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# Does mathematics really exist in nature or not?

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Human brains look for patterns, mathematics assigns names to patterns such that when the pattern is observed it can be described in reference to mathematics.

The patterns themselves are real because we seem to live in a highly ordered and organised universe.

You seem to be confusing the human activity of "doing mathematics" (and its associated notation, rules, etc) with the patterns in the universe, which could be called "mathematics" (they are certainly mathematical patterns).

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Hey, there's a valid point you raise there, but that seems to me like an important distinction. There are some publications regarding the reasonable ineffectiveness of math in some areas like biology and engineering where for various reasons the utility of the mathematics that we use doesn't do a very good job of describing the patterns in the universe.

Still now that you mention it I think that's what this entire argument has been about really.

There's the math humans do and the "math" or rather the appearance of order and consistency inherent in the universe. If you call the thing that people do math, then math is created and possibly subjective. If you call the laws and order in the universe math then clearly it's objective but also we don't necessarily understand it very well because the way we're describing it is often clunky and inefficient.

So the real question isn't whether math is objectively real, the question is or should be which do you call mathematics. Is math the stuff people do with numbers or is math the ordered consistency of the universe.

I would argue it is the work of humans, because it cannot be known that the order and consistency will hold.

For instance you can't prove the sun will rise tomorrow, because there's always some small chance that in defiance of every rule mankind has conceived it will do something we could not have predicted or even imagined.

So if we say math is the order and consistency of the universe you're making a very bold assumption that the universe is, at it's core, ordered and consistent, which is only probabilistically knowable.

You could say that as long as the consistency and order hold, then we can treat them as certain, and I would roughly agree, but it's safer to simply say that mathematics is the work humans do to understand the order of the universe based on various assumptions which may or may not hold.

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Hey, there's a valid point you raise there, but that seems to me like an important distinction. There are some publications regarding the reasonable ineffectiveness of math in some areas like biology and engineering where for various reasons the utility of the mathematics that we use doesn't do a very good job of describing the patterns in the universe. ...

The Fibonacci sequence is found in biology, most familiarly to me in botany where it underlies phyllotaxis. This underpinning of math-in-nature exists and has existed with no regard to humans' conception of it.

In botany, phyllotaxis or phyllotaxy is the arrangement of leaves on a plant stem (from Ancient Greek phýllon "leaf" and táxis "arrangement").[1] Phyllotactic spirals form a distinctive class of patterns in nature.

...

Phyllotaxis and mathematics

Physical models of phyllotaxis date back to Airy's experiment of packing hard spheres. Gerrit van Iterson diagrammed grids imagined on a cylinder (Rhombic Lattices).[8] Douady et al. showed that phyllotactic patterns emerge as self-organizing processes in dynamic systems.[9] In 1991, Levitov proposed that lowest energy configurations of repulsive particles in cylindrical geometries reproduce the spirals of botanical phyllotaxis.[10] More recently, Nisoli et al. (2009) showed that to be true by constructing a "magnetic cactus" made of magnetic dipoles mounted on bearings stacked along a "stem".[11][12] They demonstrated that these interacting particles can access novel dynamical phenomena beyond what botany yields: a "Dynamical Phyllotaxis" family of non local topological solitons emerge in the nonlinear regime of these systems, as well as purely classical rotons and maxons in the spectrum of linear excitations.

Close packing of spheres generates a dodecahedral tessellation with pentaprismic faces. Pentaprismic symmetry is related to the Fibonacci series and the golden section of classical geometry.[13][14]

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Hey, there's a valid point you raise there, but that seems to me like an important distinction. There are some publications regarding the reasonable ineffectiveness of math in some areas like biology and engineering where for various reasons the utility of the mathematics that we use doesn't do a very good job of describing the patterns in the universe.

it would definitely help your case if you provided us with some citations.

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I will give it one final go. People see the face of Jesus in toast for the same reasons they see math in the universe.

Human brains look for patterns, mathematics assigns names to patterns such that when the pattern is observed it can be described in reference to mathematics.

The patterns themselves are real because we seem to live in a highly ordered and organised universe.

At the same time they are not real because the universe does not consult mathematical laws in order to form patterns in the same way bread does not pull information about the face of Jesus in order to form a pattern.

Math is only "discovered" because the universe is very ordered, but the universe doesn't need math to be ordered, humans need the universe to be ordered in order to create math from it.

