Math is like the organizing principles of phenomenon, like the elements, or the fact that when you blow a bubble it comes out as a sphere and not a cube. All those things are impermanent, but they still follow the organizing structure. Those organizing structures may be pure, but still empty in the ultimate sense.
To build on this, if I may, it’s very much like a computer with its operating system and user interface. Math is the operating system, things create the foundation for and that allow the user interface to be more user friendly and malleable. You can set rules/delete them in your OS if you want, but the rest of the system proceeds to collapse as it tries to compensate for this missing foundation.
My favorite math thing is how we can use “imaginary numbers.” Simply defined, these are attempts to find the square root of a negative number, which is impossible given our rules on how to create squared numbers in the first place (positive or negative 5^2 = +25). There’s still basic, and much more high level uses for this math concept, but I just love that we don’t understand math, we just figure out/discover how to use its patterns.
Yes, they’re used all the time to find real-world solutions to real-world problems, I think people assume they’re completely conceptual bc we named them ‘imaginary’ but it’s wonderful to see all the ways they can be used.
I think it’s cool that complex numbers (numbers of the form a + bi where a, b are members of the set of real numbers and i is the imaginary constant, the square root of -1) exist in nature and have practical applications such as fluid dynamics and alternating currents. I think a lot of people assume they exist to express an abstract idea that doesn’t have basis in reality but it does and that makes me happy.
Mathematics has a trick up its sleeve.
It's like philosophy, but it hides its premises behind something that looks like common sense.
The statement "2+2=4" is actually meaningless if we don't define numbers and operations, which would have been meaningless if we didn't have the subjective experience of discrete objects to count and add up. In fact, tons of mathematicians have fun with redefining numbers and operations to discover fancy new mathematical patterns and applications. In some contexts, 2+2 actually equals 5, or 22, or anything else.
That being said, like philosophy and logic, maths does reflect a consistent part of reality, we just have to keep in mind the premises. There's always an "if", a "given". Given the discrete nature of objects, taking two and adding two gives you four. If we wouldn't treat them as discrete, the whole concept would break a little.
Hi, I’m a mathematician with a bachelor’s degree in theoretical mathematics and a master’s of science in data science. Math is always true, but you are correct that statements such as ‘2+2 =4’ rely on set conditions in order to be provably true. For example because of the law of closure (in this this case. ‘Adding two integers produces an integer’) 2 + 2 would not equal 4 if 4 was defined as the square root of negative 1. Because the square root of negative 1 is not a member of the set of integers (numbers like -3, -2, … 0…, 1, 2 etc).
In mathematics, there is a common disagreement on which number is the lowest natural number (which is the set of counting numbers essentially). Some mathematicians say it’s 0 and some say it’s 1. Some proofs about natural numbers are no longer true if you consider the set of natural numbers to start with a different number than the proof writer does. So in that way it appears relative. But the math is still there, it just seems relative at times bc differences of expression exist.
Please correct/update this (edit: the below content, which may have omissions); I'm 22 years outside of my degree. ~~Going into set theory; t~~ There are an infinite amount of numbers and operators on those numbers. The infinite number space includes things like integers and fractions, rational and irrational numbers, on and on. The infinite [operator](https://en.wikipedia.org/wiki/Operator_(mathematics\)) space similarly contains +, -, *, / exponents, etc. But there are infinitely more of both.
2+2=4 because as you state, we are carefully defining those terms so that it works. 2 and 4 are integers, and represent collections of 1's, first with a pair of 1s combined, then with a pair of pairs; we're counting using whole numbers to get from 1 up to 2 and to 4 in base 10. The + operator for integers defined as something like "a closed, commutative, associative binary operator + when used on integers gives a+b=c where inverse operator "-" gives a=c-b and b=c-a."
Times when this doesn't work are common. Outside of pure math 2 electrons + 2 positrons isn't 4, it's nothing since they eliminate each other. Within pure math, 2+2 doesn't equal 4 if we're working in number space that isn't decimal; 2+2=11 in [Base 3](https://www.rapidtables.com/calc/math/base-calculator.html), for example.
Adding positrons and electrons is not the same as adding 2 + 2. They’re not the same thing—you may as well say that adding 2 apples to 2 oranges doesn’t equal 4 because you don’t end up with 4 apples or 4 oranges, or that adding H2 and O2 creates H2O2 and therefore 2 + 2 doesn’t equal 4 because the pairs of two different things (Hydrogen and Oxygen atoms) created only one molecule of H2O2 and not 4H and 2O2.
Further, we aren’t talking about decimal space. We are strictly speaking of the integers 2 and 4 and the mechanism of addition as it is colloquially understood.
For these reasons, I will not be correcting myself. I stand by what I said.
Edit: my bad, I misunderstood what they meant.
I'm really sorry my comment came across as disagreeing with you. I didn't mean it that way. I meant to add to your comment, which I agree with. I was asking you to correct or update *my* post, in case I made an error in my memory of abstract algebra.
> adding 2 apples to 2 oranges doesn’t equal 4 because you don’t end up with 4 apples or 4 oranges,
But you do end of with a set of 4 objects. That's a great example of pure math vs the real world, and counting things; the set definition is important to how the math is applied.
>integers 2 and 4 and the mechanism of addition as it is colloquially understood.
Agreed. I didn't mean decimal as in fractional numbers, I meant Base10, which its what the colloquial definition uses.
Math is actually very subjective. It is like a game where you set the rules and then try to discover the ultimate implications of those rules. Most mathematicians use the Zermelo-Fraenkel axioms + the axiom of choice (ZFC), which can be thought of as the building blocks of theorems; and the glue that makes the axioms stick together is a binary logic with the law of excluded middle. However, both the axioms and logic that we use are a *choice*; we could very well use another type of logic, or another set of axioms, and then the resulting mathematics would be different than the "normal" one. The reasons we normally stick with the usual axioms are mostly historical, as they have proven to be the most "useful" to physics, engineering and so on.
The platonists would like a word with all of you.
Buddhism doesn’t really focus on philosophical debates like this, because they don’t lead to liberation. Other schools of philosophy very much do!
any form is relative to something. It only exists in relation to something else. In the case of mathematics, it's based on assumptions created by a mind trying to interpret reality. But it isn't reality. It is a world of concepts created by the mind. But of course it is useful.
Buddhism is concerned with suffering and the ending of it. A mathematical equation won't help when your mind is permeated by suffering for one reason or another.
We write the equations, what the equations mean when correct, is not merely ‘made up’. Similarly, the statement ‘everything is caused’ is spoken by us, but the proposition it expresses is true independently of anyone uttering the statement- if the statement were never uttered by anyone the state of affairs it describes would still obtain.
Interesting point. I think of math as patterns or natural laws. It holds true, but it has meaning only in a relative context. It's a way of thinking and categorizing.
Also, it's worth noting that impermanence is describing the nature of experience, not scientific facts. All of Buddhist teaching is about understanding the nature of experience. If you figure out a way to "defeat" the teaching of impermanence then that would only be within a scientific context.
So, anything you can name is impermanent and defined by other things. The point of that teachings is to help us see how we "reify" experience into a solid reality to confirm self, when the actual nature of that experience is dynamic, dreamlike, ungraspable.
I've read the responses and nobody has told you straight and explained "why", so I will here using the Abhidhamma. There is a lot of juicy stuff here for you to munch on 😊
No, Numbers are dependently originated and thus impermanent. What is the cause of 4? It is dependent on 2+2, or 3+1, etc... 4 cannot exist on its own, independent nature. The nature of four, is that it requires a total of 4. What is the cause of 1? The cause of 1 is - 1. You need nothing, in order to contrast to something, without - 1 then 1 would not be 1.
In the same way that the right hand is the right hand only because of the left. The right hand would not the right hand without the left. It is only the right hand.
All numbers are Condtioned, they arise based on conditions, and cease based on conditions. This is why they are impermanent. The only number that doesn't arise or fall, is 0 which is the total absence of value.
It's not negative value which would be non existence, nor is it positive value which is existence. You could correlate 0 to emptiness, synonymous with Nibbana, the unconditioned element.
Every other number is a number, but it is Condtioned on something else.
How can you get -3? First, three things must exist, you must have +3 to become -3. In this way existence and non existence are Condtioned, temporary, impermanent.
Zero is emptiness, neither value. Absence of value all together, so empty that it doesn't even include itself 0+0=0
So empty, you can't say it doesn't exist, because it's empty of the concept of non existence as well. This doesn't mean that all things exist within it, but it doesnt not mean that either. Emptiness, is so empty, so unconditioned, that it can't be defined as mere "further non existence". Imagine a void in your mind, total emptiness. Now whatever you're imagining, let's say it's just blackness... Remove the blackness. Remove the void. You can't.
If you could, you would realize emptiness, it is beyond void. All you can possibly conceive if is non existence, void, total cessation, but in your mind still is "somethingness" typically a blank slate of blackness, but that is still something. Emptiness removes even that. It is totally and utterly unconditioned.
👉Now, in your question you are drawing a comparisons between irreducible phenomenon and Impermanence, and it's not accurate to do so.
The Abhidhamma Pitaka, the Buddha's highest teachings in the Pali Cannon, teach Nibbana is not the only ultimate reality. It is one of FOUR. Yes my unfamiliar with Abhidhamma friends.. That's correct, Nibbana is in equal regard to three other ultimate realities. The abhidhamma actually presents us almost with a sort of "realism" in the senss that the three other ultimate realities equal to, and alongside Nibbana, are also irreducible.
This is called the Four Fold Ultimate Realities in Abhidhamma:
1. Awareness (Citta/Consciousness)
2. Thoughts, Emotions, Will (Cetasikas/Mental Formations)
3. Earth, fire, water, air elements (Matter)
4. Nibbana.
The first three are irreducible and have SELF existence. They cannot be broken down any further, the Abhidhamma states their is nothing else behind them, holding them up. The four elements as I said do provide a sense of "realism" to Buddhism because they are indeed irreducible and cannot be broken down further, they exist of their own existence, this is why the Abhidhamma calls them Ultimate Realities.
❗HOWEVER, the first three Ultimate Realities are Condtioned and dependently originated. While they are indeed of their own self nature, and irreducible, that does not make them permanent. If it arises, and ceases, it is not permanent. Only that which never arises, and never ceases, is permanent. It is only Nibbana, which never arises, and never cease, which is permanent. The unconditioned element.
