Is Mathematics Invented or Discovered? | Episode 409 | Closer To Truth
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- čas přidán 14. 05. 2024
- Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans-like chisels and hammers and pieces of music? Or is mathematics discovered-always out there, somewhere, like mysterious islands waiting to be found? Featuring interviews with Roger Penrose, Mark Balaguer, Gregory Chaitin, Stephen Wolfram, and Frank Wilczek.
Season 4, Episode 9 - #CloserToTruth
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Closer To Truth host Robert Lawrence Kuhn takes viewers on an intriguing global journey into cutting-edge labs, magnificent libraries, hidden gardens, and revered sanctuaries in order to discover state-of-the-art ideas and make them real and relevant.
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Closer to Truth presents the world’s greatest thinkers exploring humanity’s deepest questions. Discover fundamental issues of existence. Engage new and diverse ways of thinking. Appreciate intense debates. Share your own opinions. Seek your own answers.
#Philosophy #Mathematics
Mathematical relationships are discovered. The language describing them is invented.
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all that Is, all that Was, and all that Will Be, in this and any other universe of existence. This expression facilitates self discovery of Intelligence with Itself within the 'physical' universe through the filter of us All.
I was just thinking the exact same thing before i read this
The expression is physics the words are mathematics
Prove it.
@@Z-Diode If you have 1 coin and another coin, then you have 2 coins.
Whether you call it 1 or 2, or purple or whatever.
The value is universal, the name for it is man-made.
2 plus 2 equals 4. No matter where in the universe you are.
For those who has the same homework with me ....
2:15 Roger Penrose
7:20 Mark Balaguer
12:10 Gregory Chaitin
16:22 Stephen Wolfram
21:40 Frank Wilczek
Lmao you're a G for that. I don't have any homework, I just found this because I was interested in it
19:53
My all time favorite episode of all that you’ve made. Thank you Dr. Kuhn, staff and production crew.
omg what pleasure to be seen this doc , math always intriguing me about their origins
So wonderful what this series tells and although it does not bring you any closer to the truth, it does bring you closer to the people who are so passionate and full of knowledge. What a beautiful journey in itself. Thanks.
This episode, like the rest, is a wonderful exploration of people -- even if ostensibly through their ideas.
I just love the intro scoring, so enigmatic.
We invent the axioms and discover the consequences
Interesting
Excellent! I choose the Platonic view of mathematical information functioning on the boundaries of our spacetime limits molding our reality simulation according to its invisible prototype
the most underrated show about our most fundamental questions.
again a wonderful video in this series.
Dear Robert, I'm a math professor who follows your channel and especially this series about mathematics. I am very surprised that when you interviewed specialists about the nature of mathematics, you actually avoided speaking to any pure mathematician! You have certainly interviewed some outstanding and renowned experts whose work can be described as mathematical, but whose main research activity is actually not on core mathematics (i.e., algebra/analysis/geometry/number theory/combinatorics etc.) and belong to certain other research communities such as theoretical physics/theoretical computer science/logic-foundations etc. The lack of any pure mathematician in your interviews about the nature of mathematics is so striking that it cannot be accidental, and I find it very regrettable. It gives a skewed picture, because it is well known that the further from core math somebody is, the less likely they are to be a platonist, as can be seen from your interviews with Balaguer and Wolfram, for example (similarly Chaitin was the most purely mathematical of your interviewees and also the most platonist). It is true that most pure mathematicians are not very interested in the philosophy of mathematics (unlike theoretical physicists and logico-foundational people who tend to have a relatively strong interest in philosophy), but surely you could have found somebody.
I've noticed that as well. Most devoted mathematicians have a platonic view of math, and consider it an objective abstract reality that can apply to physical reality, but is not dependent on it.
Platonic reality was mentioned by Roger Penrose as most likely the case in Robert’s interview with him. Please reply as I’m very interested in this subject but not a mathematician.
@@bob9732 How can I help?
I think it seems like a valid complaint. But he phrased the question as a philosophical one. It sounds a little like: if you want to know about the daytime ask the sun. But what does the sun know about daytime? That being said yes I would have liked to hear from a mathematician myself.
Well ..... I guess it all depends on the definition you choose for mathematics for you to consider it invented or discovered, platonic or fictional. I’m no mathematician but I think it’s a more of a methodology or a technique we use creating the axiom, quantify the world accordingly to predict , operate and make sense of the physical world ( or at least how it started ) , therefore it can not be a platonic object nor fictional.