Here you go again using mathematical concepts such as "ordered" to try and refute that math doesn't occur naturally. Your logic is akin to how creationist argue the existence of god except you are arguing against something that actually does exist. You also have completely ignored my statements and have failed to answer any of the questions I've proposed.

It is impossible for you to describe the arrangements of atoms, and your example proves it!!! "There is a carbon atom to the left of the reference, below the reference, and positioned at the leading edge." You are referencing mathematical terms that describe position. The term "reference" itself means origin point within a local coordinate system, which is purely mathematical. You seem to think math is concerned with only numbers, but you are seriously mistaken in your assumption. Stating direction such as left or below is no different than stating $a_1.x < a_0.x$ and $a_2.y < a_0.y$. Just because you decide to use algebraic description of position and arrange the statement as a word problem does not result in you successfully describing the arrangment of atoms without using math. For instance, try comparing the size of the Earth to the size of the Sun without any mathematical concepts whatsoever... It's impossible. Sure, you could say the Sun is bigger than the Earth, but that is a mathematical relationship that can be expressed in an extension of our language which uses mathematical symbols and expressions such as $S > E$. Just because you use words to describe something doesn't mean you did a comparison without using math. Size is a mathematical relationship and we do not need exact numbers to compare the sizes of the Earth and Sun as my example has clearly shown. So... no, you cannot describe the arrangment of atoms without referring to position, size, or any other mathematical relationship, regardless of how abstract you wish to make the comparison. Mathematics isn't just about numbers because it exists in nature and cannot be so easily explained away.

So, I reassert my statement. Define the arrangment of atoms without referring to any mathematical terms. This includes relative terms such as left, right, top, bottom, front, or back, which are nothing more than words used to represent mathematical language. Do you know why we invented less than < , greater than > symbols or any mathematical symbol? It's so that we don't have to write a paragraph of words to describe the same thing that the symbols represent. So, you cannot simply use mathematical terms such as left, right, top, bottom, etc... and claim they have no basis in mathematics because each of those words describe a relative position.

If that's not enough to convince you, then tell me how many people are on Earth without using any mathematical terms or relationships.

Sure, there are components of mathematics that have no natural relationships, but that's no different than components of our language that refer to imaginary things. The point being is that this order you are referring to can only be constructed through mathematical relationships. If mathematics wasn't inherent to nature, then we simply wouldn't exist. There would be no position, size, or quantity.

You can continue to refuse the facts and believe that mathematics is some abstraction that people created, but that doesn't change the reality that mathematics occurs naturally.

Edited by Daedalus
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Sure, there are components of mathematics that have no natural relationships, but that's no different than components of our language that refer to imaginary things. The point being is that this order you are referring to can only be constructed through mathematical relationships. If mathematics wasn't inherent to nature, then we simply wouldn't exist. There would be no position, size, or quantity.

this and your above paragraph in no way exclude the option that mathematics is just a useful and potentially necessary "fiction" for describing the universe, and it also doesn't have to do with the question of whether mathematical entities (such as numbers) actually exist (perhaps you should read the op).

what you assert amounts to "it is essentially impossible to not use mathematical terminology to describe nature," and i don't really disagree with that, but it's not clear how you can get to the conclusion that maths is necessarily in nature.

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this and your above paragraph in no way exclude the option that mathematics is just a useful and potentially necessary "fiction" for describing the universe, and it also doesn't have to do with the question of whether mathematical entities (such as numbers) actually exist (perhaps you should read the op).

what you assert amounts to "it is essentially impossible to not use mathematical terminology to describe nature," and i don't really disagree with that, but it's not clear how you can get to the conclusion that maths is necessarily in nature.

It most definitely excludes the option that mathematics is just a useful and potentially necessary "fiction" for describing the universe. The mere fact that matter is quantifiable and conforms to goemetric structures proves that mathematics occurs in nature. You cannot have an arrangment of atoms if geometric properties did not exist, and there would be no such thing as groups of atoms if it were impossible to count them. So, yes, it is very clear that mathematics is fundamental in nature and we can eaily see how it is derived naturally.

Sure, there are components of mathematics that have no natural relationships, but that's no different than components of our language that refer to imaginary things. The point being is that this order you are referring to can only be constructed through mathematical relationships. If mathematics wasn't inherent to nature, then we simply wouldn't exist. There would be no position, size, or quantity.