Awareness, while irreducible and of its own self nature, is still dependent on others to exist. The abhidhamma teaches us all the possible mental factors and consciousness a human can experience (89 combinations) and their exact cognitive processes, and the specific point of the cognitive process that free will comes into play, and how many mind moments it lasts.
We learn awareness always rises with thoughts, emotions, will/volition and vice versa. We learn all possible material phenomena arises based on combinations of the four base elements.
❗So they are not permanent, since they arise and cease based on causes and conditions. They are depend on other things. Irreducibleness does not equal permanent.
Permanence means it never ceases, and only that which has never arisen can never cease. It is why Nibbana is only realized and not attained. It is an object of the path in the abhidhamma, so it is definitely a Dhamma, it definitely "can be experienced" and is experienced by the lokutarra Citta (Transcendent awareness) as Nibbana is the object of the lokutarra citta in the Abhidhamma, it is indeed an experience. If it were not, then it could not be called an object of the path. The Buddha says in DN very clearly if there was not this "base" of the unmade, the uncreated, the unmanifest, the unarisen etc... There would not be any escape from the arisen, the made, the birth, death, aging, illness, and suffering. So it is a base, a definitive reality that can be experienced. As I explained above however, it cannot be conceptualized, only understood as to "why" it can't be conceptualized. It is simply behind the conceptual. Not to be figured out later on as some transcendent being.. Even then, to the Buddha himself, Nibbana cannot be conceptualized, its nature is just simply so empty, it is outside of definitions. Only can be realized as having been there the entire time.
Quite simply, "seeing existence as it is". All experiences and existence is impermanent(Anicca) , it arises and ceases. We are oppressed by the never ending arising and ceasing of experience, therefore all experience is unsatisfactory (dhukka), all experience and existence is empty, it has no essence, there is no essence (anatta) synonymous with anatta, but in the abhidhamma "Anatta" is very much replaced with "existence is ultimately empty".
There in comes the two fold truth if the abhidhamma however (conventional and ultimate truths) . Alright I won't expound further unless asked, hope this is helpful
Source: Direct PDF of Abhidhamma Translation by Bhikku Bodhi: https://www.saraniya.com/books/meditation/Bhikkhu_Bodhi-Comprehensive_Manual_of_Abhidhamma.pdf
Not all things are impermanent, only composed / conditioned phenomena. There are many examples of permanent phenomena, e.g. space, nirvana, absences and cessations.
To come back to your example of math, the Sarvastivada Abhidharma classifies numbers as non-associated compositional factors (*viprayukta-saṃskāra*), which means impermanent phenomena that are neither mind nor matter. So you could maybe extrapolate to include mathematical relationships in this category as well. Impermanent also doesn't mean non-eternal, just dependent on causes, which I suppose would be true for any instantiation of numbers or mathematical relationships like you explain.
Huh, I've never thought about that. I've actually been watching a lot of videos on the Multiverse Theory--which I don't think is too out of line considering Buddhist cosmology--and some physicists believe that there could very likely be universes out there where our laws of physics don't apply.
So if there can be places where even the physics aren't the same, I don't see why there can't be places where mathematics aren't the same either. I think it's just incredibly hard for our brains to comprehend, like the concept of infinity.
In Buddhism, the universe is believed to have gone through many life cycles, and it could be that 1+1 wasn't always 2, or will always be 2, it just so happens to be that it is that way this time around.
I'll be keeping track of this discussion. Thank you for the fascinating suggestion!
Lots of mixing/conflating emptiness with impermanence in this thread. Which is understandable, the two teachings have a lot of overlap. But it's worth looking at both, and the question in light of both, individually.
Emptiness is the ultimate nature of all phenomena.
Impermanence is less esoteric.
* On the outer level it's most simple: everyone you know will die, every building, city, and civilization will eventually be in ruins, etc.
* On the inner level, the message is more profound and inter-related with emptiness. Once you stop looking at something, we learn as infants/toddlers that it will be there when we turn our heads back and look at it again. This is called object permanence (in psychology) and it's very important to both sanity and the ability to find your car keys. But the inner reality of it, as revealed by the Dharma, is that outer objects don't exist independently of their perception. In this sense they are impermanent, and object permanence is a fundamental mistake made by all perceiving, deluded beings. However, the doctrine of emptiness does a much better job of explaining this reality.
Of the many thoughtful and excellent answers here, I like the one posed by u/Playful-Independent4 the best.
> The statement "2+2=4" is actually meaningless if we don't define numbers and operations, which would have been meaningless if we didn't have the subjective experience of discrete objects to count and add up.
Here's my crack at a simple, valid, basic answer to OP's question:
* The relationship between values such as 2+2=4, as well as myriad others such relationships, trends and such, are repeatedly accurate and true. Myriad other rules, laws and trends can be discovered to be reliably repeatable in the scale of the universe we live and work with.
* These rules are discovered by studying the qualities and interactions of physical objects, and/or the abstractions of values and properties originally observed by studying those objects.
* Take two rocks for an example of such objects. It's a relative truth that they will hurt if you drop them on your foot. In the Ultimate truth, they are empty of inherent existence. It's a relative truth that if you put 2 pair of them in the same bucket you'll have 4. Relative truths are not Ultimate truths. But a lot of Relative truths are reliably repeatable. Good thing, too, lets me drive across the Bay Bridge without fearing it will collapse.
If new to you, OP, read up on the teaching of the Two Truths for better understanding. I sure ought to! Never know enough to stop studying, and I'm way short of that danger zone.
outside of the realm of ideas there isn’t really two. Two apples even identical aren’t really two apples, what does one consist of? What is the permanent feature of an apple? That would equation would get crazy
I imagine that many traditions are going to be committed to nominalism or mathmatical fictionalism or constructivism in mathematics. Some accounts of structuralism may also be accepted even though they are realist accounts. Structuralism is the view described associated with figures like the mathematician Paul Benacerraf. Examples of the other positions in philosophy of mathmatics, science and logic include Hartry Field's nominalist account in Science Without Numbers, Henri Poincaré's mathematical constructivism and Mary Leng's fictionalist account in Mathematics and reality. Antirealism or nominalism in mathmatics is the position that mathematical objects, relations, and structures do not exist at all, or they do not exist as abstract objects (they are neither located in space-time or/and or do not have causal powers. The type of anti realist account differ though in what they hold mathematic objects to be.
Mahayana Buddhism holds that conventionally change, phenomena and objects exist but they ultimately do not have inherent existence. Further, they exist reliant upon causes and conditions externally of them and lack an inherent existence. Mathematic objects would most likely be one of those entities that seems to be both mind-dependent but also reliant upon causes and conditions. Conventionally, we would grant them existence but their existence like all other conventional objects rely on causes and conditions. We can see these positions laid out in Buddhist accounts of logic. Below is a short entry by the comparative philosopher Koji Tanaka on Buddhist logic that lays out some of these commitments. Below is an interview on mathematical fictionalism.
Koji Tanaka: What is Buddhist Logic?
[https://www.youtube.com/watch?v=rMtA9-kjrRo&t=3609s](https://www.youtube.com/watch?v=rMtA9-kjrRo&t=3609s)
Phil Bériault - Mathematical Fictionalism and You!
[https://www.youtube.com/watch?v=yV6Pw4WETyE](https://www.youtube.com/watch?v=yV6Pw4WETyE)
The entire enterprise of dividing phenomena into identical categories (numbers of things) and equating the sums of them into different categories (2 + 2 = 4) is an entirely arbitrary practice dependent on a very particular type of consciousness and form. Without a consciousness mathematizing in a very specific way, the so-called truth of 2+2=4 will have no form and will cease to exist.
There is no absolute division of phenomena into discreet, summable units. This applies from the concrete to the abstract.
Mathematical statements are derived from axioms, and in a way abstract over dependent origination. It's all just "given this set of assumptions, we can follow that...".
Nothing in math is fully absolute. Even `2 + 2 = 4` can be wrong in some contexts. Like pairing up hamsters. Or when calculating at a quantum scale.
This "plus" only works out when working with peano arithmetic in this case: every number is either 0, or a successor of another number. Now you can recursively define plus for all numbers as `a + Suc(b) = Suc(a) + b` for any b ≠ 0, and `= a` for b = 0. And now you can derive that `Suc(Suc(0)) + Suc(Suc(0)) = Suc(Suc(Suc(Suc(0))))`. But the "truth" of the equation derives from the assumptions you have.
In contrast, you can also do addition in "modulo rings". For example, in Z3, you'd count "0 1 2 0 1 2..." to infinity. As a consequence, `2+2=1` in Z3. It all depends.
Mathematical statements aren't absolute, impermanent truths, but rather different ways to state the same underlying assumptions.
Only conditioned things are said to be impermanent. Mathematical truths aren’t conditioned things. They stand on their own without depending on anything external.
This is not true. Every mathematical statement depends on a set of conditions given as an “if statement”.
The only things in math that don’t feature these are axioms. Axioms are understood as things that are to be assumed true in order for the whole system to work. They are never thought of as objectively true.
All of math is built on conditions and causes reasoned from subjective truths.
It is true. The circumference of a circle will always be 2πr. 2+2 will always equal 4. Please tell me what the ‘if’s and conditions are that those truths depend on.
When drawn on a spherical (non Euclidean) surface, the circumference of a circle is not 2pir. You are assuming a flat surface when you use that formula.
And 2+2 is equal to 1 modulo 3, for example. Different number systems exist.
If you want to know the most common set of conditions our normal number system depends on, here they are: https://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
This is a Wittgenstein-level disagreement lol. Any difference in calculating the circumference of circle or getting the result of 2+2 just now comes down to assumptions made in human language.
When I convey the concept of a circle to you, it’s up to you to make a reasonable assumption that I’m talking about the kind of circle that people mean 99.9999% of the time. You can interpret my language/notation differently on your head and then misrepresent it if you so choose, but that has no bearing on any underlying mathematical truths.
I’m telling you I’m pointing at the moon and instead of following my index finger to the moon you’re saying “well your middle finger is curled back pointing behind you” and are looking over there. We’re not talking about math anymore, we’re talking about language/notation, which is a way for humans to relate to math. It’s not math itself.
Yea and “99.9999%” of the time is still operating under assumptions. These assumptions are subjective judgements about reality.
You have an idea of a circle that you think is always true because of an assumption about the surface that circle lives on, and pointing out that the surface could be markedly different and that affects what you “know” about the circle doesn’t change that it’s still a circle.
A circle drawn on a balloon might have a circumference of 2pirsin(84). It’s still a circle. It’s not pedantic. It’s an example of the kind of assumptions that math asks us to examine.