In the last 200 years alone, science has made so many discoveries. The revelations or findings by observation, trail and error, show the answers were always there; just not yet understood or proven.
Math is like the finest poetry. Something so enlightening that dazzles us sometimes. But, as poetry, is only language, a language that we invented to describe the Universe.
Great topic
Wonderful!
0:57 exactly thankyou
Wonderful👌
Math, as is commonly known, is an expression of the "reality" as we perceive it.. Whether our perceived "reality" is the only "reality"? I think, we don't have any formal way to know it for sure... We may apply empiricism or theoretical explanation. But all these will be limited by our understanding or perceptions of "reality". So we arrive at kind of circular arguments only, I think. Any way, a beautiful video raising these quests.. Thanks RLK..
Excellent.
Roger Penrose seems to be his expert friend for all subjects
Penrose kinda acts like a dick. I still like the guy, but sheesh.
@@mindofmayhem. How does he "act like a dick"? Penrose is one of my favorite people on the planet.
Penrose is fake news
@@m3dia95 Except you saying some words is not an argument
@@Raptorel I don't argue with people determined to drag me down to their level.
Man's really just went on a world tour in the name of mathematics
Its so he can call his holiday a business expess and have it as a tax write off
Haven't we been doing that for the longest? How did knowledge of mathematics travel from culture to culture to begin with?
@@ascensionunlimited4182
This is obviously a oversimplification, each step would’ve been repeated/stolen, lost and invented an uncountably different number of ways by even more cultures.
First a culture was trying to show the difference between quantities of things and counting was invented
A culture took their invention of counting and introduced subtraction, eventually another culture ran into negative numbers and the another culture invented 0. Then another culture tried simplifying some questions and invented multiplication then later division. From that another culture invented powers and roots. After that a another culture was thinking more abstractly and tried to create a consistent set of rules. That collective decentralised work is what we call number theory
Another culture started thinking more abstractly about number theory then created algebra. Another culture was trying to simplify some questions from algebra and a 14 year old created abstract algebra. Then our culture found some questions abstract algebra couldn’t answer and created calculus from there
Today all of mathematics (from typology to derivatives) is a combination of number theory with either calculus and or abstract algebra.
@@ascensionunlimited4182
math is a tool; it arises out of need. it needn't travel from culture to culture in order to see its use across cultures. new world peoples invented their systems independently of old-world cultures, and some current cultures are entirely anumeric, and have no maths at all.
KEvron
A good thought provoking discussion. Penrose said it is not us that that imposes math on the world, it's out there. In other words, a controlling intelligence = G-D. So from time to time, we humans discover a fundamental law following mathematical principles. There are however other mathematical edifices such as String Theory that have no basis in reality at all. So we could describe it as a mathematical game. In other words mathematics is a non physical construct, which can be applied to the real world when circumstances require it. However you need to bear in mind that both Newton and Einstein employed their own mathematical theories to describe the same thing. e.g. Gravity. Both were correct, but Einstein's theory proved to be a more accurate representation of reality, but that does not mean that is the end of the story.
This unarguably has to be one of the best YT Channels that exist today.
I found this discussion very interesting because I Am a Numerologist & student of Astrology - Which has been confused as different sciences (What Ever That Word Means)...
I can fully understand why most folks get loss in their discussions, because they are talking about complicated theories. And Einstein was absolutely Correct, that Everything is Connected.
The Simple version to understand, Represents how We All Are Connected to the Circle (The Universe as Planets within us.
When you study your Birth chart as to the meaning of Each House on the Zodiac, you will learn that each Planet in Your Chart - Represents your entire Personality as Players Upon the Stage .... Shakespeare once revealed that Earth represents a Stage and We All Are But Bit Players Upon it”
Then the Queen who lost her own head - after Shakespeare did a live show of the characters from the Village ... the thief lost his head for stealing something to Eat.
Kings & Queens Created Words to keep their subjects Confused.. So in closing - Numbers are the Language of the Universe - In the Biblical studies of Satan, he had to reverse engineer Everything that GOD CREATED.