You can continue to refuse the facts and believe that mathematics is some abstraction that people created, but that doesn't change the reality that mathematics occurs naturally.

This quote goes back to SciWiz12's fallacious statmements:

Here, let me use more formal logic.

If a system is objectively real, then we will be able to observe any aspect of that system in nature.

If an element of a system does not and cannot exist in nature, the system cannot be objectively real.

I hoped that I wouldn't have to explain why his statements are wrong. Just because an element of a system does not and cannot exist in nature doesn't mean that the system itself cannot occur in nature. Our language exists to describe things that exist in nature as well as things that don't exist. According to SciWiz12's statements, then nothing is objectively real, which is clearly a logical fallacy. No different than how our langauge is used to communicate things that are real and things that are not, mathematics also describes things that are real and things that are not. Sure, you can believe that math doesn't exist in nature but, when you can go outside and can clearly count things that naturally occur, why would you?

Edited by Daedalus
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Although I have previously discussed counting and number in this thread I really can't see why members are so obsessed with restricting Mathematics to number.

I have, in my library a book entitled

The Mathematical Description of Shape and Form.

It is a most useful and practical textbook for the subject, which is a part of Mathematics at least as old and important as counting.

But here's the rub.

There is all this nonsense about order and pattern being spouted, as though there were shapes and forms that were mathematical and those which were not.

Mathematics can and does describe any shape whatsoever, as well as regular ones.

So the shape of say the earth is well, Earth shaped.

That shape is unique but appears in the set of all possible shapes in Mathematics and in the Earth in Nature.

I think we can take it as read that we are not debating the existence of the Earth in this discussion. If the very existence of Nature itself was under debate then there would be no point in this thread.

Edited by studiot
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I think we can take it as read that we are not debating the existence of the Earth in this discussion. If the very existence of Nature itself was under debate then there would be no point in this thread.

Why not?

Science doesn't need anything to exist except experimental results and the definitions and axioms to define them.

Indeed, it's the very lack of assuming reality that allows a thread like this to exist.

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OK, yeah, I see that it was a mistake to try anything one more time, we apparently just aren't even communicating on the same level, I say something and you focus on the most irrelevant slices of my position.

Although I'll agree that I should definitely cite my sources, sure, but here's my reverse ask, why the fuck should I bother?

Is there some magical point at which I'm going to say something in a specific enough way that you look at it and go, "huh, you know actually that's a good point, I think if I could look at these particular sources directly with my own eyes I would be inclined to agree." Or, "you know, I don't think I fully agree but I think the better perspective is somewhere in between our perspectives."

Because so far I keep seeing rehashing of the same arguments phrased slightly differently and it honestly wasn't convincing the first time, or any of the subsequent times.

I was hoping that I could phrase my position in a different way to elicit a different response, I got maybe one thing that was different, kind of, but this was a failed experiment on my part, clearly those that disagree are just going to keep responding the same fundamental concept indignantly until I just stop the conversation by leaving.

I would have liked to make some sort of progress, I really don't know why I'm surprised at this point honestly, I should just expect it at this point. Everywhere you go, no matter how intelligent and we'll educated the group, some faction will always hold contrasting views and resist any form of compromise and persuasion. FCK it, screw me for even bothering, who gives a FCK about advancing the discourse, it's all about being right and mocking anyone who disagrees because people who disagree are stupid. Clearly. Whatever, I'm done, have fun.

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You cannot have an arrangment of atoms if geometric properties did not exist

you can't have geometry until you define the objects and properties in question

Although I'll agree that I should definitely cite my sources, sure, but here's my reverse ask, why the fuck should I bother?

because for all i know you could be making assertions about reality which are not true merely to support your position

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you can't have geometry until you define the objects and properties in question.

Really? Please, don't make this a circular argument. We are simply disccussing if mathematical entities exist in nature. These objects and properties already exist. If you can accept that nature is quantifiable and has structure and that we have invented language to describe quantities and structure, then I can't see why you won't accept that mathematics is inherent to nature. From a physical standpoint, numbers are nothing more than words and symbols that define natural quantities. Sure, we have learned how to abstract the concepts of numbers but, when dealing with physics, numbers represent measurements of physical quantities and scalars that relate one quantity to another. Now if you were arguing whether or not a particular physical theory predicts the universe exactly, then I would agree that there is no way beyond observation to state that such mathematics is inherent to nature. However, the mere fact that nature is quantifiable, proves that mathematics is inherent to it. Otherwise, we wouldn't be able to construct mathematical models, and mathematical properties such as quantity, size, and position would not exist.

