The necessary truth of mathematics (?)

[James R]

Mathematics are a necessary property of spacetime.

You haven't got a third of the way to first base in trying to support that extravagant claim.

There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations.

Show me a number that exists independently of a human being.

But Einstein was talking about the human symbolization of generic natural mathematics.

No. He never mentioned the words "generic natural mathematics", to my knowledge.

It would be surprising - to say the least - if he had, seeing as "generic natural mathematics" is a term you made up long after Einstein's death.

Don't try to put your words in Einstein's mouth.

 

[Write4U]

You can't explain how a concept can affect a physical object, can you?

I can explain how a function can affect the interaction of physical objects. And so can you.

Note that + identifies an additive function, whereas * identifies a multiplication. Given the constituent parts, the result is the same via different mathematical functions.

 

[Write4U]

Meaningless verbiage does not give its author the right to demand courtesy. Even if one were to extend you that courtesy, how can one "consider" something that seems just a random jumble of sciency terms?

But that goes both ways. You use human symbolized mathematics as the language best suited to describe physical interactions via a self-ordering process, but then you just dismiss the inherent mathematical truths that are testable and usable as representative of how things actually work.

What can physics do without mathematics? What can the Universe do without mathematics?

 

[Write4U]

No. He never mentioned the words "generic natural mathematics", to my knowledge.

Right, he was talking about human mathemathics, not the generic maths inherent or emergent from the spacetime geometry.
See, that's what I mean!

What exactly is the objection to a mathematically ordered universe? Telling me that human maths is a human invention is a meaningless tautology.
Note that most scientist admit to at least some universal mathematical properties to the natural world.

What is an axiom if not a cognition of existing universal or local conditions? Is that just something scientists say?

In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful. “Nothing can both be and not be at the same time and in the same respect” is an example of an axiom. The term is often used interchangeably with postulate, though the latter term is sometimes reserved for mathematical applications (such as the postulates of Euclidean geometry). It should be contrasted with a theorem, which requires a rigorous proof. https://www.merriam-webster.com/dictionary/axiom

What we have named the Fibonacci Sequence is axiom that can be observed in nature in daisies, for one.
If you want a list of naturally occurring patterns based on the Fibonacci Sequence, from spiral galaxies to slug shells, be prepared for a book.

This mathematical growth sequence is a result of evolution via "natural selection". It is the result of a self-organizing mathematical pattern for vertical stability, best energy reception, maximum storage of seeds, etc.

 

[exchemist]

But that goes both ways. You use human symbolized mathematics as the language best suited to describe physical interactions via a self-ordering process, but then you just dismiss the inherent mathematical truths that are testable and usable as representative of how things actually work.

What can physics do without mathematics? What can the Universe do without mathematics?

Physics can do a lot less, certainly. But then physics is a human enterprise, using human tools of reasoning and description, of which mathematics is one.

As for the universe, being physical, it does what it does without reference to abstractions.

 

[Write4U]

Regulation of a physical process requires something to cause that regulation.

----> What you need to do is to explain to me how mathematics could possibly cause anything in the physical world.

Mathematics is not causal to anything. From observation it appears to be functional to everything..

Humans use mathematics to describe and theoretically model physical processes.

And what is it that human-symbolized mathematics describe and model? It describes the way things work and are regulated, right?

So far, you haven't even come up with an in-principle argument for how it could conceivably do anything like that.

So far you have not provided an alternative "model" of the universe at all, other than the science of physics, via the use of mathematical symbolization.

Humans and most all living things on earth evolved to utilize the mathematics of natural patterns.
Humans are not the only creature that have symbolically formalized mathematics into a language.

Single-celled slime molds practice mathematics in solving a maze. They use the mathematical function of subtraction.

How Brainless Slime Molds Redefine Intelligence [Video]

Single-celled amoebae can remember, make decisions and anticipate change, urging scientists to rethink intelligent behavior

www.scientificamerican.com

The Honey Bee Dance Language​

There can be no argument that the most famous aspect of honey bee biology is their method of recruitment, commonly known as the honey bee dance language. It has served as a model example of animal communication in biology courses at all levels, and is one of the most fascinating behaviors that can be observed in nature.

