The Meaning in Numbers

[Write4U]

Your replying to this plug shows again how little you understand of what people say.
EB

This comment shows your "intellectual resistance". I understand very well what people say. OTOH, some people like you, seem to have a problem understanding me.

Can't you grasp that the word "rock" is a human symbolic literary representation of a nameless universal object, a generic physical qualitative pattern?

Can't you grasp that the word "two" and the number (2) are human symbolic mathematical representations of a relationship between two nameless generic universal objects, a specific quantitative pattern?

The meaning of numbers for humans is that using symbolic language to identify and explain physical values and functions are human shortcuts, enabling us to understand these pre-existing, but otherwise nameless universal values and functions.

When are you going to read my posts with a little mental effort, instead of responding with your knee-jerk ad hominems.

 

[Yazata]

Is there any intrinsic meaning in numbers?

They are symbols used to symbolize quantity. And more abstract relationships, inspired by the relationships between quantities I guess. (I'm not sure what quantity imaginary numbers represent.)

There's a whole specialty of mathematics that examines what numbers are about: number theory.

So I don't think that there is any intrinsic meaning to the number symbols themselves. They are pretty much arbitrary and historically contingent.

But I do think that what we use them to symbolize is basic and fundamental to reality itself. They somehow capture some of reality's most interesting metaphysical properties.

 

[Yazata]

Is there any intrinsic meaning in anything?

I'm undecided.

I'm influenced by Charles Sanders Peirce's early (1860's) theory of signs. (Peirce was continually tinkering with his theory of signs throughout his life and produced several rather different versions at various points.)

https://plato.stanford.edu/entries/peirce-semiotics/

The earlier version is actually quite simple and common-sensical and the SEP outlines it this way:

"What we see here is Peirce's basic claim that signs consist of three inter-related parts: a sign, an object, and an interpretant. For the sake of simplicity, we can think of the sign as the signifier, for example, a written word, an utterance, smoke as a sign for fire etc. The object, on the other hand, is best thought of as whatever is signified, for example, the object to which the written or uttered word attaches, or the fire signified by the smoke. The interpretant, the most innovative and distinctive feature of Peirce's account, is best thought of as the understanding that we have of the sign/object relation. The importance of the interpretant for Peirce is that signification is not a simple dyadic relationship between sign and object: a sign signifies only in being interpreted. This makes the interpretant central to the content of the sign, in that, the meaning of a sign is manifest in the interpretation that it generates in sign users."

Which would suggest that there isn't any intrinsic between relationship between a number sign ('2' for example) and its object (the quantity two, pairs, metaphysical dyads or whatever it is). What's still needed is an interpretant that interprets the number 2 as a sign for its quantitative object. Different cultures may (and historically have) invented different number signs to represent whatever our '2' refers to. (What the objects of number signs actually are is still a metaphysical mystery.)

But it may be more complicated than that. Pierce was always chasing the complications which generated the later elaborations in this theory. The SEP again:

"Put simply, if we come to interpret a sign as standing for its object in virtue of some shared quality, then the sign is an icon. Peirce's early examples of icons are portraits and noted similarities between the letters p and b. If on the other hand, our interpretation comes in virtue of some brute existential fact, causal connections say, then the sign is an index. Early examples include the weathercock, and the relationship between the murderer and his victim. And finally, if we generate an interpretant in virtue of some observed general or conventional connection between sign and object, then the sign is a symbol. Early examples include the words 'homme' and 'man' sharing a reference."

So perhaps not all number signs should receive the same analysis. The Roman numeral 'II' might arguably be an icon of its mysterious dyadic object. While the numeral '2' would seem to be more of a symbol. So perhaps one could argue that the Roman numeral 'II' has more of an intrinsic number-meaning than our more familiar '2'.

 

[Write4U]

But I do think that what we use them to symbolize is basic and fundamental to reality itself. They somehow capture some of reality's most interesting metaphysical properties.

Can anyone come up with anything in physical or metaphysical reality that cannot be symbolized by mathematics?

I keep coming back to the basic understanding that the universe consists of Values and Functions which is present in all things as "potential" (that which may become reality).

In Nature, there are only physical and metaphysical permissions and restrictions and the mathematics of these permissions and restrictions becomes manifest as "patterns", both physical and metaphysical .