Each Letter is Matched & Connected to two sets of Numbers reduced to their lowest common denominators. Because the Numbers Represents Portals leading to other Universes as follows:
A= 1 - 10 - 19
B= 2 - 11 - 20
C= 3 - 12 - 21 represents the number of the Adult Universe - 12 also represents Zodiac
D= 4 - 22 represents the second Master Number - 13 Transformation & O Karma reborn
E= 5 - Education & Learning & Teaching (Creativity & Art) 5th House/Home of Leo etc
F= 6
G= 7
H= 8
I= 9
K= (10 = 1)Graduation or Wheel of Fortune - start over if failed back to 1 or 19= Sun Energy has been learned to proceed to (22).
As this applies to the year like 2020 ... the end of the Zodiac Chart 12th House
2+2 = 13 or the New Zodiac begins the New House or moving into the 4th Dimension #4
13 also Represents the ending of an Era of 2020 years for the time period of each House as the Universe keeps Traveling as WE Do.
This is the simple outline to understand about Yourself - because we all are made with Atoms/Adams who was cast out of Heaven and Eve represents the light of Day as in New births.
Science is Theory & Numbers Are the Reality of Who We Are...
The first number after each Number Represents the First Set of Numbers
It’s like when you turn 10 years old to complete your first cycle in this life time (1-9)
if You Are The Universe When Born as anew Star 💫
Maths maybe part of the ruleset of this reality. Thanks again! 👩🏽🚀🙈🙉❤️
Watched this twice now, and will probably watch and refer back to it again in the future, but I can't seem to shake that old metaphor attributed to several musicians ... 'Talking about music is like dancing about architecture.' 🤣
If we all agreed with that, it would be very difficult to explain music theory or write a song with other musicians. If a musician said that, they were probably high.
It’s analytical a-posteriori. People are still struggling with arriving at the a-posteriori though. Deriving complex analytical truths requires a lot of experience, you need to know what to look for. Which is why often in statically typed programming languages, you do need type annotations even if there is type inference. Those type systems can easily go undecidable and need a human guide.
This is a very well made, extremely interesting film.
I would wish to ask this question to Kurt Godel for a most memorable anwser !
Godel already answered it in his incompleteness theorem. My take is you can be more and more precise but you will never arrive at exactness because the physical universe isn’t exact.
Gödel gave a hint by explaining that a set of rules and laws in mathematical systems cannot be described nor explained from within that system. You need an external standpoint or viewpoint. But that is impossible as you would need to exit from your own reality or the material world. So again you are thrown back to merely imagine that it is discovered as it exists on a higher level of reality or a different dimension of mind space and time. It's transcendental like e is!
I suppose, Idk though the way I see it math has to be somewhat of an interpretation, all it is is a structure that we lay over the world to understand things and describe things, some people who really get it better than I call it a language, but what math is, is as it is a sort of layer of constructive thought we put over the world that we bring into the physical world by minipulation (making things like phones or designing machines ectectect) and because it's evolving one day may simply just be a physical exploration that is complete and exact, but as is right now is still just a mental framework we all need to kind of at least hear about to be able to choose to chip in on or not, I mean it's really close in some areas, but until we can seriously describe it all and all the dots we need are in place to fill out this chart of all of reality as we expirience it and know it to be. I'd say we just have a very in tune mental framework for what really is there. And these professors or whatever are over thinking it.
Now thats a good question, best question i seen asked all day.
Beautiful episode. Can't really still make out if it is discovered or invented. However, if there exist other intelligent civilizations in Universe, then, they ought to do so by use of complex maths.
Fascinating! But needs WAY more commercials! 😃
Handy tip. Forward the video until the end then restart and the adds will be gone.
We have been trying to reach you about your car's extended warranty.😏
Whole questions arises from confusion with surface appearance of language as if the question meant the same thing to everyone. Mathematical structures have risen from the need to represent relationships in the real world via attempts to generalize, simplify and get to get into the essence of the internal logic these representations. For example, it is extremely easy to invent scenarios how a smart carpenter working on wheels would end up formulating the axioms for the theory of finite groups.
One can formulate an infinite amount of axiomatic systems and structures that are consistent with each other. Thus, is does not make any sense to state that structures such as groups or real numbers are the unique thing that represents nature. They just have risen representations via the human process of generalization and simplifcation.
I wished he'd have brought up things like how did Peter Higgs sit down with pencil and paper to figure out the Higgs' boson years ago or Gödel's Incompleteness Theorems one and two that shocked the math world and others beside. It basically states that you cannot prove the math by the math. Abstract world or not I have always been amazed at how Higgs did what he did or how a consistent system cannot prove itself. I studied engineering, but I had formulas I didn't need to understand to use. I then studied biology and the math changed, but it was doable though genetics was challenging and the math was there too. I'm like the host a bit confused, but I want to say invented yet it exists in the construction of how the Universe runs. Two dimensional.