Edited by Daedalus
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Although I have previously discussed counting and number in this thread I really can't see why members are so obsessed with restricting Mathematics to number.

i'm not sure that anyone is obsessed or trying to restrict the discussion, and only mentioning number because:

1. it is a mathematical object which easily comes to mind simply because of everyday use

2. it is an example that is mentioned in the question of the OP

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i'm not sure that anyone is obsessed or trying to restrict the discussion, and only mentioning number because:

1. it is a mathematical object which easily comes to mind simply because of everyday use

2. it is an example that is mentioned in the question of the OP

And we use numbers everyday becuase they exist as quantities in nature. If there was no such thing as quantitiy, then we wouldn't exist much less have words and symbols to describe them.

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Really? Please, don't make this a circular argument.

it's not a circular argument. not sure what your understanding of a circular argument is.

We are simply disccussing if mathematical entities exist in nature. These objects and properties already exist.

they exist in a mathematical sense perhaps, such as when a mathematician says

"there exists...such that..."

but they are not talking about something in the natural world, they are talking about there being at least one abstract object (specifically a mathematical object) in the universe of discourse conforming to the rules of the formal system in question.

a simple example i used in another thread:

there exists a real number r such that r + r = r*r

f you can accept that nature is quantifiable and has structure and that we have invented language to describe quantities and structure, then I can't see why you won't accept that mathematics is inherent to nature.

because the phenomena in and of itself and the description of the phenomena in mathematics are two distinct things.

From a physical standpoint, numbers are nothing more than words and symbols that define natural quantities. Sure, we have learned how to abstract the concepts of numbers but, when dealing with physics, numbers represent measurements of physical quantities and scalars that relate one quantity to another.

exactly, they are used represent the phenomena but are not the phenomena.

and i'm not sure what you mean when you say "we have learned how to abstract the concepts of numbers," numbers are abstract objects as are other mathematical objects.

From a physical standpoint, numbers are nothing more than words and symbols that define natural quantities.

then what defines the numbers and their properties, or "the pieces and rules of the game" according to this view?

your entire argument takes for granted that numbers indeed exist and have properties (somehow in nature) and ignores such formal things as peanos axioms which underlie numbers.

And we use numbers everyday becuase they exist as quantities in nature.

the quantities are numbers assigned in accordance to the units and theory (or theories) of the measuring device (or what it is measuring). there can be several layers of abstraction (using several independent equations for example) between some initial measurement of a physical quantity and calculation of some other physical quantity.

take the single slit diffraction experiment:

say you have a beam of monochromatic light with wavelength λ, slit width a and distance to screen L

you want to find the displacement of the first minimum, so you calculate θ from asinθ = mλ and plug it in to tanθ = y/L to calculate y.

Edited by andrewcellini
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I haven't given up on this conversation. I just am taking a few days to gather my thoughts and solidify my arguments. You guys showed me I hadn't worked this out all the way, I am not done but it's coming along.

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Why not?

Science doesn't need anything to exist except experimental results and the definitions and axioms to define them.

Indeed, it's the very lack of assuming reality that allows a thread like this to exist.

The only thing that is clear here is that you have either not read the original post properly or that you have ignored it.

To refresh your memory the question was and still is

"Does Mathematics exist in Nature?"

If Nature does not exist then nothing it contains can exist and we have no discussion.

So for the purposes of having this discussion we need to assume the existence of Nature.

For those who think that the original question did not include the possibilty that some part of the whole of Mathematics is manifest in Nature and wish to stick to numbers, why would you expect counting in Nature to be the same as counting by humans?

For one thing counting by humans is not always accurate, humans make mistakes.

Animate entities already discussed also make mistakes.

But inamate Nature can count with 100% accuracy.

For example when sodium chloride or calcium chloride dissociate into ions, exactly the right number of electrons is always transferred.

Never ever one too many or one to few or 1.3 times the correct number.

That fellow fallible humans is counting.

Edited by studiot
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The only thing that is clear here is that you have either not read the original post properly or that you have ignored it.

To refresh your memory the question was and still is

"Does Mathematics exist in Nature?"