Human physics is just a human invented discipline codifying "potentials" and human mathematics is the language which codifies these universal values and functions and their resulting expressed patterns in reality.

This is why I intuitively tend to agree with Tegmark. His hypothesis of a Universe which is inherently mathematical in nature (essence), makes perfect logical sense to me.
3 fundamental physical particles, 32 numbers (relative values) and a "handfull" of equations (functions). Sounds like a doable program for a functional self-ordering system.....

All physical things are made from three fundamental values (electrons , quarks), and all meta-physical things are perfectly describable and provable as fundamental functions (forces) from their recurring identical phenomenal patterns.

If it works don't dispute it. Theoretically, if our mathematics are insufficient to explain a natural phenomenon, the fault lies with human mathematical limitation, not potential physical natural ability to follow natural mathematical permissions and restrictions based on "value and function" (inherent potential).

IOW, human "mathematics of values and functions" give human "meaning" to everything ......

We ask what the odds are of several earthlike planets in the greater universe.

But, what are the odds of the Fibonacci Sequence occurring often in a host of different phenomena? It's everywhere!!!

 

[arfa brane]

What are the consequences of making a unit distance into a line with a Euclidean length of $$ \sqrt 2 $$?

Or of finding a map from both a unit and $$ \sqrt 2 $$ to $$ \frac {\sqrt 5} 2 $$? We simply map numbers to numbers through addition or multiplication?

Another numerical question: what are the consequences of projecting the "north pole" on the sphere to infinity? What if the region around it goes there?

 

[Write4U]

What are the consequences of making a unit distance into a line with a Euclidean length of $$ \sqrt 2 $$?

Or of finding a map from both a unit and $$ \sqrt 2 $$ to $$ \frac {\sqrt 5} 2 $$? We simply map numbers to numbers through addition or multiplication?

Another numerical question: what are the consequences of projecting the "north pole" on the sphere to infinity? What if the region around it goes there?

Why are we doing these exercises in the first place, if we did not have a sense of meaning in the exercise?
The consequences apparently have some meaning to the experimenter, no?

Moreover, not all theoretical mathematics needs to be employed by the universe.
It functions in a much simpler chronological order of interacting values and functions.

Theory is for humans to understand the future implications (consequences, meaning) inherent in a dynamic hierarchical system of ordering values (mathematics).

 

[Write4U]

They are symbols used to symbolize quantity. And more abstract relationships, inspired by the relationships between quantities I guess. (I'm not sure what quantity imaginary numbers represent.)

Patterns.

Tests show that Lemurs are as adept at identifying "more" from "less" as humans. They don't count 1,2,3,4,.., but have the ability to compare "quantities" (numbers) as "patterns".
Even single-celled organisms can have a sense of "time" and anticipate certain recurring phenomena, such as a regular change (patterns) in environmental conditions.

In a mathematical universe, these imaginary (inate) abilities for abstract cognition of relative quantities (patterns, values, numbers) may be present at very fundamental levels, IMO.

 

[arfa brane]

What are the consequences of making a unit distance into a line with a Euclidean length of √2?

Or of finding a map from both a unit and √2 to √5/2?
We simply map numbers to numbers through addition or multiplication?

Another numerical question: what are the consequences of projecting the "north pole" on the sphere to infinity? What if the region around it goes there?

Some logical consequences: A topological unit can be stretched, because that's a legal move. In other words you can draw a nice neat looking polygon, then redraw it with edges of an arbitrary (but affine) length (make it into one of a possibly infinite set of topological equivalents).

To recover the regular graph or polygon, just weight the edges, or maybe fix the vertices and let the edges contract into nice straight lines.

If you project the point at the top of the sphere to infinity, it "takes" a circle with an infinite radius with it. If you project say, a square region as well, it takes a section of $$ S^2 $$ to infinity.

Topologically you project a spherical cap; if this cap is a section with unit length sides, the result is the plane quotiented by these sides (it has regular sides at infinity). The projection removes the section (its interior is at the same place as its boundary) but not its geometry, from the plane.

It might seem a bit tedious, but understanding projective spaces is a topological skill we need to understand to try to see some meaning in things like infinity, or a set of vertices fixed to the plane and connected by straight, or not-straight, lines.