I don't think these people made things up from the spot but rather had an intuition that these things should be true and then went about proving/modelling. I haven't studied particle physics properly but I'm pretty sure higgs modelled the higgs field in order to complete the set of objects that obey the symmetries of special relativity (so he took an aesthetic approach - striving for symmetry) and gödel probably (I'm completely guessing) noticed that certain examples of consistent axioms had unprovable statements and *then* tried to see if this was true in general. These guys were definitely smart, but it's not magic. Sorry if I'm misunderstanding what you're saying
9:11 Mark Balaguer outlines 4 different views of the origin of Mathematics:
(1) A _mentalist_ view - It exists only subjectively, in the mind
(2) A _physical_ view - It exists objectively, in the universe
(3) A _Platonic_ view - It has an abstract, yet real, existence of its own, independent of both of the above
(4) An _anti-realist_ view - It's an abstract, but fictional, human invention, with no existence of its own. Indeed, the idea that it "exists" at all is nonsense.
2 & 3 differ about how they define reality, whereas 1 & 4 seem complimentary.
What do you think of his classification into these 4 views and which of them, if any, do you think are correct?
i agree: 1 & 3 seem most complimentary. both are consistent with a determinist pov. 2 & 3 would seem to bear a greater burden of proof, but then again, mind-dependent cases are beyond proof, except maybe to the bearer.
KEvron
A policeman sees a drunk man searching for something under a streetlight and asks what the drunk has lost. He says he lost his keys and they both look under the streetlight together. After a few minutes the policeman asks if he is sure he lost them here, and the drunk replies, no, and that he lost them in the park. The policeman asks why he is searching here, and the drunk replies, "this is where the light is”.
I think that mathematics is the light in this joke. But why mathematics? Because is the only thing we know. At least for now.
Walking in the dark hoping to stumble upon it, that's philosophy.
i agree totally. It just seems to work and that's all we really know. Whether math is "real"(or whatever) is an nonsensical question almost. We don't even know what we mean when we say, well is math platonic or not or real or whatever. In a certain sense math can't not exist, then in the other math can't exist. We don't even know what we're talking about so what's the point.
@@BLUEGENE13 One could argue that math couldn't exist without objects to describe, eg count figures.
ie, math is an emergent property of the Universe...no?
@-GinPi Gamma Relationship between diameter and the circle.
Safe to assume that pi wouldnt exist without circular objects in a physical universe, no?
@-GinPi Gamma 69
Great conversations
Does nyone recognise the shot at 07:00, just before the Oxford shots of Broad Street and the High? There's what looks like an Oxford tourist bus in the background but I'm pretty sure that's not Oxford!
The invention of the automatic transmission still blows my mind.
Developing new math seems less like "finding" something than comparing it with an established system to check for consistency.
Please write a book about "Closer to truth: best interviews"
through invention we discover and vice versa
The chorus reminds me of the character out of the Alan Partridge "Dr No Vocal Chords" episode. Perhaps they convinced the production team that using the new Fisher-Price toy that distorts your voice with a Scandinavian accent was a great idea, even if no one can understand a thing you say because of the reverb. It really doesn't sound like many voices, but a single distorted voice of a Musk bot with laringitis.
mathmatics is the proof of intelligent design and humans use of it proves our close relationship with the creator
Mathematics is the symbolic language that describes and explains reality to a conscious mind. It is to whom mathematics is useful
When Wolfram talks about 'other mathematicses' is he talking about p-adic numbers and similar wildly different number systems? Or is he talking about different axioms rather than ZF? Thanks
I'm not convinced that the fact maths are derived from roughly the same set of axioms constitutes evidence that it is discovered.
Does an author 'discover' the sequel to her or his novel by deriving some set of logical consequences? See, when the author adds new variables, these variables that the author invents are still designed to obey the initial set of axioms that the author has set of the world of his or her story. The next chapter 'feels' right because it follows the same principles and is made to stem smoothly from the earlier part of the story, as though it was all there from start, only unveiled one step at a time.
But in reality, the author just thought of a working framework, imagined an outline, then planned and/or pantsed the rest via some kind of intuitive (or non intuitive) inference reasoning.