The dance language is used by an individual worker to communicate at least two items of information to one or more other workers: the distance and direction to a location (usually a food source, such as a patch of flowers). https://content.ces.ncsu.edu/honey-bee-dance-language#

Distance and direction are mathematical measurements! Bees practice mathematics!

 

[Write4U]

As for the universe, being physical, it does what it does without reference to abstractions.

Yet it creates the most beautiful recurring physical patterns imaginable! So, how does it do that without some form of inherent guiding principle?

Describe it to me. To claim "it just does it without reference to anything" is hopelessly incomplete in describing how things happen, while we have invented the most intimate forms of knowledge via our axiomatic understanding of how things work

There simply is no alternative to what we have named "mathematical order" emerging from chaos.

Note: I am not talking about a "motivated causal agency". I am talking about an "impersonal guiding principle" that is both permissive and restrictive depending on the physical relational "values" involved in the dynamics of change.
Some things can happen, some things cannot happen.

 

[exchemist]

Yet it creates the most beautiful recurring physical patterns imaginable! So, how does it do that without some form of inherent guiding principle?

Describe it to me. To claim "it just does it without reference to anything" is hopelessly incomplete in describing how things happen, while we have invented the most intimate forms of knowledge via our axiomatic understanding of how things work

There simply is no alternative to what we have named "mathematical order" emerging from chaos.

Note: I am not talking about a "motivated causal agency". I am talking about an "impersonal guiding principle" that is both permissive and restrictive depending on the physical relational "values" involved in the dynamics of change.
Some things can happen, some things cannot happen.

As you have decided to misquote me, I am going to ignore this.

 

[Write4U]

As you have decided to misquote me, I am going to ignore this.

Your words: "As for the universe, being physical, it does what it does without reference to abstractions"

Ok, I have now quoted it verbatim. What exactly does the universe reference to if it just "does what it does"?
It must necessarily be doing something, no? Does it add, subtract, multiply, divide, etc?

I see dynamics as causal to change and mathematically interactive functions as guiding principles of how that change becomes manifest.

Isn't the Table of Elements a perfect axiomatic example of self-ordering patternsin accordance with mathematical principles?
Seems to me that Determinism is not just "doing what it does". It follows strict rules of self-ordering patterns.

I only seek clarity, nothing else. The concept of mathematical guiding principles does provide clarity and utility, insofar as they relate to our relationship with reality.

Taken from A Dictionary of the Social Sciences eds. J. Gould and W. Kolb, Free Press, 1964.

A. The term determinism denotes a doctrine which claims that all objects or events, or all objects or events of some kind (for instance, falling within the range of some scientific discipline) are determined, that is to say must be as they are and as they will be, in virtue of some laws or forces which necessitate their being so.

B. Determinism is in fact the name of a whole class of theories which have the above feature in common. The term becomes the name of a specific doctrine when the kind of determinism is indicated, implicitly or explicitly. The specification may indicate either the class of things that are determined, or the type of thing that does the determining, or both. For instance, economic determinism tends to mean the doctrine that economic factors determine others, historical determinism tends to mean the theory that events in history are determined, sociological determinism is likely to mean the assertion that social facts are determined, and that they are determined by social factors.

C. An important characterization of determinism, cutting across the sub-division in terms of field, or subject, arises from describing it as causal determinism, which means the doctrine that events are determined causally. This idea can be opposed, for instance, to statistical or to theological determinism, i.e., to theories which claim that events are determined non-casually by statistical probabilities, or by the deity. It is arguable whether these types of determination should be seen as fundamentally non-causal, or whether ultimately they are but a special case of causation.

It may be argued that statistical probabilities are to be interpreted as consequences of causes too complex or minute to be isolated in individual cases and that even transcendental determinants are to count as causes.

Definition Determinism

I would hesitate to call mathematical functions as "causal", and rather use the term "guiding" due to the dynamically changing environment.

 

[James R]

You can't explain how a concept can affect a physical object, can you?

I can explain how a function can affect the interaction of physical objects.

Your post does not even address that. And you tried to dodge the question I asked, AGAIN.