So here we go again:






The projection preserves the geometry of the orange square; one way to think about the picture on the right is a projective view of the picture on the left, looking at the center of the white coloured face, or from underneath the projective plane, in which case the orange face is hidden.

The image is a square because each of its edges has a pair of lines which converge to a pair of parallel lines at infinity in the plane. So that lines from adjacent edges of the right hand image are perpendicular at infinity, and the geometry of the region also at infinity is a square with infinite sides. Hence the right hand image is as complete as the left hand one, it contains the same information.

Reconnect the lines on opposite edges and recover the sphere after some stretching and gluing.

 

[Write4U]

I've been thinking about Platonic solids and the questions about their abstract existence in nature.
IMO, Platonic solids are the symbolic representations of various patterns and their functional geography in nature.

Nowhere does it say that Platonic patterns have to become expressed as perfect symmetrical examples, but may be expressed as variants in practice, i.e. Circles, Ovals, Parabola, Ellipse, Eggshape.

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size) regular (all angles equal and all sides equal) polygonal faces with the same number of faces meeting at each vertex.

Five solids meet these criteria:


Tetrahedron, Four faces
(Animation)
(3D model)

Cube, Six faces
(Animation)
(3D model)

Octahedron, Eight faces
(Animation)
(3D model)

Dodecahedron, Twelve faces
(Animation)
(3D model)

Icosahedron, Twenty faces
(Animation)
(3D model)

Geometers have studied the Platonic solids for thousands of years.[1] They are named for the ancient Greek philosopher Plato who hypothesized in his dialogue, the Timaeus, that the classical elements were made of these regular solids. Their expressed patterns in nature.

https://en.wikipedia.org/wiki/Platonic_solid

These structures are found in nature in many disguises, from the very subtle to gross expression as patterns.
What is a snowflake?
List of Snowflake Shapes and Patterns,

Hexagonal plates are six-sides flat shapes. The plates may be simple hexagons or they may be patterned. Sometimes you can see a star pattern in the

center of a hexagonal plate.

Note that if you inflate the center equally in all directions, you end up with a perfect circle.

6. All Snowflakes Have Six-Sides, or "arms."
Snowflakes have a six-sided structure because ice does. When water freezes into individual ice crystals, its molecules stack together to form a hexagonal lattice. As the ice crystal grows, water can freeze onto its six corners multiple times, causing the snowflake to develop a unique, yet still six-sided shape.

7. Snowflake Designs Are a Favorite Among Mathematicians Because of Their Perfectly Symmetrical Shapes.
In theory, every snowflake nature creates has six, identically shaped arms. This is a result of each of its sides being subjected to the same atmospheric conditions, simultaneously.

However, if you've ever looked at an actual snowflake you know it often appears broken, fragmented, or as a clump of many snow crystals — all battle scars from colliding with or sticking to neighboring crystals during its trek to the ground.

https://www.thoughtco.com/science-of-snowflakes-3444191

 

[arfa brane]

Note that the word topology is from the Greek root topos, which translates as "place", roughly. It also means status or standing (like, in society or the military).
So roughly, topology is about what things look like when they're put in the same place, or given the same status (e.g. sums of numbers with the same value, or graphs with the same number of vertices).

 

[Write4U]

Note that the word topology is from the Greek root topos, which translates as "place", roughly. It also means status or standing (like, in society or the military).
So roughly, topology is about what things look like when they're put in the same place, or given the same status (e.g. sums of numbers with the same value, or graphs with the same number of vertices).

Topology
Description
In mathematics, topology is concerned with the properties of space that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing. An n-dimensional topological space is a space with certain properties of connectedness and compactness. Wikipedia

*Möbius strips, which have only one surface and one edge, are a kind of object studied in topology*.

are another kind at much smaller scales....

https://en.wikipedia.org/wiki/Topology

Question; Can space pass through space as long as it does not tear or glue either topology? Tunneling?

 

[arfa brane]

In a Temperley-Lieb diagram you have a set of points along an upper boundary (given at least one dimension that points can stick to, i.e. one-dimensional surfaces), and a corresponding set below on a similar (but distinct!) boundary.