It seems that this appearance that the structure is being uncovered is the byproduct of a commitment to self-consistency, not some kind of unknown realm that is being unveiled one area at a time.
The system in which we describe our reality was discovered, but was it understood?
And is the function we attribute to Math the reason why we can’t understand?
In this world there was wood and stone, a man put them together to form a hammer to build his house.After 20 years someone came and asked "was hammer invented or dicovered?" So everyone do you need to know the answer?
yes.
If postulating the existence of some types of hammers allowed you to predict the workings of physical reality, your analogy would be a good one.
Why are you watching this?
@@suntzu7727
"Electricity at the beginning was used for magic show now it's used to power up our current world."
You can learn from the use of something evolve(at first maths was not used to calculate the physical reality) and the other is that just like the magician"we don't need to question the existence(electricity,maths) to make use of it unless it prevent further research."
@@cindyo6298
My answer is to be closer to the truth!
If you don't understand,you can ask.
I would have to say that after considerable effort it is "revealed" having always been there in hiding....
Mathematics is discovered. It has always existed but took we are slowly discovering how to express it. Not all the math we know today is correct, therefore from time to time there is a refining and getting closer to the correct mathematics, closer to the truth.
Math is logical, so is nature. The difference is that nature exists by itself; math, not so. Philosophers, not nature, invented logic. So, mathematics is a human invention. Nature is logical simply because it works. What doesn't work can't exist in the first place! There is no intention anywhere. Logic happens by itself. It has rules, but nature doesn't know that. The AND operation occurs with a chain: all links have to work for the chain to work. A river flowing down will split in two streams when an obstacle is hit. That's the OR operation. If it doesn't rain for a long time, the grass will turn yellow. That's the IMPLICATION operation. Logic just happens in nature. Math doesn't just happen.
@@jeancorriveau8686 Math does just happen in nature in very similar ways as you mentioned per logic. What other than mathematics could explain the logic of how a flower grows and changes?
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all the Is, all that Was, and all that Will Be, in this and any other universe of existence.
Encouraged at every turn to "think outside the box" perhaps it's time for a closer look at what got us into boxes in the first place. If you proceed, keep in mind, ahead are precise scale models of existing structures designed and assembled in prehistory, before the catastrophe that drove humanity mad by amnesia fell upon us: brainelevator.org
Maths can't be wrong. Axioms of today may describe something else, not the same thing that some entity in the future might want to describe, but all things that are proven from the axioms today are absolutely correct in this system of axioms. No god can piss on that.
In one sense, I think it's a bit of both; In a second, it seems to be invented. It's discovered in the sense that psychology discovered the mechanics of sensation and perception, not to mention other subconscious complexes that presumably existed throughout the entirety of human existence (that is to say, prior to the science itself). It is invented in the sense that glasses and binoculars are inventions we use when we need to see the phenomenal world more accurately. I didn't think I would get closer to truth so soon. After that first interview, I instantly knew that no one could actually prove whether math was invented or discovered. The idea that it was discovered seems to me to be nothing less than unwarranted speculation.
what i find interesting is that mathematicians and scientists seem to see maths as perfect and ideal, and physical reality as an approximation to that. when it should be thought of the other way round: mathematics is a simplified model of reality. mathematics is a system of pure logic, extending from some basic principles; we are fortunate to live in a reality which is logically consistent, and we have chosen the basic principles of mathematics to describe what we observe in the universe - so its no surprise that mathematics describes the universe so well
宇宙是用数学语言阅读和书写的。
I think you've got the idea of what math really is. It's the three laws of logic: identity, excluded middle, and non-contradiction expressed symbolically. From these simple rules all mathematics are derived. So logic and math are the same. They're non-material. I'm not certain what physical reality is and it's most basic form. Most mathematical laws are approximations of physical relationships. Which tells me that the rules of logic are somehow more fundamental than physical or conceptual reality. The implementation of mathematics is sometimes wrong but that doesn't mean that the logical rules themselves are. Sometimes people do math wrong doesn't make math wrong.
Maths is the perfect tool to do research on the physical reality.That's why scientist and mathematicians give it so much importance."It is in human nature to value what is of use to them."
@@levipack3835 identity and excluded middle are just different flavors of non-contradiction. Mathematics and logic both answer to physical reality as the former two are human inventions about the latter.
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all that Is, all that Was, and all that Will Be, in this and any other universe of existence. This expression facilitates self discovery of Intelligence with Itself within the 'physical' universe through the filter of us All.