The only question left to ask now is: why won't you be honest?

No. He never mentioned the words "generic natural mathematics", to my knowledge.

Right, he was talking about human mathemathics, not the generic maths inherent or emergent from the spacetime geometry.

You should have stopped at "Right".

Tell me: why did you lie about what Einstein was talking about?

What exactly is the objection to a mathematically ordered universe?

My objection is that mathematics cannot "order" anyting physical, and that applies to universes.

You have failed to establish that it can. In fact, you haven't really tried. You have tried to dodge the question, over and over. And now you've resorted to just telling blatant lies.

Do you think your behaviour is appropriate?

Telling me that human maths is a human invention is a meaningless tautology.

I did not say "human maths". I said "maths". And even then, you're putting words into my mouth that I didn't say.

If you want to comment on something I wrote, quote me. Because I now know that you tell lies when you feel backed into a corner.

Note that most scientist admit to at least some universal mathematical properties to the natural world.

I discussed that in several previous posts. For example, one that I posted only yesterday. How do you respond to what I wrote? (You ignored it last time.)

What we have named the Fibonacci Sequence is axiom that can be observed in nature in daisies, for one.

No. There is no sequence of numbers in daisies.

If you want a list of naturally occurring patterns based on the Fibonacci Sequence, from spiral galaxies to slug shells, be prepared for a book.

I assume you're referring me to a book in which a human being identifies mathematical patterns in describing nature. Right?

This mathematical growth sequence is a result of evolution via "natural selection".

The word "mathematical" is not required, there.

It is the result of a self-organizing mathematical pattern for vertical stability, best energy reception, maximum storage of seeds, etc.

Mathematical patterns do not self-organise.

I explained why just yesterday, to you.

 

[James R]

Mathematics is not causal to anything. From observation it appears to be functional to everything.

How do you respond to what I wrote to you yesterday about your "mathematical guiding" assertion?

And what is it that human-symbolized mathematics describe and model? It describes the way things work and are regulated, right?

Yes. Among other things.

So far you have not provided an alternative "model" of the universe at all, other than the science of physics, via the use of mathematical symbolization.

It is you who is asserting that mathematics has physical effects on the world. It is therefore up to you to show that your claim is true.

I have not proposed a "model" of the universe for consideration - other than the model in which mathematics has no physical effects. But that's just saying to you: make your case. In response, you seemingly have nothing to support your claim.

Humans and most all living things on earth evolved to utilize the mathematics of natural patterns.

Give me an example of how a living thing (other than a human being) utilised mathematics.

Humans are not the only creature that have symbolically formalized mathematics into a language.

Name one other creature that has "symbolically formalised mathematics".

You're just making shit up now, aren't you? That's telling lies, Write4U. You stop that.

Single-celled slime molds practice mathematics in solving a maze. They use the mathematical function of subtraction.

Explain.

Bees practice mathematics!

It is possible that bees understand some mathematical concepts instinctively. So what?

Yet it creates the most beautiful recurring physical patterns imaginable! So, how does it do that without some form of inherent guiding principle?

I haven't claimed that the universe has no "inherent guiding principles". Quote me if you want to debate me.

There simply is no alternative to what we have named "mathematical order" emerging from chaos.

Huh? There are obvious alternatives. Think about it.

 

[Write4U]

Show me a number that exists independently of a human being.
It doesn't. Numbers are human symbolic representations of quantity. All living things recognize quantity without using numbers.

James R :

You should have stopped at "Right".

And ignore the argument that the universe operates by self-ordering regular patterns, that humans have dubbed "mathematical" in essence

James R:
My objection is that mathematics cannot "order" anyting physical, and that applies to universes.

Yet the universe is rife with examples of self-ordered patterns. Explain that.

What Is Self-Organization?

Technological systems become organized by commands from outside, as when human intentions lead to the building of structures or machines. But many natural systems become structured by their own internal processes: these are the self-organizing systems, and the emergence of order within them is a complex phenomenon that intrigues scientists from all disciplines. —
F. E. Yates et al., Self-Organizing Systems: The Emergence of Order.