If both sets of points have the same size, n, then the diagram is a monoid in TLn. TLn has a 'bare' version of its algebra on n + n points, in which any loops in the vertical composition of diagrams are contracted and vanish (they aren't stuck to either boundary), because the operation of diagram compositions makes everything on the intervening boundary vanish except any "through lines", here's a diagram:

​

If you compose two of these vertically, you get a yellow mid-boundary with a closed loop on it, everything else is a through line, or stays glued to an upper (counit) or lower (unit) boundary.
In TLn algebras you give a (unit)⋅(counit) loop a complex value, and count them as powers of this complex value which then are or aren't roots of complex polynomials.

The number n (a natural number that can't be negative) is then related to how many ways there are to compose diagrams that generate loops and that don't.

 

[Yazata]

Can anyone come up with anything in physical or metaphysical reality that cannot be symbolized by mathematics?

Beauty, pleasure, love, good...

A couple of less 'touchy-feely' examples might be truth and life in the biological sense. Biology doesn't really lend itself to mathematization like physics does.

I keep coming back to the basic understanding that the universe consists of Values and Functions.

So what accounts for values and functions? They aren't self-explanatory, you know.

There seem to be implicit assumptions built in there about the reality of universals and about the uniformity of nature.

https://www.iep.utm.edu/universa/

https://www.iep.utm.edu/mathplat/

In Nature, there are only permissions and restrictions and the mathematics of these permissions and restrictions becomes manifest as "patterns", both physical and metaphysical .

That's a very strong metaphysical belief that I don't think that I share at the moment.

This is why I intuitively tend to agree with Tegmark. His hypothesis of a Universe which is inherently mathematical in nature, makes perfect logical sense to me.

I haven't read his book. (Nor am I sure that I want to.)

I get the impression that he's just turned the manner in which theoretical physicists are trained into a metaphysics. If a physical problem arises, how is it addressed in the university classroom? Often times, the response is to scrawl some mathematical equations on a chalk board. So slippy-sliding from scrawling equations on a chalkboard to believing that the equations are somehow more real than reality itself, that the mathematics is what lies behind the phenomenal screen so to speak, is a short step.

But it's not a step that I feel comfortable making.

I perceive the universe around me as a mystery, the most profound mystery there is. I'm not ready to abandon that by leaping prematurely at proposed solutions to the ultimate nature of everything. Particularly solutions that seem to me to beg as many questions as they answer.

 

[Write4U]

Beauty, pleasure, love, good.

I bet they can. These emotions are chemical reactions to physical or mental stimulation and can be quantified. This is how we experience "empathy", an emotional mirroring. We use measuring equipment to quantify the chemical production in the brain. Pheromones, endorphins, dopamine, etc.

In the attraction stage, a group of neuro-transmitters called 'monoamines' play an important role:

• Dopamine - Also activated by cocaine and nicotine.
• Norepinephrine - Otherwise known as adrenalin. ...
• Serotonin - One of love's most important chemicals and one that may actually send us temporarily insane..
• BBC Science | Human Body & Mind | Science of Love

https://www.bbc.co.uk/science/hottopics/love/

Just think of the chemicals involved in the act of achieving an erection. Testosterone, L-Arginine, nitric oxide, zinc. These chemicals are naturally produced by people who are in love. People with ED receive benefits from proper dosage of these chemicals. Mathematics are very much involved in functional emotional responses.
As Tegmark posits; There is no mathematical difference in the molecular components of a dead beetle and a live beetle. The molecules are just arranged in two different patterns.

 

[DaveC426913]

I bet they can. They are chemical reactions and can be quantified.

Ah, no. Those are qualia. They can't be measured - at least not directly. We can ask a subject how he feels about something, and he can tell us - but that is an interpretation.

 

[Write4U]

Ah, no. Those are qualia. They can't be measured - at least not directly. We can ask a subject how he feels about something, and he can tell us - but that is an interpretation.

We can measure electro-chemical responses in the brain.

The thalamus and hypothalamus are located within the diencephalon (or “interbrain”), and are part of the limbic system. They regulate emotions and motivated behaviors like sexuality and hunger.

Hypothalamus,
The hypothalamus is a small part of the brain located just below the thalamus. Lesions of the hypothalamus interfere with motivated behaviors like sexuality, combativeness, and hunger.