In a way, a block of marble contains all possible sculptures but really it contain none, except that it is a block. You create the sculpture than you look at it to find the different meanings that can fit that creation.
It is even more worrying that mathematics appears to have no content. As all proofs can ultimately be broken down into a sequence of syllogisms, however lengthy, theorems are essentially tautological or analytic and amount to no more than restatement of the axioms in other words, i.e. the assertion that A is A.
Platinism to me can best be describe as a particle-wave. It's both and you can't really pin point it. Because observing changes it
Question - might the singularity at the center of a black hole be everywhere in the same place?
Great episode and great discussions but I will criticize one thing : why there were no pure mathematician in the episode ? A pure mathematician (espacially an abstractionist) would have some interesting insight.
i'm not so sure. math and philosophy are fairly different disciplines, and the nature of existence is a philosophical pursuit. sure, there's some overlap, but the fundamentals are quite different. mathematicians seem to be overwhelmingly platonists on the matter in question, and it's the "overwhelmingly" - the lack of more diverse opinion in the field - that leads me to tend to think they're not so up on their philosophy, where platonism, while it still has its notable adherents, receives a good deal of pushback.
KEvron
3 6 9 holds the key to everything.
I'm on the side of discovered, but everyone really gave great points.
Balaguer: Do black holes exist, do Higgs bosons exist, does Bitcoin exist? If so, in what sense do they exist? Do you need a village in Nepal you can go to and find them? To understand Platonism one has to have a broader understanding of the notion of existence. There are precise senses in which mathematical objects exist, for example that they form an indispensable part of successful/useful scientific theories about the world (Quine).
A lot of problems are raised in this video, but none really seems to be solved. That shows, I think, how difficult it is to grasp what really mathematics is about. But, the raising of problems is really interesting here, because the solution to those problems would be the discovery of truth. For everything harmonize with truth ! Problems kind of show us where to look. Aristotle shows the necessity of problems raising, or doubt, in the part of philosophy called wisdom or, by a more abstract word, metaphysics, in the third book of his Metaphysics. And the question here treated is really a question for the wise man, for the metaphysicians.
Everyone who is interested in finding truth about the question raised in this video should read Aristotle's, and Thomas Aquinas following him, treatment of the question. Aristotle discuss this in the second chapter of the second book of his so called Physics, which title would be better translated as Natural Hearing. In this chapter, he inquires what separates natural philosophy from mathematics. He starts by raising problems : natural philosophy and mathematics seems to overlap. On one hand, natural philosophy seems to be a part of mathematics, as in the case of what was called harmony and astronomy, which were, in ancient times, parts of mathematics studying natural phenomena. On the other hand, mathematics seems to be a part of natural philosophy, for it concerns quantity, which is a property of natural beings; but to study natural beings and their properties belongs to natural philosophy. Aristotle solution is that pure mathematics, i.e. arithmetic and geometry, is about quantity of natural beings but not as such, not as it is the quantity OF a natural being. Math is a consideration of quantity in itself, separated from that of which it is the quantity, i.e. natural being. So it is an abstract knowledge about a property that really exists in the natural world, although it does not exist in separation in the natural world. Aristotle adds : and there are no falsity in considering quantity separated from its subject. The falsity would come if we consider that it exists separated from its subject, as Plato thought.
We find the same thoughts in Aquinas. One passage I can point to is his commentary of Boethius' De Trinitate, question 5, articles 1 and 3.
An audio course by the late Duane Berquist is also available on that question in one of his natural philosophy courses. It is actually a commentary on Aristotle's passage I pointed to. You can find it on www.mediafire.com/?kzjpdo455wpoq for free. The passage in question is in the third course and it starts at 44 minutes 18 secondes. The audio quality is bad, but the teaching is good. It really worths the listening ! This teaching really shed light on the relationship between mathematics, natural sciences, human mind and the natural world.
The discovery of invention is the truth of your words and feelings put in to action or made into an object(ive)
The distance from earth to the moon can be calculated, measured, viewed, adjusted. Its a way to conclude, not something that yields any kind of monopoly. It just is. As is for simple questions being presented as complicated.
"Be carefull seeking meaning, where there is none."
Even a block to carve the sculpture out of has to be discovered first and chiseled out of later, just so it LOOKS good.
Number 0 does not exist in our word and number 1 seems to consist out smaller 1's infinitely...