What Is Self-Organization? - Princeton University​

W4U:
Telling me that human maths is a human invention is a meaningless tautology.

James R:

I did not say "human maths". I said "maths". And even then, you're putting words into my mouth that I didn't say.

Are you now conceding that there are maths aside from human maths?

No. There is no sequence of numbers in daisies.

Really? You may want to revisit growth patterns in biology. Explain this.



The Fibonacci sequence can be seen in two different places in flowers. The most visible place is the petals of a flower. Several flowers have petals that are numbers of the fibonacci sequence. Lilies have 3 petals, buttercups have 5 petals, and daisies have 34 petals, for example. Scientists have theorized that petals that fit the Fibonacci sequence absorb more sunlight, among other uses.

Natural selection selected the Fibonacci Sequence in a host of biological organisms as the most efficient growth pattern, for several reasons.

The Fibonacci Sequence​

Fibonacci numbers do appear in nature often enough to prove they reflect some naturally occurring patterns. You can commonly spot these by studying the manner in which various plants grow.

Many seed heads, pinecones, fruits and vegetables display spiral patterns that when counted express Fibonacci numbers. Look at spirals of seeds in the center of a sunflower and you'll observe patterns curving left and right. If you count these spirals, your total will be a Fibonacci number. Divide the spirals into those pointed left and right and you'll get two consecutive Fibonacci numbers. You can decipher spiral patterns in pinecones, pineapples and cauliflower that also reflect the Fibonacci sequence in this manner.

The word "mathematical" is not required, there.

Yes it is, it is a naturally occurring mathematical "growth pattern" that humans have symbolically described as the Fibonacci Sequence.
_________________________________________________________________________

Let's cut to the chase and do away with this endless nitpicking.

Physics​

The laws of physics appear to follow a mysterious mathematical pattern​

The symbols and mathematical operations used in the laws of physics follow a pattern that could reveal something fundamental about the universe
By Alex Wilkins, 21 October 2024

A strange pattern running through the equations of physics may reveal something fundamental about the universe or could be a sign that human brains are biased to ignore more complex explanations of reality – or both.

The laws of physics appear to follow a mysterious mathematical pattern

The symbols and mathematical operations used in the laws of physics follow a pattern that could reveal something fundamental about the universe

www.newscientist.com

What Is Superposition and Why Is It Important?

In mathematical terms, superposition can be thought of as an equation that has more than one solution. When we solve x2 = 4, x can either be 2 or –2. Both answers are correct. Superposed wave functions will be more complicated to solve, but they can be approached with the same mindset.

While waves on the surface of a pond are formed by the movement of water, quantum waves are mathematical. They are expressed as equations that describe the probabilities of an object existing in a given state or having a particular property. The equations might provide information on the probability of an electron moving at a specific speed or residing in a certain location.

When an electron is in superposition, its different states can be thought of as separate outcomes, each with a particular probability of being observed. An electron might be said to be in a superposition of two different velocities or in two places at once. Understanding superposition may help to advance quantum technology such as quantum computers.

What Is Superposition and Why Is It Important?

One of the fundamental principles of quantum mechanics, superposition explains how a quantum state can be represented as the sum of two or more states.

scienceexchange.caltech.edu

The point is that human maths are approximations of Universal mathematical properties and functions that may run much deeper than we can observe.
But the limitations of human maths is not in any way a negation of the concept of Universal mathematics which may exist even at Planck scales.

 

[Write4U]

W4U:
And what is it that human-symbolized mathematics describe and model? It describes the way things work and are regulated, right?

James R:
Yes. Among other things.
It is you who is asserting that mathematics has physical effects on the world. It is therefore up to you to show that your claim is true.

Every regular pattern in nature you see is a mathematical construct

My objection is that mathematics cannot "order" anyting physical, and that applies to universes.

Order is an expression of mathematical function.

Give me an example of how a living thing (other than a human being) utilised mathematics.

The single-celled multi-nucleic slime mold has no brain or neural network, Yet it uses subtraction to solve a maze. A mathematical function.

It is possible that bees understand some mathematical concepts instinctively. So what?