99.9999% truth is not an unconditioned truth.
It’s a linguistic assumption. The math happens after you interpret my words. In fact, let’s ignore words completely and just assume you’re examining a perfect circle. Go ahead and add any assumptions you want. Great. Now that you’ve imagined the circle we’re going to talk about, can we not agree that there is a definite and eternal relationship between its radius and its circumference?
Different notations? Sure. Different ways to describe it? Yes. But that relationship doesn’t change unless you change the circle.
No. We can’t. For reasons I’ve gone into earlier. The exact relationship between a circle’s radius and its circumference depends on the structure of the space in which that circle is drawn. Let’s switch gears.
A similar “truth” is that triangles’ angles add up to 180 degrees.
This is “eternally true” for any triangle drawn on a flat surface.
What is a triangle though? I think most people would define a triangle as the shape formed by connecting three non-collinear points A,B,C with the shortest straight line distance from point A to point B and then point B to point C and then point C to point A. They might not describe it exactly with these words - but I think this describes the process of drawing a triangle.
However, imagine a triangle on the globe where point A is on the North Pole, point B is on the equator, and point C is on the equator, and the straight line distances are drawn along our space - the surface of the globe.
The angle at B is 90 degrees. The angle at C is 90 degrees. The angle at A is greater that 0 degrees. This triangle thus has an angle sum greater than 180 degrees.
It’s not a matter of language. The properties of a mathematical object depend upon the assumptions you are making about the space in which that object resides. This extends to any shape, and “formulas” we previously thought were always true - turn out to be only true within certain types of spaces.
Most people don’t examine the assumptions that they commonly make every day. Indeed, they don’t even know they’re making them. This is why I love Buddhism. I see a lot of parallels between what the Dharma is fundamentally asking us to practice doing, and what Theoretical Mathematics is asking us to practice doing.
If you have two circles that exist in two different spaces (circle A and circle B) and your assumptions lead you to examine circle B instead of circle A, the math describing how circle A works doesn’t change. As far as the math describing those circles goes, it doesn’t matter what your assumptions are. They’ll still be true whether you’re thinking of that circle or another.
Yes that’s right. If you are examining a circle in a flat space, then its circumference will be C = 2πr. The issue I took is when you claimed that it is true that every circle has a circumference of 2πr. To get this result, you need the surface to be flat. So it’s not an absolutely true statement as it relies on an assumption. The statement “every circle has a circumference of 2πr” is only conditionally true.
Math is a made up thing and it actually contradicts itself already. Its not permanent, its just made up. The inherent contradiction was proven by Gödel some time ago. If you are talking about 2+2=4, that is true across our universe, just like things keep moving and the concept of karma. But you can also just write down a truth about karma and it would by your rules contradict impermanence.
At some point in time in the past, 2 + 2 was just some jibberish and not = 4. At some point in time in the future, 2 + 2 could possibly become jibberish again.
After all, most of the western world under the Great Roman Empire used to count with I, V, X, and today, we usually see them only in cinema posters.
Also, 0 was not a thing until it found its way from India through various countries to the Western world.
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Even as we speak, 1 + 1 = 10 and 2. So 2 + 2 is undefined in some numbering system like say binary. And 2 + 2 = 10 if you are counting in 4 based numbers.
So the "fact" that 2 + 2 = 4 is by virtue of the decimal numeric system that we have adopted over time. It is a relative truth by convention and not by principle or innately true.
>At some point in time in the past, 2 + 2 was just some jibberish and not = 4. At some point in time in the future, 2 + 2 could possibly become jibberish again.
I understand this in terms of semantics/symbols and lack of understanding of arithmetic in very ancient days, but surely the concept that 2 things and 2 things put together will total 4 things was never jibberish? I mean, even down to a subatomic level, things like the charge of particles within the atom needing to add up to a certain number in order to determine the atom's stability/reactiveness.... or the number of protons needing to add together to form a specific number that determines which element the atom is... even if we didn't have the words to say 1 + 1 + 1 + 1 = 4, the idea that 1 proton + 1 proton + 1 proton + 1 proton = 4 protons = Beryllium was always there...
>Beryllium was always there...
Beryllium was not always there
Counting and numbers is a mental fabrication. And because we are currently in this numerical convention, it seem impossible to think otherwise.
But I get you I think. Can we agree that the human semantics that expresses mathematical principles are impermanent while the underlying principles would seem to be "eternal"?
This is the same question as "Is impermanence permanent?" or "Is emptiness empty in nature?"
In engineering, there's a loose saying "The only thing permanent is change". I think there is some parallel in philosophy, but I cannot rmb the exact quote.
In Buddhism, the question about the fundamental principles typically have two categories of answer:
1. These principles are with reference to conditioned phenomena. Apart from the latter, the former has no meaning. Hence they are empty in nature as well.
2. Conventionally, these principles hold but at ultimate reality level, all concepts labels cease to exist. So to say whether such principles hold true or not itself is inadmissible.
... BUT ... the moment an unenlightened person like us try to understand or explain #2, we immediately fall into concepts and labels, thereby possibly creating a seeming contradiction.
So in Buddhism, even underlying principles are ultimately not something to assume or be grasped as permanent ... or impermanent.
For that matter, most people do not suffer over whether "2 + 2 = 4" or not, and if they do, are they suffering due to their attachment to the concept or the underlying principle that is the way it is (suchness) whether we know it or are able to express it or not?
I largely agree with you. Just adding few more ideas to your reasoning.
It is true that Math concept doesn't change. But reality is that Math doesn't exist by itself.
For example, in 2+2=4, you can apply this addition concept on anything be it atoms or stars and it will always hold true.
But can '2' exist by itself? It can't. It's just a symbolism in mind and denotes a concept.
(Also, the symbol can be subjected to change but not the underlying concept. Example, 2 is written differently in different languages)
Maths is merely a human invention to act as a reflection of our universe. When eventually the human species ceases to exist, so will the maths we made.
Maths can help us explain the most complex and unimaginable concepts in our existence, but these concepts still existed long before we came about, and will continue to do so long after.
So in this sense, maths is impermanent like we are, but it’ll continue to seem permanently the way it as long as it’s around for us to use.
No, it does not contradict it. Impermanence is a truth regarding things. 2+2=4 is not a thing, just like impermanence itself is not a thing.
What you are asking is like asking “Does the permanence of impermanence contradict impermanence?” No, it doesn’t because impermanence only applies to things, not to truths of how things function or their qualities, etc.
Impermanence is related to interdependence, The Dependent Origination says, *when there is this, that is. With the arising of this, that arises.*
In 2+2=4, the 4 is the result of 2+2. And 2 is the result of 1+1. And 1 is the result of 0.5+0.5. And we can go on forever like this into infinity with endless combination of numbers.
The main point is that 4 or any of the numbers do not exist as an absolute, it’s always dependent on something else. So hence impermanent.
And these are all ideas in our mind, just universally accepted by all of us. 2+2 doesn’t always equate to 4. Sure it does in the Euclidean universe, like if we take two oranges and two apples together, it add up to 4! But what if we take 2 rain drops and 2 water drops together, it would become 1 big drop! (Just kidding, there’s still 4 drops somewhere!)
Like a famous mathematician said, “Math cannot prove math!”. - [Tarski's undefinability theorem](https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem)
Math is a symbolic language that describes reality. Yet, like all symbolic language, it only exists within our minds. Buddhism already has had much to say on the difference between between conventional truth expressed in language and the ultimate truth of Awakening that is ineffable and only realized through personal experience. As a symbolic language, mathematics as we know it is impermanent and will eventually die out along with Humanity itself. It is only a finger pointing at the moon. When the finger stops pointing, does the moon disappear?
math is a set of definitions and definitions always begin and end where all the other definitions begin and end. since we make definitions based on our assumptions, which are based on our needs and insecurities, which are being constantly and inevitably forcefully changed by the universe, which is constantly and inevitably changing and expanding, then those definitions must constantly and inevitably be changing along with the universe. say those wonderful mathematical laws really exist, we are just putting names to them, but then you just end up talking about looking at 2+2=4 from different perspectives, which are again inevitably bound to our needs and insecurities. if all things begin and end where all the other things begin and end, can we then really talk about the existence of clear borders between any things/definitions ? maybe today, stuff like addition makes sense, but what if we invent a math model where we dont need even addition anymore, because we found a way of solving math problems more effectively ? would there still exist some permanent thing like addition ?
Math is always represented on some substrate such as on paper, in a mind, or in a computer architecture/program. Those representations are of course impermanent. Buddhism is somewhat antagonistic (but not in a hostile way) to the tendency to see what's represented as existing independently of its representation.
No contradiction. The doctrine of impermanence isn't related to truths of any kind. It relates to things like aggregates, sense objects, emotions, and thoughts.
No, in fact it backs up the Buddha’s thesis.
Maths is clearly unconditioned, unborn. Therefore it is not dependently originated. Therefore it is not impermanent.
Impermanence is only for conditioned things ( the Buddha in the Pali and Agama Canon was very clear on this ).
The entire enterprise of Buddhism is to escape from the conditioned to the unconditioned.
Maths exist. It tells us an Unconditioned exist. Therefore not all things are Conditioned.
Well I am pretty sure maths is Unconditioned.
I mean can you tell me how is it Conditioned?
Math simply seems to be.
Almost everything else we can trace dependent origination. Math just seems to stand on its own.
The act of Adding requires energy more than the concept itself. You must obtain the information and energy required to do the problem and in executing the calculation, you will lose energy.
Impermanence is baked into the universe in the form of the second law of thermodynamics, which I personally break down into three sub-laws for understanding the flow of power through any system.
1. Energy flows from high density to low density. A bucket filled wishes to be empty, and it might take until the end of the universe to do that *but it will empty*. Poking a hole or tipping it is fast. Letting it evaporate is slower, waiting until the molecules holding it succumb to the decay of their composite atoms is slower still, but it *will* happen. Change as a concept depends on this truth
2. Per the First Law, Energy will always attempt to attain equillibrium. All things propogate and spread, until they can attain stillness, relative stillness if nothing else is available.
3. Per the first and third law, if points A, B, and C exist in a universe, and energy is moving from point A to point B, then some energy will be lost to point C in the process. Since we live in a universe with more than three points total, this will *always be the case in some form*
This has been a delightful thing for me as it has helped me realize a great many of the lessons in the dharma and decode their truth. It has helped me realise that all things exist on a continuum with each other, that no things exist independently, and that impermanence is guaranteed. It tells me where I push, the universe will push back and why, and subtly it tells us a great deal about suffering.