It is both invented and discovered, just like there is no 'yes', or 'no', only in between.
Sometimes the answer is way closer than you think: mathematics comes from the latin root: to learn, to study. Therefore it is an invention. Physics is also an invention, the study of nature at the physical level. The only reason, i believe, that mathematics and physics are able to sync with the Universe, and describe it to high accuracies, is that the Universe is very very ancient and very very big, which means some or more order eventually arises from chaos, through different interactions, repetitions, or other simple mechanisms, which can be captured by our mental tools. Another way to see this is that many mathematical theorems can be proven not to apply to physics, and many physical phenomena have yet any scientific explanation at all, therefore, a healthy mix between invention and discovery is the more rational, correct, and even humble solution
So Pythagoras / Plato might be right and all the maths that's of no use for describing our universe, might be the description for other universes in a (infinite?) multiverse i.e. all maths is ultimately descriptive, useful and relates to something / some principal of somewhere.
A discovery in mathematics could feel like an invention through consciousness which it is. Mathematics invented by consciousness is also a discovery.
The laws of the universe will never change. It is simply up to humanity to create the right formulae to accurately describe the experience.
Breakthroughs don't actually mean new physics, but we as a species are simply catching up to what already *is.*
Discovered, however there is certain order in things that seem to rely upon mathematical principals. What we have for measuring is the result of motion of all things. This motion IS matter, and it's origin so to speak is metaphysical intent for lack of a better term. The intent was the reconciliation of the inability for nothing to exist.
Finally got to know, Mathematics is both realistic and poetic as well.
(25:35) *"Math is either physical, or mental, or platonic, or fictional ... Choose only one."* ...Why are we restricted to only one choice?
I was thinking the same thing, also why are we restricted to choosing any of them at all? Math is really just a description, and does a description fit perfectly into one of those options? Not really.
Numbers are all around us and they guide us by showing up in our reality. In a way they know us as well as we know ourselves and create a path, a structure, for us to exist in. What kind of structure, this is, I don’t know. A platonic one I suppose.
There is a unique platonic space for the English alphabet, grammar and couple of dictionaries.
Why would this artificial garbage, called "natural" language by those who can't even appreciate the irony, have any place in the Platonic realm?
Mathematics is a universal form of communication even animals can communicate counting.
Animals sense quantity, eg, a cat sensing his power to jump onto a fence. There is no counting, which requires units, eg, a five-foot high fence. Man counts by abstracting, ie, selectively focusing (on quantity, here, the length of a ruler relative to to the length of a fence). There are many ruler-lengths to one fence, each one having a name, eg, five ruler-lengths,ie, counting.
Intro. To Objectivist Epistemology-Ayn Rand
Leap Of Logic-David Harriman
@@TeaParty1776 If you think concerning predicting a thing that does not exist in front of you at that exact moment , but can predict it will soon happen at a certain time and place your doing math at least counting. Migration patterns show this these things must be learned to be performed.
Mathematics is clearly more than an abstract object, it is the underlying fabric of reality. It transcends human ideas like emotions, civilization and processes, to name a few examples of abstract objects. For example, no matter what universe or reality, no matter what type of particles and physical structures exist, no matter how many amount of dimensions an existence has, 2 plus 2 is always 4. There is no reality where 2+2=5, because one such a contradiction implies a contradiction of the entire system. One can argue that the concept of mathematics is a human invention, but it transcends humanity and thought. Even many species without brains or sentience have some form of counting and calculation. Any life with sufficient intelligence would come to the exact same conclusions in mathematics as we would.
*"There is no reality where 2+2=5"*
in this reality, there is no proposition that may exist absent a proposing agent. if the proposition "2+2=5" may exist absent such an agent, then the proposition "this sentence is nether true nor false" may exist absent one, and reality then incurs a genuine paradox.
the existence of concepts absent the process of conceptualization results in paradox.
KEvron
a better question is why is september the 9th month october the 10th month and december the 12th month ,what difference does changing a system base from 12 to 10 do and why was it done ,answer that and then you have a starting point
Randomly existed from something, before it enovated logically
Epistemologically, mathematics is primarily based on rationalism or one can also say it's axiomatic. Hence mathematics is both discovered and invented. At the same time it explains the empirical world as well as rationalize the abstract
I think physicists saying that math is foundational is a circular argument. Of course they’ll say it is, as science is based on math! And as scientists they willfully ignore/dismiss all things that can’t be explained by physics and math (e.g. consciousness, “the observer”, the measurement problem, Godel/Tarskis theorems, etc.). I love science, but I also realize it is foundationless... as is math. Foundationaless doesn’t mean useless, but it does mean it’s incomplete and will always be such. It’s just a tool, not the whole toolbox.