Is it necessary that an organism is aware it is using maths? Does a spider need to be consciously aware it's web is a mathematial object?

What kind of pattern is spider web?

These patterns are called fractals. A fractal is a never-ending pattern, one that is made by repeating a simple process. Spider webs are one place we can see fractals in nature. We can also see them in seashells, snowflakes, and trees.
chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.hpl.ca/sites/default/files/Spider%20Science.pdf

The consensus among mathematicians is that theoretical fractals are infinitely self-similar iterated and detailed mathematical constructs, of which many examples have been formulated and studied. Fractals are not limited to geometric patterns, but can also describe processes in time.

Fractal - Wikipedia

en.wikipedia.org

James R:
I haven't claimed that the universe has no "inherent guiding principles". Quote me if you want to debate me.

To my knowledge you haven't mentioned any. I have asked you many times to provide an alternative to an inherent mathematical essence to the fabric of spacetime. AFAIK, self-organization and self-ordering are mathematical functions.

Self-organization - Wikipedia

en.wikipedia.org

One moment, please...

Interesting tidbit:

Irreducible complexity 21, 22 does not and cannot arise by chance or necessity. When the whole is greater than the sum of its parts, and where the sophisticated function of that whole cannot be maintained with the loss of any one of its parts, we know immediately that formal choices were involved in its organization. Conceptually complex machines don’t just happen. Take one part away from a mousetrap, and see how many mice you catch!

Ever considered the Venus flytrap? It is a complex machine that needed no help from engineers. Natural selection was the evolutionary engineer long before humans came along.

Where did any of the mousetrap parts come from? How did they . get assembled into a useful conceptually complex machine? Only by clever engineering choices specifically designed to catch mice. The simplest know cell seems almost infinitely more conceptually complex than a mouse trap. How did the first cell form?

Self-ordering in nature is the subject of Chaos theory. 1, 23, 24
Chaos theory only addresses self-ordering phenomena (“dissipative structures”). Self-ordering phenomena are fully explainable from nothing but the laws of physics.

This article seems to disagree.

The laws of physics appear to follow a mysterious mathematical pattern

The symbols and mathematical operations used in the laws of physics follow a pattern that could reveal something fundamental about the universe

www.newscientist.com

Huh? There are obvious alternatives. Think about it.

I can't think of any. Please, you name one that is not mathematical in essence.
The expression "Laws of Physics" does not explain anything about their nature.

But this does.

Evolutionary dynamics is the study of the mathematical principles according to which biological organisms as well as cultural ideas evolve and evolved.[1] This is mostly achieved through the mathematical discipline of population genetics, along with evolutionary game theory. Most population genetics considers changes in the frequencies of alleles at a small number of gene loci. When infinitesimal effects at a large number of gene loci are considered, one derives quantitative genetics. Traditional population genetic models deal with alleles and genotypes, and are frequently stochastic​

Evolutionary dynamics - Wikipedia

en.wikipedia.org

In mathematics, a law is a formula that is always true within a given context.[1] Laws describe a relationship, between two or more expressions or terms (which may contain variables), usually using equality or inequality,[2] or between formulas themselves, for instance, in mathematical logic.

Mathematical laws are distinguished from scientific laws which are based on observations, and try to describe or predict a range of natural phenomena.[5] The more significant laws are often called theorems.

Law (mathematics) - Wikipedia

en.wikipedia.org

 

[James R]

Write4U:

Numbers are human symbolic representations of quantity. All living things recognize quantity without using numbers.

Huh? What do you mean by "quantity", if it doesn't involve numbers?

And ignore the argument that the universe operates by self-ordering regular patterns...

Patterns do not "self-order". How could they? A pattern is a concept.

Yet th universe is rife with examples of self-ordered patterns. Explain that.

It's not.

"But many natural systems become structured by their own internal processes: these are the self-organizing systems, and the emergence of order within them is a complex phenomenon that intrigues scientists from all disciplines."

This is referring to physical systems. See the word "natural systems"? That means physical systems - systems that exist in the physical world. It does not mean mathematical systems, which exist in people's heads.

Are you now conceding that there are maths aside from human maths?