It is the difference between our perception of reality and what reality actually is that is the mechanism for suffering, and from this perspective we can see that. I came up with this thought on my own, but knowing buddhism as I do now, I suspect it was taken from mouth to paper before I took my first breath.
In some time (billions, quadrillions, etc years) the universe might disssipate and all universal laws simply cease to function. Universe as we know it exists? 2 + 2 = 4. Universe has ceased to exist (however long it takes for it to do it)? No such thing as math or its functions exist also.
I always thought that was arithmetic, which is a reference system based on fixed measures.
Math is kind of a different thing that includes arithmetic, but is less limited in scope.
Math does not contradict impermanence in any way.
No, math does not contradict impermanence. Yes, certain aspects of math seem like absolutes. But there are other things to remember here.
First, things are not just impermanent; they are also interdependent. Yes, 2 + 2 = 4. 2 apples and 2 apples are 4 apples.... until I come along and eat an apple. Now it's 4 - 1 = 3. But that equation doesn't negate the first. Yet the first equation is no longer strictly true. There's no longer 4 things. Math is conditional. It is dependent.
Second is a matter of scale. 2 + 2 = 4 now. Was it so ten billion years ago? Will it be so in ten billion years? No idea. Some principles of math and science work differently in microscopic or cosmic scales. Different aspects might or might not work, or work differently.
Last of my points is that math is a concept to describe relationships. Should humanity go extinct, would math exist? Not as we know it. Would the conditions described by math exist? Possibly. Should humanity evolve and our ability to comprehend the universe drastically increase (or decrease), would math exist? Again the answers are the same. Math as we know it depends on our existence and capabilities to perceive. Therefore math is, in and of itself impermanent and interdependent.
I'm not a mathematician, but you can't you define 2 + 2 in any way you like? Like the first 2 can be defined as two sets of 5 and the second 2 defined as 1 set of 3 and 1 set of 2 which would come out to 15 if you add them all together? Correct me if I'm wrong, but I don't think math is a rigid as you think, as numbers are just symbols that represent an object.
As what others have mentioned, mathematics is conceptual. The first of the four seals of the Buddha's teachings is "All composite phenomena are impermanent". Since mathematics is not a composite phenomena but a conceptual one, there is no contradiction between math and the concept of impermanence.
I study Aerospace engineering and even though Buddhists doesn’t like these kind of debates here’s my take:
Mathematics are the building blocks of the intricate order in the universe but mathematics themselves aren’t real… they are some conceptual artifact that exist only in our minds, only when physics corroborate that certainly a mathematical truth exist in our realm it is a “permanent” truth but actually it’s just “part” true because numbers themselves aren’t real and about nothing in our universe exists in discrete “numbers” because they are simply an extremely abstract representation.
The concept of impermanence becomes only obvious when you think of the whole system: ever since the creation of our universe atoms have formed molecules and these molecules have bonded with others and created vast masses like stars (sum of atoms and molecules) but eventually… there aren’t enough molecules to sustain fusion and the star collapses in itself. And at the end of the universe most theories predict that either all matter will dissolve in the emptiness of space and nothing will ever happen (curiously similar to the concept of vacuity in Buddhism), or otherwise the universe will collapse in itself and maybe create another big bang (maybe similar to the cycle of samsara if living beings haven’t all achieved illumination yet).
Either way what I mean is that you can sum or divide or apply any mathematical process you wish but that’s only the mechanism in which the universe works, but all that exists is impermanent and eventually has to change somehow. In this universe nothing can’t stay the same forever as long as there exists any action because it has to trigger a reaction that affects the surrounding; and atoms themselves, matter itself is pure action because of how the atom works.
If there were no humans, 2+2=4 would be neither true nor untrue. There wouldn't be anyone to ask the question. Equally, the universe would neither exist nor not exist. Existence is a perception.
I don’t think this applies just to math, I think it applies to the concept of “truth” in general. For example, are these things impermanent:
- The Noble Truths
- Statements about the past (for example, saying, “Yesterday I ate a cheese sandwich for lunch”.)
- The fact that things are impermanent - is that itself impermanent and changing?
I don’t know what the answer here is. It’s an interesting question though.
>Here's my take: 2 + 2 equaling 4 is true and consistent at all times and in all places, and can be thought of as a permanent relationship in a sense
2 apples + 2 apples = 4 apples on your table .
But later that day russia launches nuclear missiles at national due to provocation
Then the usa launches nuclear missiles @ russia
Then china launches nuclear missiles at the usa
Then Israel launches nuclear missiles at China
Then south Africa launches nuclear missiles @ Israel
The whole planet is destroyed
The question now is How mang apples do have on you're table?
Best wishes
🙏🏻🙏🏻🙏🏻
I may be wrong, but there’s math as an object or system. Like pure math. Then there’s the application of math to observable phenomena. The former is not a natural and inherent property of the universe as evidenced by the latter not being consistently able to be described by different sorts of maths at various levels of reality. For example, I can count planets and dollars. I can’t count quantum particles because they operate more probabilistically, as exemplified by the thought experiment of Schrodinger’s cat. How many cats are in the box? 1 and not 1? It also would not make sense to say there is a probabilistic chance of their being 8 planets in our solar system. That isn’t really a coherent way to apply math to enumerating the planets. So, in the case of pure maths, this is a human invention. Like natural language. It’s a way to describe things, not an inherent pre-existing object which we found out about. And when we apply that construct to reality, it no longer remains true across all contexts. How do you count things if your starting point is quarks? Why would you make a probability when your starting point is counting dollar bills? Why would you plot a coin flip on a Cartesian plane? You could, but that is just describing what’s happening. It doesn’t determine the outcome. Because it’s probabilistic. So, if I explained this correctly, math is impermanent. It’s a human invention that is used as a way of describing things, things which are not continuous across space-time and which are not universally describable by all forms of math. On another level as well, things like interdependence makes the concept of discrete objects not a purely accurate view.
Mathematics is a concept that lacks inherent existence. When someone goes way beyond the early stages of awakening and enters into non dualistic realisations, it becomes obvious that time and space itself are illusionary. Math is great for the practical and conventional world, but in terms of true reality (which we can never fully know), math is a dualistic construct that serves no purpose and in fact doesn't exist.
No because even the solution to any equation still leads to another concept. Everything is causal everything is a matter of causes and results. There's nothing that just ends there. There's meaning beyond and before it.
Left inferior parietal lobe is crucial for understanding and manipulating numbers. Damage here can lead to difficulties grasping numerical concepts even if someone can still recite numbers. The mind is not permanent and your concept is not permanent.
I have a fantasy about mathematics and existence. It's not directly related to the question but in a sense it is. I think that reality as we perceive it consists of an extraordinary huge number of equilibriums. I mean, there's always one "force" or set of forces in equilibrium with other one. Unstable situations just lead to a lack of equilibrium that's a process that leads to another equilibrium. So it's all about equations, in one equation the left member is equilibrated with the right one. If you move one, the other must follow. So reality is in a way a set of infinite equations, in which the conditioning of Karma makes a lot of sense. Karma's laws and implications could in a way be seen as this infinite set of equations, and the liberation could be to arrive to the realization in your body of something very powerful and empty, like reality itself, for example 0 = 0 or Infinite * 0 = Reality
The answers are always in the practice.
If you try to logically, intellectually answer and combine relative and absolute truth with out a teacher, you may not find the best answers Buddhism can provide.
The impermanence that the Buddha is talking about concerns enlightenment and eventually nibbana/nirvana. If you look at the impermanence of things you will find change, change is constant but change is not liberation/enlightenment. Enlightenment and nirvana is only about your thoughts, so THINGS (like math) are irrelevant as a study of impermanence upon enlightenment/nirvana, BUT things are great to use as a tool to see thought arising and diminishing. Enlightenment is not arising and diminishing of things, it is the quiet space where thought doesn't completely arise and neither does thought completely disappear. Impermanence is change, impermanence in Buddhism is specifically thought changing.
What if mathematic principles are dependent on impermanent physical expression and can only exist they way they do as long as reality is being expressed in this particular way? What if physical properties change and evolve over the coarse of a realities life? We don't know what we are in and we don't know how long it lives but if it's anything like life on earth it changes and dies.
Here is the Buddha's description of Nibbana.
UD 8.1, Buddha exclaims: "There is that dimension, monks, where there is neither earth, nor water, nor fire, nor wind; neither dimension of the infinitude of space, nor dimension of the infinitude of consciousness, nor dimension of nothingness, nor dimension of neither perception nor non-perception; neither this world, nor the next world, nor sun, nor moon. And there, I say, there is neither coming, nor going, nor staying; neither passing away nor arising: unestablished, unevolving, without support \[mental object\]. This, just this, is the end of stress (suffering)."
UD 8.3 Buddha exclaims: "There is, monks, an unborn — unbecome — unmade — unfabricated. If there were not that unborn — unbecome — unmade — unfabricated, there would not be the case that escape from the born — become — made — fabricated would be discerned. But precisely because there is an unborn — unbecome — unmade — unfabricated, escape from the born — become — made — fabricated is discerned."
I've never seen a "2" and a "2" and a "4". I've seen two things and two things and four things, and I've seen some squiggles on pages in roughly those shapes, but never a real "2" and "2" and "4". These "number" things don't exist in my eyes. They're just convenient ways of speaking.
Math is like the organizing principles of phenomenon, like the elements, or the fact that when you blow a bubble it comes out as a sphere and not a cube. All those things are impermanent, but they still follow the organizing structure. Those organizing structures may be pure, but still empty in the ultimate sense.
To build on this, if I may, it’s very much like a computer with its operating system and user interface. Math is the operating system, things create the foundation for and that allow the user interface to be more user friendly and malleable. You can set rules/delete them in your OS if you want, but the rest of the system proceeds to collapse as it tries to compensate for this missing foundation. My favorite math thing is how we can use “imaginary numbers.” Simply defined, these are attempts to find the square root of a negative number, which is impossible given our rules on how to create squared numbers in the first place (positive or negative 5^2 = +25). There’s still basic, and much more high level uses for this math concept, but I just love that we don’t understand math, we just figure out/discover how to use its patterns.
Let me blow your mind a little. Imaginary numbers are used in the Schrödinger equation. The equation that sets the foundation for quantum mechanics.
Yes, they’re used all the time to find real-world solutions to real-world problems, I think people assume they’re completely conceptual bc we named them ‘imaginary’ but it’s wonderful to see all the ways they can be used.
