boson was a major triumph for applied mathematics.

 

[Write4U]

If nature includes human life forms, then pi is an abstract concept in the brain, which refers to the ratio of circumference to diameter, other abstract concepts in the brain.
That is all human knowledge can be, abstract concepts representing the physical reality outside the brain. The brain and its neural network is physical. The world as it exists in the mind is perception, which may or may not agree with the world outside.

You're just stuck on humans, aren't you? Without humans, the world would still be there and work exactly as it does now.

If nature excludes human life forms, then what purpose would pi serve?

It's an axiom! It exists in and of itself. It's an abstract self-referential equation, a universal constant.
https://www.mathsisfun.com/geometry/circle.html

 

[exchemist]

You're just stuck on humans, aren't you? Without humans, the world would still be there and work exactly as it does now.
It's an axiom! It exists in and of itself. It's an abstract self-referential equation, a universal constant.
https://www.mathsisfun.com/geometry/circle.html

π is a number.

It is not an "equation".

It is not an "axiom".

It is a number.

The definition of π in terms of the ratio of the circumference of a circle to its diameter is not universal. It applies only in Euclidean geometry. The geometry of spacetime is not Euclidean.

π does appear in a non-geometrical way in Euler's relation: exp(iπ) -1 =0. This relation is entirely abstract.

 

[phyti]

You're just stuck on humans, aren't you? Without humans, the world would still be there and work exactly as it does now.
It's an axiom! It exists in and of itself. It's an abstract self-referential equation, a universal constant.
https://www.mathsisfun.com/geometry/circle.html

I'm considering human experience.
It's human curiosity that wants to know how the world works.
It's human conceptualization of axioms and postulates that form the basis of knowledge, just like the sources you refer to. Mathematics is a language of human origin, and only meaningful to humans.
The universe did exist before humans, and still exists independently of humans.

 

[Write4U]

π is a number.

It is not an "equation".

It is not an "axiom".

It is a number.

The definition of π in terms of the ratio of the circumference of a circle to its diameter is not universal. It applies only in Euclidean geometry. The geometry of spacetime is not Euclidean.

π does appear in a non-geometrical way in Euler's relation: exp(iπ) -1 =0. This relation is entirely abstract.

Thank you for the clarification.

Question: Aside from the human symbolic representation, does the "value" exist in the abstract?

ax·i·om, noun

1. a statement or proposition which is regarded as being established, accepted, or self-evidently true.

MATHEMATICS

2. a statement or proposition on which an abstractly defined structure is based.

The number Pi, denoted by the Greek letter π - pronounced 'pie', is one of the most common constants in all of mathematics.

p.s. AFAIK, Pi does not only pertain to circles. It also applies to the laws of probability.

 

[Write4U]

Mathematics is a language of human origin, and only meaningful to humans.

That's a very limited interpretation of natural mathematics. Mathematics is inherent in all universal dynamics.

The universe did exist before humans, and still exists independently of humans

Yes, and it had mathematical properties from the very beginning. Mathematics exist independent of human symbolic representations. Reality is based on mathematical values (patterns) and processes (algebraic functions).

All orderly patterns are mathematical in essence.

Abstraction (mathematics)

Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.[1][2][3][4] Two of the most highly abstract areas of modern mathematics are category theory and model theory.[4]

Description

Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures. For example, geometry has its origins in the calculation of distances and areas in the real world, and algebra started with methods of solving problems in arithmetic.

Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract.

For example, the first steps in the abstraction of geometry were historically made by the ancient Greeks, with Euclid's Elements being the earliest extant documentation of the axioms of plane geometry—though Proclus tells of an earlier axiomatisation by Hippocrates of Chios.[5]

In the 17th century, Descartes introduced Cartesian co-ordinates which allowed the development of analytic geometry. Further steps in abstraction were taken by Lobachevsky, Bolyai, Riemann and Gauss, who generalised the concepts of geometry to develop non-Euclidean geometries. Later in the 19th century, mathematicians generalised geometry even further, developing such areas as geometry in n dimensions, projective geometry, affine geometry and finite geometry. Finally Felix Klein's "Erlangen program" identified the underlying theme of all of these geometries, defining each of them as the study of properties invariant under a given group of symmetries. This level of abstraction revealed connections between geometry and abstract algebra.[6]

In mathematics, abstraction can be advantageous in the following ways:

• It reveals deep connections between different areas of mathematics.
• Known results in one area can suggest conjectures in another related area.
• Techniques and methods from one area can be applied to prove results in other related areas.
• Patterns from one mathematical object can be generalized to other similar objects in the same class.

Bertrand Russell, in The Scientific Outlook (1931), writes that "Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say."[9]

https://en.wikipedia.org/wiki/Abstraction_(mathematics)#

 

[Write4U]

phyti said: ↑
Mathematics is a language of human origin, and only meaningful to humans.

Yes and "Universe" is a language of human origin and only meaningful to humans.

Are you suggesting that without humans the Universe does not exist?

On second thought, "Mathematics " is also meaningful to honey-bees. Ever heard of the honey-bee dance where a scout explains the precise location of a patch of blooming flowers.