You couldn't be more wrong and the answer remains unchanged. Math does not exist in nature. Math is a human construct which is unreal and only works because it is based on the same natural logic as nature itself. There is no math in nature and nature doesn't even agree that one plus one equals two. You can't see this because you understand everything in terms of science and math so it simply doesn't exist for you. It doesn't matter how many examples I provide or how many perspectives because you believe in your heart of hearts that one plus one equals two. If you believed in the Almighty then everything you saw would support this belief. Indeed, no matter what you believe you are on your way to becoming that.

This is caused by the operating system we use called modern language.

If Nature does not exist then nothing it contains can exist and we have no discussion.

I didn't say reality doesn't exist. I said the existence of reality is beside the point to science. "I think therefore I am" is sufficient. This is why you can't see the nature of language. It was your consciousness that gave you birth therefore language is beside the point to you. As such reality is defined by your beliefs which are derived from the effect of reality on experiment. Other people believe in other things. Everybody is on a different page as exemplified by this very thread.

So for the purposes of having this discussion we need to assume the existence of Nature.

For those who think that the original question did not include the possibilty that some part of the whole of Mathematics is manifest in Nature and wish to stick to numbers, why would you expect counting in Nature to be the same as counting by humans?

For one thing counting by humans is not always accurate, humans make mistakes.

Animate entities already discussed also make mistakes.

But inamate Nature can count with 100% accuracy.

For example when sodium chloride or calcium chloride dissociate into ions, exactly the right number of electrons is always transferred.

Never ever one too many or one to few or 1.3 times the correct number.

That fellow fallible humans is counting.

Science does not assume the existence of reality. Need I remind you that cosmologists now say there are an infinite number of pyramids built with an infinite number of ramp? How far outside of reality do we have to get before it becomes obvious? An infinite number of earths is as absurd as no earths or negative twenty earths. Reality isn't necessary to perform experiments or to derive theory. It was intentionally excluded because the inventors of science knew reality was subjective but theyt didn't know this subjectivity is chiefly the result of language which simply isn't reflective of either reality or a good means to discover or communicate reality.

You can't see this because you know what you'll see before you look. I know you'll see your beliefs and scoff at ideas that don't reflect those beliefs. You know math exists in nature because you love elegant equations and getting the right answer. You love the way everyone can get the same answer and can't notice when they get the wrong answer.

But inamate Nature can count with 100% accuracy.

Nature can not do math and can (must) only count to one.

People count and invented math for the purpose of counting.

As an aside it's quite likely that our math wasn't invented so much as discovered from an ancient source. Ancient math went with ancient language probably but it was adaptable to modern language. It's this adaptation we use as the basis of math.

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...

You can't see this because you know what you'll see before you look. I know you'll see your beliefs and scoff at ideas that don't reflect those beliefs. ...

Pot calls kettle black.

Again, it doesn't matter one way or the other; get over it.

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Pot calls kettle black.

Again, it doesn't matter one way or the other; get over it.

We all do it. But it does matter.

It matters very much.

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In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1) The orbit of a planet is an ellipse with the Sun at one of the two foci.
2) A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
3) The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

These laws of planetary motion can be drived from Newton's theory of Gravitation.

Since the motion of the planets can be predicted from a mathematical derivation based on Newton's theory of Gravitation, arn't the planets "doing the math" as they orbit around the Sun?

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So you have done the test I asked about above? If not how can you be so sure? What's your evidence?

I'm not taking any side, I think people need to think very carefully about what they mean with their questions and how you can make any definitive answer which can be backed by evidence.

There isn't any evidence for the existence of human conceptions, which are mostly about limiting the amount of information that our tiny primate minds can process. We speak in languages every day, but you won't find a scrap of evidence that our language is inherent in the warp and woof of the universe as a mystical kabalah.

Likewise, our mathematics mostly rests upon our tendency to separate and focus on limited relationships. On the very surface of reason, for example, I could count and say I had five apples. But that's actually specious. Are the apples identical on the molecular level? Not a chance. Are they even the same species of apple? Maybe not, but the language that I use suggests that I can call them all 'apples', but that's really a lazy shorthand because I don't want to individually name every single thing I come across.. My counting of five is actually an arbitrary distinction of my limited senses and my inculcated idea that I can keep items in my possession as 'mine'. In reality there isn't five of anything in the universe.

Edited by kisai
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In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1) The orbit of a planet is an ellipse with the Sun at one of the two foci.

2) A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

3) The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

These laws of planetary motion can be drived from Newton's theory of Gravitation.