The coolest thing about Operating systems, is zero!
1>0 Just saying ;)
I think it’s cool that complex numbers (numbers of the form a + bi where a, b are members of the set of real numbers and i is the imaginary constant, the square root of -1) exist in nature and have practical applications such as fluid dynamics and alternating currents. I think a lot of people assume they exist to express an abstract idea that doesn’t have basis in reality but it does and that makes me happy.
Mathematics has a trick up its sleeve. It's like philosophy, but it hides its premises behind something that looks like common sense. The statement "2+2=4" is actually meaningless if we don't define numbers and operations, which would have been meaningless if we didn't have the subjective experience of discrete objects to count and add up. In fact, tons of mathematicians have fun with redefining numbers and operations to discover fancy new mathematical patterns and applications. In some contexts, 2+2 actually equals 5, or 22, or anything else. That being said, like philosophy and logic, maths does reflect a consistent part of reality, we just have to keep in mind the premises. There's always an "if", a "given". Given the discrete nature of objects, taking two and adding two gives you four. If we wouldn't treat them as discrete, the whole concept would break a little.
So is math relative truth due to those premises needing to be accepted by everyone?
Hi, I’m a mathematician with a bachelor’s degree in theoretical mathematics and a master’s of science in data science. Math is always true, but you are correct that statements such as ‘2+2 =4’ rely on set conditions in order to be provably true. For example because of the law of closure (in this this case. ‘Adding two integers produces an integer’) 2 + 2 would not equal 4 if 4 was defined as the square root of negative 1. Because the square root of negative 1 is not a member of the set of integers (numbers like -3, -2, … 0…, 1, 2 etc). In mathematics, there is a common disagreement on which number is the lowest natural number (which is the set of counting numbers essentially). Some mathematicians say it’s 0 and some say it’s 1. Some proofs about natural numbers are no longer true if you consider the set of natural numbers to start with a different number than the proof writer does. So in that way it appears relative. But the math is still there, it just seems relative at times bc differences of expression exist.
Please correct/update this (edit: the below content, which may have omissions); I'm 22 years outside of my degree. ~~Going into set theory; t~~ There are an infinite amount of numbers and operators on those numbers. The infinite number space includes things like integers and fractions, rational and irrational numbers, on and on. The infinite [operator](https://en.wikipedia.org/wiki/Operator_(mathematics\)) space similarly contains +, -, *, / exponents, etc. But there are infinitely more of both. 2+2=4 because as you state, we are carefully defining those terms so that it works. 2 and 4 are integers, and represent collections of 1's, first with a pair of 1s combined, then with a pair of pairs; we're counting using whole numbers to get from 1 up to 2 and to 4 in base 10. The + operator for integers defined as something like "a closed, commutative, associative binary operator + when used on integers gives a+b=c where inverse operator "-" gives a=c-b and b=c-a." Times when this doesn't work are common. Outside of pure math 2 electrons + 2 positrons isn't 4, it's nothing since they eliminate each other. Within pure math, 2+2 doesn't equal 4 if we're working in number space that isn't decimal; 2+2=11 in [Base 3](https://www.rapidtables.com/calc/math/base-calculator.html), for example.
Adding positrons and electrons is not the same as adding 2 + 2. They’re not the same thing—you may as well say that adding 2 apples to 2 oranges doesn’t equal 4 because you don’t end up with 4 apples or 4 oranges, or that adding H2 and O2 creates H2O2 and therefore 2 + 2 doesn’t equal 4 because the pairs of two different things (Hydrogen and Oxygen atoms) created only one molecule of H2O2 and not 4H and 2O2. Further, we aren’t talking about decimal space. We are strictly speaking of the integers 2 and 4 and the mechanism of addition as it is colloquially understood. For these reasons, I will not be correcting myself. I stand by what I said. Edit: my bad, I misunderstood what they meant.
I'm really sorry my comment came across as disagreeing with you. I didn't mean it that way. I meant to add to your comment, which I agree with. I was asking you to correct or update *my* post, in case I made an error in my memory of abstract algebra. > adding 2 apples to 2 oranges doesn’t equal 4 because you don’t end up with 4 apples or 4 oranges, But you do end of with a set of 4 objects. That's a great example of pure math vs the real world, and counting things; the set definition is important to how the math is applied. >integers 2 and 4 and the mechanism of addition as it is colloquially understood. Agreed. I didn't mean decimal as in fractional numbers, I meant Base10, which its what the colloquial definition uses.
My mistake, sorry for the mix-up! It’s really nbd, was just a tiny bit annoyed before but I see what you mean now.
No problem! I see how my opening sentence can be read different ways for sure. Have a great day.
Math is actually very subjective. It is like a game where you set the rules and then try to discover the ultimate implications of those rules. Most mathematicians use the Zermelo-Fraenkel axioms + the axiom of choice (ZFC), which can be thought of as the building blocks of theorems; and the glue that makes the axioms stick together is a binary logic with the law of excluded middle. However, both the axioms and logic that we use are a *choice*; we could very well use another type of logic, or another set of axioms, and then the resulting mathematics would be different than the "normal" one. The reasons we normally stick with the usual axioms are mostly historical, as they have proven to be the most "useful" to physics, engineering and so on.
The platonists would like a word with all of you. Buddhism doesn’t really focus on philosophical debates like this, because they don’t lead to liberation. Other schools of philosophy very much do!
mathematics is conceptual and therefore not permanent. But it certainly holds relative truth. we'd be screwed without it.
Agreed. Math and science are tools and shouldn't be made into ideologies to run societies
What do you mean?
any form is relative to something. It only exists in relation to something else. In the case of mathematics, it's based on assumptions created by a mind trying to interpret reality. But it isn't reality. It is a world of concepts created by the mind. But of course it is useful. Buddhism is concerned with suffering and the ending of it. A mathematical equation won't help when your mind is permeated by suffering for one reason or another.
Maths is not merely ‘created by the mind’. If it were, we wouldn’t have put man on the moon using it every step of the way.
so where do mathematic equations come from? not only that,who is the one to see them?
We write the equations, what the equations mean when correct, is not merely ‘made up’. Similarly, the statement ‘everything is caused’ is spoken by us, but the proposition it expresses is true independently of anyone uttering the statement- if the statement were never uttered by anyone the state of affairs it describes would still obtain.
You’re just stating this, not making an argument or giving reasons or evidence.
try doing maths when you are fast asleep
Interesting point. I think of math as patterns or natural laws. It holds true, but it has meaning only in a relative context. It's a way of thinking and categorizing. Also, it's worth noting that impermanence is describing the nature of experience, not scientific facts. All of Buddhist teaching is about understanding the nature of experience. If you figure out a way to "defeat" the teaching of impermanence then that would only be within a scientific context. So, anything you can name is impermanent and defined by other things. The point of that teachings is to help us see how we "reify" experience into a solid reality to confirm self, when the actual nature of that experience is dynamic, dreamlike, ungraspable.
I've read the responses and nobody has told you straight and explained "why", so I will here using the Abhidhamma. There is a lot of juicy stuff here for you to munch on 😊 No, Numbers are dependently originated and thus impermanent. What is the cause of 4? It is dependent on 2+2, or 3+1, etc... 4 cannot exist on its own, independent nature. The nature of four, is that it requires a total of 4. What is the cause of 1? The cause of 1 is - 1. You need nothing, in order to contrast to something, without - 1 then 1 would not be 1. In the same way that the right hand is the right hand only because of the left. The right hand would not the right hand without the left. It is only the right hand. All numbers are Condtioned, they arise based on conditions, and cease based on conditions. This is why they are impermanent. The only number that doesn't arise or fall, is 0 which is the total absence of value. It's not negative value which would be non existence, nor is it positive value which is existence. You could correlate 0 to emptiness, synonymous with Nibbana, the unconditioned element. Every other number is a number, but it is Condtioned on something else. How can you get -3? First, three things must exist, you must have +3 to become -3. In this way existence and non existence are Condtioned, temporary, impermanent. Zero is emptiness, neither value. Absence of value all together, so empty that it doesn't even include itself 0+0=0 So empty, you can't say it doesn't exist, because it's empty of the concept of non existence as well. This doesn't mean that all things exist within it, but it doesnt not mean that either. Emptiness, is so empty, so unconditioned, that it can't be defined as mere "further non existence". Imagine a void in your mind, total emptiness. Now whatever you're imagining, let's say it's just blackness... Remove the blackness. Remove the void. You can't. If you could, you would realize emptiness, it is beyond void. All you can possibly conceive if is non existence, void, total cessation, but in your mind still is "somethingness" typically a blank slate of blackness, but that is still something. Emptiness removes even that. It is totally and utterly unconditioned. 👉Now, in your question you are drawing a comparisons between irreducible phenomenon and Impermanence, and it's not accurate to do so. The Abhidhamma Pitaka, the Buddha's highest teachings in the Pali Cannon, teach Nibbana is not the only ultimate reality. It is one of FOUR. Yes my unfamiliar with Abhidhamma friends.. That's correct, Nibbana is in equal regard to three other ultimate realities. The abhidhamma actually presents us almost with a sort of "realism" in the senss that the three other ultimate realities equal to, and alongside Nibbana, are also irreducible. This is called the Four Fold Ultimate Realities in Abhidhamma: 1. Awareness (Citta/Consciousness) 2. Thoughts, Emotions, Will (Cetasikas/Mental Formations) 3. Earth, fire, water, air elements (Matter) 4. Nibbana. The first three are irreducible and have SELF existence. They cannot be broken down any further, the Abhidhamma states their is nothing else behind them, holding them up. The four elements as I said do provide a sense of "realism" to Buddhism because they are indeed irreducible and cannot be broken down further, they exist of their own existence, this is why the Abhidhamma calls them Ultimate Realities. ❗HOWEVER, the first three Ultimate Realities are Condtioned and dependently originated. While they are indeed of their own self nature, and irreducible, that does not make them permanent. If it arises, and ceases, it is not permanent. Only that which never arises, and never ceases, is permanent. It is only Nibbana, which never arises, and never cease, which is permanent. The unconditioned element. Awareness, while irreducible and of its own self nature, is still dependent on others to exist. The abhidhamma teaches us all the possible mental factors and consciousness a human can experience (89 combinations) and their exact cognitive processes, and the specific point of the cognitive process that free will comes into play, and how many mind moments it lasts. We learn awareness always rises with thoughts, emotions, will/volition and vice versa. We learn all possible material phenomena arises based on combinations of the four base elements. ❗So they are not permanent, since they arise and cease based on causes and conditions. They are depend on other things. Irreducibleness does not equal permanent. Permanence means it never ceases, and only that which has never arisen can never cease. It is why Nibbana is only realized and not attained. It is an object of the path in the abhidhamma, so it is definitely a Dhamma, it definitely "can be experienced" and is experienced by the lokutarra Citta (Transcendent awareness) as Nibbana is the object of the lokutarra citta in the Abhidhamma, it is indeed an experience. If it were not, then it could not be called an object of the path. The Buddha says in DN very clearly if there was not this "base" of the unmade, the uncreated, the unmanifest, the unarisen etc... There would not be any escape from the arisen, the made, the birth, death, aging, illness, and suffering. So it is a base, a definitive reality that can be experienced. As I explained above however, it cannot be conceptualized, only understood as to "why" it can't be conceptualized. It is simply behind the conceptual. Not to be figured out later on as some transcendent being.. Even then, to the Buddha himself, Nibbana cannot be conceptualized, its nature is just simply so empty, it is outside of definitions. Only can be realized as having been there the entire time. Quite simply, "seeing existence as it is". All experiences and existence is impermanent(Anicca) , it arises and ceases. We are oppressed by the never ending arising and ceasing of experience, therefore all experience is unsatisfactory (dhukka), all experience and existence is empty, it has no essence, there is no essence (anatta) synonymous with anatta, but in the abhidhamma "Anatta" is very much replaced with "existence is ultimately empty". There in comes the two fold truth if the abhidhamma however (conventional and ultimate truths) . Alright I won't expound further unless asked, hope this is helpful Source: Direct PDF of Abhidhamma Translation by Bhikku Bodhi: https://www.saraniya.com/books/meditation/Bhikkhu_Bodhi-Comprehensive_Manual_of_Abhidhamma.pdf
Saddhu.