In terms of a formalised symbolic system that represents abstract relations such as patterns and numbers? I'm not aware of any. Are you?

You're going to mention bees, again, probably. Bees have a sort of language that they use to communicate with one another. They communicate some types of information that human beings describe in mathematical terms. But it is not at all clear that bees are thinking about mathematics, as such. I very much doubt that's what they are doing. Instead, I think bees have an evolved neural network that effectively encodes certain information based on environmental and experiential cues.

It's a bit like when you catch a ball that is thrown to you. You aren't doing any mathematics when you do that, even though it is obviously quite possible to describe the flight of the ball mathematically.

It is a mistake to assume that anything that can be described mathematically must have a mathematical cause. Like I said, mathematics, on its own, can't cause anything.

Really? You may want to revisit growth patterns in biology. Explain this.

Again, the growth patterns of daisies and such have evolved through physical processes such as natural selection. There may well be good reasons why spirals in flower seeds are more efficient when they are arranged according to what we humans call the Fibonacci numbers. But those reasons will be physical reasons, not mathematical reasons. Flowers don't do maths.

Scientists have theorized that petals that fit the Fibonacci sequence absorb more sunlight, among other uses.

There's the physical explanation, then. See?

Natural selection selected the Fibonacci Sequence in a host of biological organisms as the most efficient growth pattern, for several reasons.

Again, a physical explanation.

Yes it is, it is a naturally occurring mathematical "growth pattern" that humans have symbolically described as the Fibonacci Sequence.

Yes, humans symbolically describe it. That doesn't mean that our symbolic description caused it.

Physics

The laws of physics appear to follow a mysterious mathematical pattern​

It's not that mysterious. Human beings who do physics aim to construct a coherent mathematical theory.

The point is that human maths are approximations of Universal mathematical properties and functions that may run much deeper than we can observe.

How could you possibly know that?

But the limitations of human maths is not in any way a negation of the concept of Universal mathematics which may exist even at Planck scales.

"Universal mathematics" is your own invention. You can't define what it is. Your descriptions of it are invariably a muddled, almost meaningless word salad.

Every regular pattern in nature you see is a mathematical construct

Maybe. Now think about who constructed it.

Order is an expression of mathematical function.

Often, it is not. Not consciously, anyway.

The single-celled multi-nucleic slime mold has no brain or neural network, Yet it uses subtraction to solve a maze.

Please explain. Subtraction how?

Is it necessary that an organism is aware it is using maths? Does a spider need to be consciously aware it's web is a mathematial object?

It's web isn't a mathematical object. It is a physical object.

You haven't convinced me that a spider uses maths.

To my knowledge you haven't mentioned any. I have asked you many times to provide an alternative to an inherent mathematical essence to the fabric of spacetime.

Are you talking "spacetime" as in our mathematical models of space and time, or "spacetime" as in the physical substructure of the physical universe?

I say that the essence of physical spacetime is physical space and physical time. Maths is just a thing we use to model it.

AFAIK, self-organization and self-ordering are mathematical functions.

I don't know where you're getting your information from. Whoever told you that is making the same mistakes you are making, which I suppose is not particularly surprising.

Ever considered the Venus flytrap? It is a complex machine that needed no help from engineers. Natural selection was the evolutionary engineer long before humans came along.

Okay. So where's the maths in that?

This article seems to disagree.

The laws of physics appear to follow a mysterious mathematical pattern

The symbols and mathematical operations used in the laws of physics follow a pattern that could reveal something fundamental about the universe

www.newscientist.com

That's behind a paywall.

 

[Write4U]

Huh? What do you mean by "quantity", if it doesn't involve numbers?

Oh boy, you are so entrenched. Have you ever owned a dog?

Why Some Animals Can Tell More From Less

For decades, researchers like Cantlon have been studying how animals understand quantities, and they have considered factors ranging from their social group size to diet to total brain volume. Now, drawing from published work on dozens of species, a large team led by Cantlon has found a striking pattern: The density of neurons that an animal has in their cortex predicts its quantitative sense better than any other factor.