Since the motion of the planets can be predicted from a mathematical derivation based on Newton's theory of Gravitation, arn't the planets "doing the math" as they orbit around the Sun?

I understand your point and can even agree that it often looks like nature does math. A cat walks into the room and then another cat and there are two cats in the room.

We find these elegant equations that describe aspects of reality by stepping infinitely far back through the isolation of variables and the effect of reality on experiment or through mathematics and it seems we understand the aspect we have identified. But it's obviously far more complex than this and this is what we simply choose not to see. Right off the bat the earth doesn't orbit the sun but rather the sun/ earth system orbits a point at its center of gravity. The earth is no simple thing with a name but is supremely complex just like every other real thing. If a pebble rolls down a mountain the earth accelerates toward that pebble taking it out of "orbit" and the everything must be recalculated. Even an electron deep in the earth's core must be hurtling through space while continually changing its orbit. An atom in the earth's core is affected by the pebble falling down the mountain and the earth's acceleration toward it.

Of course it's far more complex than just this since there are an infinity of other forces that affect the earth from the moon to a pebble falling down a mountain on the second planet of Alpha Centari. Of course none of these events can occur in isolation of every known and every unknown law. The planet also has a relativistic weight with magnetic effects and must plow through a solar wind and only God knows what else.

It's pretty hard for me to think of every grain of sand needing to do infinite calculations from moment to moment even if time were divisible into moments. It's far easier to imagine the universe as simply following a logic that is the same logic we have codified into mathematics. For me it's easier yet because there is another perspective I've found from the past. It's easy to see that language has been "simplified" so that it is useable but in the process of this change and the invention of modern science perspective has changed. We don't see things from the "inside" but rather we step infinitelyt far away and describe them through models and the constructs of language. Ultimately this is what our mathe is; a construct of language based on the same natural logic as the pebble rolling down the mountain.

There isn't any evidence for the existence of human conceptions, which are mostly about limiting the amount of information that our tiny primate minds can process. We speak in languages every day, but you won't find a scrap of evidence that our language is inherent in the warp and woof of the universe as a mystical kabalah.

Likewise, our mathematics mostly rests upon our tendency to separate and focus on limited relationships. On the very surface of reason, for example, I could count and say I had five apples. But that's actually specious. Are the apples identical on the molecular level? Not a chance. Are they even the same species of apple? Maybe not, but the language that I use suggests that I can call them all 'apples', but that's really a lazy shorthand because I don't want to individually name every single thing I come across.. My counting of five is actually an arbitrary distinction of my limited senses and my inculcated idea that I can keep items in my possession as 'mine'. In reality there isn't five of anything in the universe.

It would be impossible to make sense of the world without an operating system for the brain. It's this operating system that tricks us into believing five of something exists, we exist as a consciousness, and we understand existence.

WYSIWYG.

Of course what you see is defined by the operating system.

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Likewise, our mathematics mostly rests upon our tendency to separate and focus on limited relationships. On the very surface of reason, for example, I could count and say I had five apples. But that's actually specious. Are the apples identical on the molecular level? Not a chance. Are they even the same species of apple? Maybe not, but the language that I use suggests that I can call them all 'apples', but that's really a lazy shorthand because I don't want to individually name every single thing I come across.. My counting of five is actually an arbitrary distinction of my limited senses and my inculcated idea that I can keep items in my possession as 'mine'. In reality there isn't five of anything in the universe.

Hello, kisai, let me introduce the collective noun.

In the traffic queue outside my house there are 5 different types of car.

So, like the apples they are all different.

But they are all vehicles.

So there are five vehicles.

Likewise there are five fruit in the basket of apples.

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...

It's pretty hard for me to think of every grain of sand needing to do infinite calculations from moment to moment even if time were divisible into moments. It's far easier to imagine the universe as simply following a logic that is the same logic we have codified into mathematics. For me it's easier yet because there is another perspective I've found from the past. It's easy to see that language has been "simplified" so that it is useable but in the process of this change and the invention of modern science perspective has changed. We don't see things from the "inside" but rather we step infinitelyt far away and describe them through models and the constructs of language.

...

Of course what you see is defined by the operating system.

So if we accept your proclamations that language is universally inadequate, your use of it is just as useless as it is for the rest of us. But I guess you acceded to this when you replied to my pot-calls-kettle-black with , 'we all do it'. By your judgment, while we're all just pissing, you win because you're pissing into the wind.

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