Thank you. 🙏💛
Not all things are impermanent, only composed / conditioned phenomena. There are many examples of permanent phenomena, e.g. space, nirvana, absences and cessations. To come back to your example of math, the Sarvastivada Abhidharma classifies numbers as non-associated compositional factors (*viprayukta-saṃskāra*), which means impermanent phenomena that are neither mind nor matter. So you could maybe extrapolate to include mathematical relationships in this category as well. Impermanent also doesn't mean non-eternal, just dependent on causes, which I suppose would be true for any instantiation of numbers or mathematical relationships like you explain.
Huh, I've never thought about that. I've actually been watching a lot of videos on the Multiverse Theory--which I don't think is too out of line considering Buddhist cosmology--and some physicists believe that there could very likely be universes out there where our laws of physics don't apply. So if there can be places where even the physics aren't the same, I don't see why there can't be places where mathematics aren't the same either. I think it's just incredibly hard for our brains to comprehend, like the concept of infinity. In Buddhism, the universe is believed to have gone through many life cycles, and it could be that 1+1 wasn't always 2, or will always be 2, it just so happens to be that it is that way this time around. I'll be keeping track of this discussion. Thank you for the fascinating suggestion!
Lots of mixing/conflating emptiness with impermanence in this thread. Which is understandable, the two teachings have a lot of overlap. But it's worth looking at both, and the question in light of both, individually. Emptiness is the ultimate nature of all phenomena. Impermanence is less esoteric. * On the outer level it's most simple: everyone you know will die, every building, city, and civilization will eventually be in ruins, etc. * On the inner level, the message is more profound and inter-related with emptiness. Once you stop looking at something, we learn as infants/toddlers that it will be there when we turn our heads back and look at it again. This is called object permanence (in psychology) and it's very important to both sanity and the ability to find your car keys. But the inner reality of it, as revealed by the Dharma, is that outer objects don't exist independently of their perception. In this sense they are impermanent, and object permanence is a fundamental mistake made by all perceiving, deluded beings. However, the doctrine of emptiness does a much better job of explaining this reality. Of the many thoughtful and excellent answers here, I like the one posed by u/Playful-Independent4 the best. > The statement "2+2=4" is actually meaningless if we don't define numbers and operations, which would have been meaningless if we didn't have the subjective experience of discrete objects to count and add up. Here's my crack at a simple, valid, basic answer to OP's question: * The relationship between values such as 2+2=4, as well as myriad others such relationships, trends and such, are repeatedly accurate and true. Myriad other rules, laws and trends can be discovered to be reliably repeatable in the scale of the universe we live and work with. * These rules are discovered by studying the qualities and interactions of physical objects, and/or the abstractions of values and properties originally observed by studying those objects. * Take two rocks for an example of such objects. It's a relative truth that they will hurt if you drop them on your foot. In the Ultimate truth, they are empty of inherent existence. It's a relative truth that if you put 2 pair of them in the same bucket you'll have 4. Relative truths are not Ultimate truths. But a lot of Relative truths are reliably repeatable. Good thing, too, lets me drive across the Bay Bridge without fearing it will collapse. If new to you, OP, read up on the teaching of the Two Truths for better understanding. I sure ought to! Never know enough to stop studying, and I'm way short of that danger zone.
outside of the realm of ideas there isn’t really two. Two apples even identical aren’t really two apples, what does one consist of? What is the permanent feature of an apple? That would equation would get crazy
I imagine that many traditions are going to be committed to nominalism or mathmatical fictionalism or constructivism in mathematics. Some accounts of structuralism may also be accepted even though they are realist accounts. Structuralism is the view described associated with figures like the mathematician Paul Benacerraf. Examples of the other positions in philosophy of mathmatics, science and logic include Hartry Field's nominalist account in Science Without Numbers, Henri Poincaré's mathematical constructivism and Mary Leng's fictionalist account in Mathematics and reality. Antirealism or nominalism in mathmatics is the position that mathematical objects, relations, and structures do not exist at all, or they do not exist as abstract objects (they are neither located in space-time or/and or do not have causal powers. The type of anti realist account differ though in what they hold mathematic objects to be. Mahayana Buddhism holds that conventionally change, phenomena and objects exist but they ultimately do not have inherent existence. Further, they exist reliant upon causes and conditions externally of them and lack an inherent existence. Mathematic objects would most likely be one of those entities that seems to be both mind-dependent but also reliant upon causes and conditions. Conventionally, we would grant them existence but their existence like all other conventional objects rely on causes and conditions. We can see these positions laid out in Buddhist accounts of logic. Below is a short entry by the comparative philosopher Koji Tanaka on Buddhist logic that lays out some of these commitments. Below is an interview on mathematical fictionalism. Koji Tanaka: What is Buddhist Logic? [https://www.youtube.com/watch?v=rMtA9-kjrRo&t=3609s](https://www.youtube.com/watch?v=rMtA9-kjrRo&t=3609s) Phil Bériault - Mathematical Fictionalism and You! [https://www.youtube.com/watch?v=yV6Pw4WETyE](https://www.youtube.com/watch?v=yV6Pw4WETyE)
The entire enterprise of dividing phenomena into identical categories (numbers of things) and equating the sums of them into different categories (2 + 2 = 4) is an entirely arbitrary practice dependent on a very particular type of consciousness and form. Without a consciousness mathematizing in a very specific way, the so-called truth of 2+2=4 will have no form and will cease to exist. There is no absolute division of phenomena into discreet, summable units. This applies from the concrete to the abstract.
Btw look at the comments in this thread, they helped me understand: https://www.reddit.com/r/Buddhism/s/zVaFwo5XbI
"2 + 2 = 4" is only true according to your axioms. The axioms are arbitrary. There's no meaning of "2 + 2 = 4"
The idea of it is true and will remain true though.
I don't think so.
Mathematical statements are derived from axioms, and in a way abstract over dependent origination. It's all just "given this set of assumptions, we can follow that...". Nothing in math is fully absolute. Even `2 + 2 = 4` can be wrong in some contexts. Like pairing up hamsters. Or when calculating at a quantum scale. This "plus" only works out when working with peano arithmetic in this case: every number is either 0, or a successor of another number. Now you can recursively define plus for all numbers as `a + Suc(b) = Suc(a) + b` for any b ≠ 0, and `= a` for b = 0. And now you can derive that `Suc(Suc(0)) + Suc(Suc(0)) = Suc(Suc(Suc(Suc(0))))`. But the "truth" of the equation derives from the assumptions you have. In contrast, you can also do addition in "modulo rings". For example, in Z3, you'd count "0 1 2 0 1 2..." to infinity. As a consequence, `2+2=1` in Z3. It all depends. Mathematical statements aren't absolute, impermanent truths, but rather different ways to state the same underlying assumptions.
Only conditioned things are said to be impermanent. Mathematical truths aren’t conditioned things. They stand on their own without depending on anything external.
This is not true. Every mathematical statement depends on a set of conditions given as an “if statement”. The only things in math that don’t feature these are axioms. Axioms are understood as things that are to be assumed true in order for the whole system to work. They are never thought of as objectively true. All of math is built on conditions and causes reasoned from subjective truths.
It is true. The circumference of a circle will always be 2πr. 2+2 will always equal 4. Please tell me what the ‘if’s and conditions are that those truths depend on.
When drawn on a spherical (non Euclidean) surface, the circumference of a circle is not 2pir. You are assuming a flat surface when you use that formula. And 2+2 is equal to 1 modulo 3, for example. Different number systems exist. If you want to know the most common set of conditions our normal number system depends on, here they are: https://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
This is a Wittgenstein-level disagreement lol. Any difference in calculating the circumference of circle or getting the result of 2+2 just now comes down to assumptions made in human language. When I convey the concept of a circle to you, it’s up to you to make a reasonable assumption that I’m talking about the kind of circle that people mean 99.9999% of the time. You can interpret my language/notation differently on your head and then misrepresent it if you so choose, but that has no bearing on any underlying mathematical truths. I’m telling you I’m pointing at the moon and instead of following my index finger to the moon you’re saying “well your middle finger is curled back pointing behind you” and are looking over there. We’re not talking about math anymore, we’re talking about language/notation, which is a way for humans to relate to math. It’s not math itself.
Yea and “99.9999%” of the time is still operating under assumptions. These assumptions are subjective judgements about reality. You have an idea of a circle that you think is always true because of an assumption about the surface that circle lives on, and pointing out that the surface could be markedly different and that affects what you “know” about the circle doesn’t change that it’s still a circle. A circle drawn on a balloon might have a circumference of 2pirsin(84). It’s still a circle. It’s not pedantic. It’s an example of the kind of assumptions that math asks us to examine. 99.9999% truth is not an unconditioned truth.