The work, published in December in Philosophical Transactions of the Royal Society B, shows constraints from evolution—rather than learning or behavior—on cognition. They found that phylogeny, or evolutionary “distance” between species, predicts how well they do at estimating quantities compared to each other. Closely related species tend to have similar levels of skill. Distantly related ones may vary widely.

“It's an impressive study because of the enormous amount of data and all the different factors that they took into account,” says Sarah Brosnan, who researches animal decisionmaking at Georgia State University.

And not only can some animals "count", i.e. recognize the difference "between more and less" (a differential equation), here is an example of a dog making a "choice" what quantity to give his little Sus friend.. Note the little pat on the head he gives the baby. I call that remarkably intelligent!

Are you now going to quibble semantics with that example of mathematical decision-making by a non-human?

p.s. IMO "quorum sensing" in bacteria is a rudimentary mathematical function. The coordinated virulence of bacteria relies on and is regulated by quantity. When a treshold quantity is reached all bacteria become virulent at the same time.

Abstract

Quorum sensing is the regulation of gene expression in response to fluctuations in cell-population density. Quorum sensing bacteria produce and release chemical signal molecules called autoinducers that increase in concentration as a function of cell density. The detection of a minimal threshold stimulatory concentration of an autoinducer leads to an alteration in gene expression. https://pubmed.ncbi.nlm.nih.gov/11544353/

 

[Write4U]

It is a mistake to assume that anything that can be described mathematically must have a mathematical cause. Like I said, mathematics, on its own, can't cause anything

That statement is not even wrong.
I have NEVER said that maths are causal to anything . It is you who keeps insulting me by persisting in misquoting me. Stop that!

Mathematical functions are not causal, they are deterministic
If something can be described mathematically it must be mathematical in essence, else it could not be described mathematically, seeeee!

What is a Deterministic Function?​

Deterministic means the opposite of randomness, giving the same results every time. So in a sense, all mathematical functions are deterministic, because they give the same results every time; The output of the “usual” function is only determined by its inputs, without any random elements; There are exceptions in stochastic calculus.

Therefore, if you stipulate to universal deterministic functions, it must of necessity be mathematical in essence.

 

[exchemist]

p.s. IMO "quorum sensing" in bacteria is a rudimentary mathematical function. The coordinated virulence of bacteria relies on and is regulated by quantity. When a treshold quantity is reached all bacteria become virulent at the same time.

Abstract

BINGO!

 

[Write4U]

BINGO!

That does not suggest causality. The physical chemistry is causal to change. The result is mathematically deterministic of the specific change.

This is the mathematical language of bacteria.

 

[Write4U]

To clarify my use of the term Threshold as a mathematical "value"

Threshold model​

In mathematical or statistical modeling a threshold model is any model where a threshold value, or set of threshold values, is used to distinguish ranges of values where the behaviour predicted by the model varies in some important way. A particularly important instance arises in toxicology, where the model for the effect of a drug may be that there is zero effect for a dose below a critical or threshold value, while an effect of some significance exists above that value.[1] Certain types of regression model may include threshold effects.[1]

Collective behavior​

Threshold models are often used to model the behavior of groups, ranging from social insects to animal herds to human society. https://en.wikipedia.org/wiki/Threshold_model#

Such as "quorum sensing"

and

Threshold Concepts

A fundamental threshold concept in math is the understanding of Functions and their Graphs. Functions are essential mathematical objects that describe relationships between inputs and outputs. They are foundational to many areas of mathematics and have wide ranging applications in science, engineering, economics and beyond. Once students grasp the concept of functions and their graphs, it unlocks a whole new level of understanding and proficiency in various mathematical topics. https://teachanywhere.opened.ca/teaching-learning/learning-essentials/threshold-concepts/#

 

[Gawdzilla Sama]

• Lucy : Humans consider themselves unique so they've rooted their whole theory of existence on their uniqueness. One is their unit of measure, but it's not. All social systems we've put into place are a mere sketch. One plus one equals two. That's all we've learned, but one plus one has never equaled two. There are, in fact, no numbers and no letters. We've codified our existence to bring it down to human size to make it comprehensible. We've created a scale so that we can forget its unfathomable scale.