The hypothalamus also plays a role in emotion: parts of the hypothalamus seem to be involved in pleasure and rage, while the central part is linked to aversion, displeasure, and a tendency towards uncontrollable and loud laughing. When external stimuli are presented (for example, a dangerous stimuli), the hypothalamus sends signals to other limbic areas to trigger feeling states in response to the stimuli (in this case, fear).

https://courses.lumenlearning.com/boundless-psychology/chapter/structure-and-function-of-the-brain/

Note; I am not suggesting that we know everything there is to know about the brain, but we are beginning to understand the most fundamental functions which control all our "regulated" experiences.

ORCH-OR is one such proposed discipline.

My research involves a theory of consciousness which can bridge these two approaches, a theory developed over the past 20 years with eminent British physicist Sir Roger Penrose.

Called ‘orchestrated objective reduction’ (‘Orch OR’), it suggests consciousness arises from quantum vibrations in protein polymers called microtubules inside the brain’s neurons, vibrations which interfere, ‘collapse’ and resonate across scale, control neuronal firings, generate consciousness, and connect ultimately to ‘deeper order’ ripples in spacetime geometry. Consciousness is more like music than computation. Stuart Hameroff

https://www.quantumconsciousness.org/content/overview-sh

p.s. we know the exact mathematical chemistry to render people unconscious. It is a very precise mathematical procedure. Too little, the patient suffers from the surgery. Too much, the patient never wakes up. Tricky stuff and very much dependent on accurate mathematics.

 

[DaveC426913]

We can measure electro-chemical responses in the brain.

Yes we can.

However the discussion was about Beauty, pleasure, love, good.

I can measure the strokes of a conductor's wand too, but that doesn't tell me if the music is pretty.

 

[Write4U]

Yes we can.

However the discussion was about Beauty, pleasure, love, good.

I can measure the strokes of a conductor's wand too, but that doesn't tell me if the music is pretty.

If I hook your brain up to an EEG machine, I can tell if you find the music pretty.
Well, I can't, but some experts can.....

For the first time, scientists have identified which emotion a person is experiencing based on brain activity. The study combines functional magnetic resonance imaging and machine learning to measure brain signals to accurately read emotions in individuals.

The findings illustrate how the brain categorizes feelings, giving researchers the first reliable process to analyze emotions. Until now, research on emotions has been long stymied by the lack of reliable methods to evaluate them.

https://www.sciencedaily.com/releases/2013/06/130619195137.htm

IMO, anything which occurs in nature as patterns can be analyzed and mathematically quantified and qualified. It's always the emerging patterns which are measurable, quantifiable, and qualifiable from various perspectives.

As Antonsen observes, the greater the exposure to different subjective and objective perspectives of a phenomenal pattern the greater the understanding of the pattern.

Who knows, someday we might be able to recreate the music just from the brain waves. Hear what you hear, when you internally replay the music from memory.
That'd be cool....

 

[Write4U]

W4U said,
In Nature, there are only permissions and restrictions and the mathematics of these permissions and restrictions becomes manifest as "patterns", both physical and metaphysical .

That's a very strong metaphysical belief that I don't think that I share at the moment

It's not a mere belief. It's a deduction. Permission and restriction is a binary function. All natural mathematical values and functions can be simulated in binary language. Some things are allowed (by natural law) to happen, some things are not allowed (by natural law) to happen. You cannot drive a square peg in a round hole.

In nature there are always two superposed positions, of which only one will become reality.
a) the physical action is allowed (and the emergent pattern becomes expressed in reality). ON.
b) the physical action is not allowed (and no emergent pattern becomes expressed in reality) OFF.

Example of natural permission and restriction in chemistry can be found in molecular Chiralty.
Another example of conditional permission and restriction can be found in Magnetism.

Please note; these permissions and restrictions are not actively imposed by some external force. They are a result of inherent spacetime potentials as natural geometric or electrodynamic permissions (compatibilities) and restrictions (incompatibilities).
It's not complicated, IMO. I realize the devil lies in the details......

 

[Beaconator]

Density?

Density is the only thing that matters to me between the elements. Sadly Princeton has taken down their atomic density chart leaving a specific volume unattainable...