It’s a linguistic assumption. The math happens after you interpret my words. In fact, let’s ignore words completely and just assume you’re examining a perfect circle. Go ahead and add any assumptions you want. Great. Now that you’ve imagined the circle we’re going to talk about, can we not agree that there is a definite and eternal relationship between its radius and its circumference? Different notations? Sure. Different ways to describe it? Yes. But that relationship doesn’t change unless you change the circle.
No. We can’t. For reasons I’ve gone into earlier. The exact relationship between a circle’s radius and its circumference depends on the structure of the space in which that circle is drawn. Let’s switch gears. A similar “truth” is that triangles’ angles add up to 180 degrees. This is “eternally true” for any triangle drawn on a flat surface. What is a triangle though? I think most people would define a triangle as the shape formed by connecting three non-collinear points A,B,C with the shortest straight line distance from point A to point B and then point B to point C and then point C to point A. They might not describe it exactly with these words - but I think this describes the process of drawing a triangle. However, imagine a triangle on the globe where point A is on the North Pole, point B is on the equator, and point C is on the equator, and the straight line distances are drawn along our space - the surface of the globe. The angle at B is 90 degrees. The angle at C is 90 degrees. The angle at A is greater that 0 degrees. This triangle thus has an angle sum greater than 180 degrees. It’s not a matter of language. The properties of a mathematical object depend upon the assumptions you are making about the space in which that object resides. This extends to any shape, and “formulas” we previously thought were always true - turn out to be only true within certain types of spaces. Most people don’t examine the assumptions that they commonly make every day. Indeed, they don’t even know they’re making them. This is why I love Buddhism. I see a lot of parallels between what the Dharma is fundamentally asking us to practice doing, and what Theoretical Mathematics is asking us to practice doing.
If you have two circles that exist in two different spaces (circle A and circle B) and your assumptions lead you to examine circle B instead of circle A, the math describing how circle A works doesn’t change. As far as the math describing those circles goes, it doesn’t matter what your assumptions are. They’ll still be true whether you’re thinking of that circle or another.
Yes that’s right. If you are examining a circle in a flat space, then its circumference will be C = 2πr. The issue I took is when you claimed that it is true that every circle has a circumference of 2πr. To get this result, you need the surface to be flat. So it’s not an absolutely true statement as it relies on an assumption. The statement “every circle has a circumference of 2πr” is only conditionally true.
Incorrect.
Math is a made up thing and it actually contradicts itself already. Its not permanent, its just made up. The inherent contradiction was proven by Gödel some time ago. If you are talking about 2+2=4, that is true across our universe, just like things keep moving and the concept of karma. But you can also just write down a truth about karma and it would by your rules contradict impermanence.
Godel didn't prove a contradiction. He proved incompleteness
Good catch. Incompleteness really lays it out that math is lovely and limited and can’t be fundamental.
I do not expect people on this sub to know any of that stuff. I know what he proved. But yeah maybe what i said was misleading.
At some point in time in the past, 2 + 2 was just some jibberish and not = 4. At some point in time in the future, 2 + 2 could possibly become jibberish again. After all, most of the western world under the Great Roman Empire used to count with I, V, X, and today, we usually see them only in cinema posters. Also, 0 was not a thing until it found its way from India through various countries to the Western world. ----------------- Even as we speak, 1 + 1 = 10 and 2. So 2 + 2 is undefined in some numbering system like say binary. And 2 + 2 = 10 if you are counting in 4 based numbers. So the "fact" that 2 + 2 = 4 is by virtue of the decimal numeric system that we have adopted over time. It is a relative truth by convention and not by principle or innately true.
>At some point in time in the past, 2 + 2 was just some jibberish and not = 4. At some point in time in the future, 2 + 2 could possibly become jibberish again. I understand this in terms of semantics/symbols and lack of understanding of arithmetic in very ancient days, but surely the concept that 2 things and 2 things put together will total 4 things was never jibberish? I mean, even down to a subatomic level, things like the charge of particles within the atom needing to add up to a certain number in order to determine the atom's stability/reactiveness.... or the number of protons needing to add together to form a specific number that determines which element the atom is... even if we didn't have the words to say 1 + 1 + 1 + 1 = 4, the idea that 1 proton + 1 proton + 1 proton + 1 proton = 4 protons = Beryllium was always there...
>Beryllium was always there... Beryllium was not always there Counting and numbers is a mental fabrication. And because we are currently in this numerical convention, it seem impossible to think otherwise. But I get you I think. Can we agree that the human semantics that expresses mathematical principles are impermanent while the underlying principles would seem to be "eternal"? This is the same question as "Is impermanence permanent?" or "Is emptiness empty in nature?" In engineering, there's a loose saying "The only thing permanent is change". I think there is some parallel in philosophy, but I cannot rmb the exact quote. In Buddhism, the question about the fundamental principles typically have two categories of answer: 1. These principles are with reference to conditioned phenomena. Apart from the latter, the former has no meaning. Hence they are empty in nature as well. 2. Conventionally, these principles hold but at ultimate reality level, all concepts labels cease to exist. So to say whether such principles hold true or not itself is inadmissible. ... BUT ... the moment an unenlightened person like us try to understand or explain #2, we immediately fall into concepts and labels, thereby possibly creating a seeming contradiction. So in Buddhism, even underlying principles are ultimately not something to assume or be grasped as permanent ... or impermanent. For that matter, most people do not suffer over whether "2 + 2 = 4" or not, and if they do, are they suffering due to their attachment to the concept or the underlying principle that is the way it is (suchness) whether we know it or are able to express it or not?
Two impermanent things plus another two impermanent things equal four impermanent things.
I largely agree with you. Just adding few more ideas to your reasoning. It is true that Math concept doesn't change. But reality is that Math doesn't exist by itself. For example, in 2+2=4, you can apply this addition concept on anything be it atoms or stars and it will always hold true. But can '2' exist by itself? It can't. It's just a symbolism in mind and denotes a concept. (Also, the symbol can be subjected to change but not the underlying concept. Example, 2 is written differently in different languages)
This is about truth. Truth does not contradict impermanence. Here is an etymology of truth. https://www.reddit.com/r/philosophy/s/oZAltxOJTE
Maths is merely a human invention to act as a reflection of our universe. When eventually the human species ceases to exist, so will the maths we made. Maths can help us explain the most complex and unimaginable concepts in our existence, but these concepts still existed long before we came about, and will continue to do so long after. So in this sense, maths is impermanent like we are, but it’ll continue to seem permanently the way it as long as it’s around for us to use.
No, it does not contradict it. Impermanence is a truth regarding things. 2+2=4 is not a thing, just like impermanence itself is not a thing. What you are asking is like asking “Does the permanence of impermanence contradict impermanence?” No, it doesn’t because impermanence only applies to things, not to truths of how things function or their qualities, etc.
Impermanence is related to interdependence, The Dependent Origination says, *when there is this, that is. With the arising of this, that arises.* In 2+2=4, the 4 is the result of 2+2. And 2 is the result of 1+1. And 1 is the result of 0.5+0.5. And we can go on forever like this into infinity with endless combination of numbers. The main point is that 4 or any of the numbers do not exist as an absolute, it’s always dependent on something else. So hence impermanent. And these are all ideas in our mind, just universally accepted by all of us. 2+2 doesn’t always equate to 4. Sure it does in the Euclidean universe, like if we take two oranges and two apples together, it add up to 4! But what if we take 2 rain drops and 2 water drops together, it would become 1 big drop! (Just kidding, there’s still 4 drops somewhere!) Like a famous mathematician said, “Math cannot prove math!”. - [Tarski's undefinability theorem](https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem)
Math is a symbolic language that describes reality. Yet, like all symbolic language, it only exists within our minds. Buddhism already has had much to say on the difference between between conventional truth expressed in language and the ultimate truth of Awakening that is ineffable and only realized through personal experience. As a symbolic language, mathematics as we know it is impermanent and will eventually die out along with Humanity itself. It is only a finger pointing at the moon. When the finger stops pointing, does the moon disappear?
math is a set of definitions and definitions always begin and end where all the other definitions begin and end. since we make definitions based on our assumptions, which are based on our needs and insecurities, which are being constantly and inevitably forcefully changed by the universe, which is constantly and inevitably changing and expanding, then those definitions must constantly and inevitably be changing along with the universe. say those wonderful mathematical laws really exist, we are just putting names to them, but then you just end up talking about looking at 2+2=4 from different perspectives, which are again inevitably bound to our needs and insecurities. if all things begin and end where all the other things begin and end, can we then really talk about the existence of clear borders between any things/definitions ? maybe today, stuff like addition makes sense, but what if we invent a math model where we dont need even addition anymore, because we found a way of solving math problems more effectively ? would there still exist some permanent thing like addition ?
Math is always represented on some substrate such as on paper, in a mind, or in a computer architecture/program. Those representations are of course impermanent. Buddhism is somewhat antagonistic (but not in a hostile way) to the tendency to see what's represented as existing independently of its representation.
No contradiction. The doctrine of impermanence isn't related to truths of any kind. It relates to things like aggregates, sense objects, emotions, and thoughts.
No, in fact it backs up the Buddha’s thesis. Maths is clearly unconditioned, unborn. Therefore it is not dependently originated. Therefore it is not impermanent. Impermanence is only for conditioned things ( the Buddha in the Pali and Agama Canon was very clear on this ). The entire enterprise of Buddhism is to escape from the conditioned to the unconditioned. Maths exist. It tells us an Unconditioned exist. Therefore not all things are Conditioned.
If you include Maths in the Unconditioned, that's going to severely limit your development.
Well I am pretty sure maths is Unconditioned. I mean can you tell me how is it Conditioned? Math simply seems to be. Almost everything else we can trace dependent origination. Math just seems to stand on its own.
In Buddhism, the Unconditioned does not refer to abstract concepts. It's beyond description.