Note the distance indicator.
Figure-eight-shaped waggle dance of the honeybee (Apis mellifera). A waggle run oriented 45° to the right of ‘up’ on the vertical comb (A) indicates a food source 45° to the right of the direction of the sun outside the hive (B). The abdomen of the dancer appears blurred because of the rapid motion from side to side.
A waggle dance consists of one to 100 or more circuits, each of which consists of two phases: the waggle phase and the return phase. A worker bee's waggle dance involves running through a small figure-eight pattern: a waggle run (aka waggle phase) followed by a turn to the right to circle back to the starting point (aka return phase), another waggle run, followed by a turn and circle to the left, and so on in a regular alternation between right and left turns after waggle runs. Waggle-dancing bees produce and release two alkanes, tricosane and pentacosane, and two alkenes, (Z)-9-tricosene and (Z)-9-pentacosene, onto their abdomens and into the air.[7]

Description

The direction and duration of waggle runs are closely correlated with the direction and distance of the resource being advertised by the dancing bee. In an experiment with capture and relocation of bees exposed to a waggle dance the bees followed the path that would have taken them to an experimental feeder had they not been displaced.[1] The resource can include the location of a food source or a potential nesting site.[8] For cavity-nesting honey bees, like the western honey bee (Apis mellifera) or Apis nigrocincta, flowers that are located directly in line with the sun are represented by waggle runs in an upward direction on the vertical combs, and any angle to the right or left of the sun is coded by a corresponding angle to the right or left of the upward direction. The distance between hive and recruitment target is encoded in the duration of the waggle runs.[1][9] The farther the target, the longer the waggle phase.

The more excited the bee is about the location, the more rapidly it will waggle, so it will grab the attention of the observing bees, and try to convince them. If multiple bees are doing the waggle dance, it's a competition to convince the observing bees to follow their lead, and competing bees may even disrupt other bees' dances or fight each other off. In addition, some open-air nesting honeybees such as the black dwarf honeybee (Apis andreniformis), whose nests hang from twigs or branches, will perform a horizontal dance on a stage above their nest in order to signal to resources.[10]

And now an interesting factoid.

Waggle dancing bees that have been in the nest for an extended time adjust the angles of their dances to accommodate the changing direction of the sun. Therefore, bees that follow the waggle run of the dance are still correctly led to the food source even though its angle relative to the sun has changed

https://en.wikipedia.org/wiki/Waggle_dance#

See, Mathematics and Astronomy are meaningful to the honey-bee, an insect!

 

[Write4U]

But perhaps an example of how the neural network connects the parts that allow for the self-referential sensory experience and control of motor functions, which rely heavily on self-referential differential equations present while processing variable data.

Imagine some 3+ billion years of sensory sophistication and chemical refinements, the evolution of a self-referential sensory biological pattern of ever greater sophistication and ability to self-analyze and engage in abstract thought and emotions.

Actually that's one a few true analogies in the OT.

A biological organism, risen from the prehistoric mud and acquiring self-awareness, via the parable of "eating the fruit of the tree of knowledge of good and evil", and conquer the world with technology that exceeds all the evolved tricks that other species of biological life enjoy.

And maybe our own self-referential demise ....

 

[exchemist]

Thank you for the clarification.

Question: Aside from the human symbolic representation, does the "value" exist in the abstract?

ax·i·om, noun

1. a statement or proposition which is regarded as being established, accepted, or self-evidently true.

MATHEMATICS

2. a statement or proposition on which an abstractly defined structure is based.

p.s. AFAIK, Pi does not only pertain to circles. It also applies to the laws of probability.

A number is not a proposition, any more than "blue" is.

 

[phyti]

Write4U;

Name me one axiomatic natural phenomenon or artificial pattern that does NOT involve a generic (algebraic) mathematical equation that can be symbolized with human maths.

They do since math is the shorthand language used to express the physical processes.
Every equation can be translated into words.

Question: Aside from the human symbolic representation, does the "value" exist in the abstract?

ax·i·om, noun
1. a statement or proposition which is regarded as being established, accepted, or self-evidently true.

MATHEMATICS
2. a statement or proposition on which an abstractly defined structure is based.

All values resulting from measurement are abstract. The act of measurement is a comparison of an object to an arbitrarily defined standard.
1. Accepted on faith, assumed true until found false.
2. Math is a manipulation of symbols (quoted from an unkown source).
(Even though 'math' is labeled as archaic, I prefer it over 'maths', which sounds like someone talking with their mouth full.)

pi is involved in the complex plane in the form of rotation.

u=e^(x+iy)

if x=0 and y=pi, u=-1

read last line of #71

 

[Write4U]

A number is not a proposition, any more than "blue" is.

IMO, both "numbers" and "words" are human symbolic representations of natural values.

Take the human symbols away and the "natural value" remains.

 

[Write4U]

read last line of #71

See #78

 

[Write4U]

What is the source of DNA or genetic code

Evolution by Natural Selection.

Let me remind you that:

DNA has three types of chemical component: phosphate, a sugar called deoxyribose, and four nitrogenous bases—adenine, guanine, cytosine, and thymine

Figure 2-1
Chemical structure of the four nucleotides (two with purine bases and two with pyrim-idine bases) that are the fundamental building blocks of DNA. The sugar is called deoxyribose because it is a variation of a common sugar, ribose, which has one more (more...)

https://www.ncbi.nlm.nih.gov/books/NBK21261/#

A very humble beginning gaining more complexity over time. There is still simple DNA around.

Dickinsonia was one of the first animals on Earth. It lived on the ocean floor 550 million to 560 million years ago. It looked like a giant version of the modern-day Trichoplax, the simplest animal now alive.

https://www.sciencenewsforstudents.org/article/living-mysteries-meet-earths-simplest-animal