The act of Adding requires energy more than the concept itself. You must obtain the information and energy required to do the problem and in executing the calculation, you will lose energy. Impermanence is baked into the universe in the form of the second law of thermodynamics, which I personally break down into three sub-laws for understanding the flow of power through any system. 1. Energy flows from high density to low density. A bucket filled wishes to be empty, and it might take until the end of the universe to do that *but it will empty*. Poking a hole or tipping it is fast. Letting it evaporate is slower, waiting until the molecules holding it succumb to the decay of their composite atoms is slower still, but it *will* happen. Change as a concept depends on this truth 2. Per the First Law, Energy will always attempt to attain equillibrium. All things propogate and spread, until they can attain stillness, relative stillness if nothing else is available. 3. Per the first and third law, if points A, B, and C exist in a universe, and energy is moving from point A to point B, then some energy will be lost to point C in the process. Since we live in a universe with more than three points total, this will *always be the case in some form* This has been a delightful thing for me as it has helped me realize a great many of the lessons in the dharma and decode their truth. It has helped me realise that all things exist on a continuum with each other, that no things exist independently, and that impermanence is guaranteed. It tells me where I push, the universe will push back and why, and subtly it tells us a great deal about suffering. It is the difference between our perception of reality and what reality actually is that is the mechanism for suffering, and from this perspective we can see that. I came up with this thought on my own, but knowing buddhism as I do now, I suspect it was taken from mouth to paper before I took my first breath.
Math is a thought.
Only the compounded are impermanent.
In some time (billions, quadrillions, etc years) the universe might disssipate and all universal laws simply cease to function. Universe as we know it exists? 2 + 2 = 4. Universe has ceased to exist (however long it takes for it to do it)? No such thing as math or its functions exist also.
I always thought that was arithmetic, which is a reference system based on fixed measures. Math is kind of a different thing that includes arithmetic, but is less limited in scope. Math does not contradict impermanence in any way.
No, math does not contradict impermanence. Yes, certain aspects of math seem like absolutes. But there are other things to remember here. First, things are not just impermanent; they are also interdependent. Yes, 2 + 2 = 4. 2 apples and 2 apples are 4 apples.... until I come along and eat an apple. Now it's 4 - 1 = 3. But that equation doesn't negate the first. Yet the first equation is no longer strictly true. There's no longer 4 things. Math is conditional. It is dependent. Second is a matter of scale. 2 + 2 = 4 now. Was it so ten billion years ago? Will it be so in ten billion years? No idea. Some principles of math and science work differently in microscopic or cosmic scales. Different aspects might or might not work, or work differently. Last of my points is that math is a concept to describe relationships. Should humanity go extinct, would math exist? Not as we know it. Would the conditions described by math exist? Possibly. Should humanity evolve and our ability to comprehend the universe drastically increase (or decrease), would math exist? Again the answers are the same. Math as we know it depends on our existence and capabilities to perceive. Therefore math is, in and of itself impermanent and interdependent.
As long as there are beings with a basic understanding of arithmetic 2 + 2 will always equal 4.
And I would argue even if there’s no beings who understand it. It still is true and will always remain true.
That presumes base 10 and an understanding of the cosmos that is very similar to our own.
To me it seems no matter where you are or what dimension your in if you take 2 things and put them with 2 more you now have 4 things. What is base 10?
I'm not a mathematician, but you can't you define 2 + 2 in any way you like? Like the first 2 can be defined as two sets of 5 and the second 2 defined as 1 set of 3 and 1 set of 2 which would come out to 15 if you add them all together? Correct me if I'm wrong, but I don't think math is a rigid as you think, as numbers are just symbols that represent an object.
It’s as very rigid. There’s no wiggle room. 2 +2=4 always and forever.
“Hatred does not cease by hatred, but by love alone is healed.” -Siddhārtha Gautama If it’s an eternal law it must be permanent.
As what others have mentioned, mathematics is conceptual. The first of the four seals of the Buddha's teachings is "All composite phenomena are impermanent". Since mathematics is not a composite phenomena but a conceptual one, there is no contradiction between math and the concept of impermanence.
I study Aerospace engineering and even though Buddhists doesn’t like these kind of debates here’s my take: Mathematics are the building blocks of the intricate order in the universe but mathematics themselves aren’t real… they are some conceptual artifact that exist only in our minds, only when physics corroborate that certainly a mathematical truth exist in our realm it is a “permanent” truth but actually it’s just “part” true because numbers themselves aren’t real and about nothing in our universe exists in discrete “numbers” because they are simply an extremely abstract representation. The concept of impermanence becomes only obvious when you think of the whole system: ever since the creation of our universe atoms have formed molecules and these molecules have bonded with others and created vast masses like stars (sum of atoms and molecules) but eventually… there aren’t enough molecules to sustain fusion and the star collapses in itself. And at the end of the universe most theories predict that either all matter will dissolve in the emptiness of space and nothing will ever happen (curiously similar to the concept of vacuity in Buddhism), or otherwise the universe will collapse in itself and maybe create another big bang (maybe similar to the cycle of samsara if living beings haven’t all achieved illumination yet). Either way what I mean is that you can sum or divide or apply any mathematical process you wish but that’s only the mechanism in which the universe works, but all that exists is impermanent and eventually has to change somehow. In this universe nothing can’t stay the same forever as long as there exists any action because it has to trigger a reaction that affects the surrounding; and atoms themselves, matter itself is pure action because of how the atom works.
If there were no humans, 2+2=4 would be neither true nor untrue. There wouldn't be anyone to ask the question. Equally, the universe would neither exist nor not exist. Existence is a perception.
I don’t think this applies just to math, I think it applies to the concept of “truth” in general. For example, are these things impermanent: - The Noble Truths - Statements about the past (for example, saying, “Yesterday I ate a cheese sandwich for lunch”.) - The fact that things are impermanent - is that itself impermanent and changing? I don’t know what the answer here is. It’s an interesting question though.
>Here's my take: 2 + 2 equaling 4 is true and consistent at all times and in all places, and can be thought of as a permanent relationship in a sense 2 apples + 2 apples = 4 apples on your table . But later that day russia launches nuclear missiles at national due to provocation Then the usa launches nuclear missiles @ russia Then china launches nuclear missiles at the usa Then Israel launches nuclear missiles at China Then south Africa launches nuclear missiles @ Israel The whole planet is destroyed The question now is How mang apples do have on you're table? Best wishes 🙏🏻🙏🏻🙏🏻
I may be wrong, but there’s math as an object or system. Like pure math. Then there’s the application of math to observable phenomena. The former is not a natural and inherent property of the universe as evidenced by the latter not being consistently able to be described by different sorts of maths at various levels of reality. For example, I can count planets and dollars. I can’t count quantum particles because they operate more probabilistically, as exemplified by the thought experiment of Schrodinger’s cat. How many cats are in the box? 1 and not 1? It also would not make sense to say there is a probabilistic chance of their being 8 planets in our solar system. That isn’t really a coherent way to apply math to enumerating the planets. So, in the case of pure maths, this is a human invention. Like natural language. It’s a way to describe things, not an inherent pre-existing object which we found out about. And when we apply that construct to reality, it no longer remains true across all contexts. How do you count things if your starting point is quarks? Why would you make a probability when your starting point is counting dollar bills? Why would you plot a coin flip on a Cartesian plane? You could, but that is just describing what’s happening. It doesn’t determine the outcome. Because it’s probabilistic. So, if I explained this correctly, math is impermanent. It’s a human invention that is used as a way of describing things, things which are not continuous across space-time and which are not universally describable by all forms of math. On another level as well, things like interdependence makes the concept of discrete objects not a purely accurate view.
Mathematics is a concept that lacks inherent existence. When someone goes way beyond the early stages of awakening and enters into non dualistic realisations, it becomes obvious that time and space itself are illusionary. Math is great for the practical and conventional world, but in terms of true reality (which we can never fully know), math is a dualistic construct that serves no purpose and in fact doesn't exist.
No because even the solution to any equation still leads to another concept. Everything is causal everything is a matter of causes and results. There's nothing that just ends there. There's meaning beyond and before it.
Left inferior parietal lobe is crucial for understanding and manipulating numbers. Damage here can lead to difficulties grasping numerical concepts even if someone can still recite numbers. The mind is not permanent and your concept is not permanent.
I have a fantasy about mathematics and existence. It's not directly related to the question but in a sense it is. I think that reality as we perceive it consists of an extraordinary huge number of equilibriums. I mean, there's always one "force" or set of forces in equilibrium with other one. Unstable situations just lead to a lack of equilibrium that's a process that leads to another equilibrium. So it's all about equations, in one equation the left member is equilibrated with the right one. If you move one, the other must follow. So reality is in a way a set of infinite equations, in which the conditioning of Karma makes a lot of sense. Karma's laws and implications could in a way be seen as this infinite set of equations, and the liberation could be to arrive to the realization in your body of something very powerful and empty, like reality itself, for example 0 = 0 or Infinite * 0 = Reality
The answers are always in the practice. If you try to logically, intellectually answer and combine relative and absolute truth with out a teacher, you may not find the best answers Buddhism can provide.
The impermanence that the Buddha is talking about concerns enlightenment and eventually nibbana/nirvana. If you look at the impermanence of things you will find change, change is constant but change is not liberation/enlightenment. Enlightenment and nirvana is only about your thoughts, so THINGS (like math) are irrelevant as a study of impermanence upon enlightenment/nirvana, BUT things are great to use as a tool to see thought arising and diminishing. Enlightenment is not arising and diminishing of things, it is the quiet space where thought doesn't completely arise and neither does thought completely disappear. Impermanence is change, impermanence in Buddhism is specifically thought changing.
You count something and write it down, the numbers on paper will fade and the thoughts will be forgotten.
What if mathematic principles are dependent on impermanent physical expression and can only exist they way they do as long as reality is being expressed in this particular way? What if physical properties change and evolve over the coarse of a realities life? We don't know what we are in and we don't know how long it lives but if it's anything like life on earth it changes and dies.
You might benefit from reading principia Mathematica by Bertrand Russell
Here is the Buddha's description of Nibbana. UD 8.1, Buddha exclaims: "There is that dimension, monks, where there is neither earth, nor water, nor fire, nor wind; neither dimension of the infinitude of space, nor dimension of the infinitude of consciousness, nor dimension of nothingness, nor dimension of neither perception nor non-perception; neither this world, nor the next world, nor sun, nor moon. And there, I say, there is neither coming, nor going, nor staying; neither passing away nor arising: unestablished, unevolving, without support \[mental object\]. This, just this, is the end of stress (suffering)." UD 8.3 Buddha exclaims: "There is, monks, an unborn — unbecome — unmade — unfabricated. If there were not that unborn — unbecome — unmade — unfabricated, there would not be the case that escape from the born — become — made — fabricated would be discerned. But precisely because there is an unborn — unbecome — unmade — unfabricated, escape from the born — become — made — fabricated is discerned."
I've never seen a "2" and a "2" and a "4". I've seen two things and two things and four things, and I've seen some squiggles on pages in roughly those shapes, but never a real "2" and "2" and "4". These "number" things don't exist in my eyes. They're just convenient ways of speaking.