It's currently the best tool we have, I'd be happy to hear of any replacements you might know of
@@trybunt so how would you prove science is the “best tool we have”? With math? With even more science? 🤓
@@hckytwn3192 I'm not trying to prove anything, I'm asking you- do you know any tool for searching for truth which works better than science?
I'm fully aware that it's not perfect, it's made up of people trying to seperate their own biases from their results (that's literally what science does, it's a method designed to counter bias) but its still being used by people who make mistakes. Unfortunately, we haven't found any better way to reliably learn about the world, so we'll just have to tentatively put our trust in this method, while understanding that anything we think we know could be wrong, until someone comes up with a better method of investigating the universe
@@trybunt Right, but that's exactly the point. You made the statement that science is the "best" tool we have, but we only judge that tool by using that tool (i.e. proving out science only using science). I am saying that is a logical fallacy. If we present any other possible tool--introspection/meditation, metaphysics, mysticism, religion, etc.--our first inkling would be to dismiss them using the scientific method, right? However, we know for a fact we can't use science to validate scientific truth, so how can it possibly be used to determine the truth of another tool? Really think about that. It's pure circular reasoning and very hypocritical. Also, if that weren't enough, the scientific method is deeply flawed. Science is based on observation and measurement, and yet it can't explain what those are really. So, if science can't even explain it's own internal processes, how can we assign words like better/best to it? I would expect a process to have internal consistency and completeness before we do that--but science doesn't have that, nor will it ever.
Art
There are set relationships and dependencies between things and phenomena in the universe and math is a way to discover and describe those. That's my view. Am I wrong?
matter interacts, observers relate. a relationship is a description of members of a set, and descriptions and sets are products of the mind.
KEvron
@@KEvronista Gibberish
@@stefansoder6903
that just means it's over your head.
relationships don't exist until we create them, stupid.
KEvron
@@KEvronista More gibberish
It may sound philosophical..
But if we give a closer look to things.
"NOTHING IS INVENTED but DISCOVERED".
If you ascribe to the many worlds model of reality that allows for infinite dimensions of infinite variance from our own, then every tangent of reality already exists simultaneously within that multidimensional fabric of ulterior reality. In effect that would mean everything is deterministic in their own regard to their own reality/plane, lending to the philosophy that everything is preset and is only being discovered rather than originating spontaneously.
A good way of visualizing it, is like a fractal pattern, similar to how a tree branches off. From root timeline, or ultimate moment of potentiality fractaling/branching off from every other ensuing potentiality, explored to the degree of their potential. The same visual phenomenon can be seen intrinsically across almost all fields, scales and spectrums of our material reality. Which like a snake eating its own tail, brings it back to the conversation to begin with. Its through this observation of these various patterns repeated across reality that we can begin to understand the greater and greater nature of reality
@Mr Right - the iPhone is comprised of electronic components such as the transistor and other devices, these devices were developed using mathematical derivatives associated with current flow (electricity), which was discovered.
Can the human mind invent abstraction like mathematics? How would the human mind create / invent an abstraction / mathematics?
Mathematics is a perception within your mind. The mind is describing the world through the medium of mathematics.
Both. While the more practical parts are discovered as provable representations of elements of the real world, in usage today, particularly in astrophysics, key elements can be invented, or perhaps more to the point, concocted out of thin air. In common practice, assumptions are made that are both unprovable and logically fallacious. A very clear example of this is contained in the alleged four kinds of black holes, for instance. Einstein didn't believe any of them could exist, but most people nowadays think Einstein was wrong on that point.
e, 1+ 5^1/2÷ 2 and pi were discovered. They have always been there in the design of the universe. Mankind has only recently had the conditions necessary to grasp them.
Does it mean something that mathematics used to measure space and time?
It’s an expression like music, arts and literature.
Music is maths
Music, arts and literature do not precisely define reality like mathematical equations do. But yes it can be like that for instance the Euler equation.
Math is the expression of the objectively simplest things we can think of, with the goal of precise understanding.
Art is an expression of the complicated mess of human emotion and experience, designed to affect other, equally complicated and messy human beings.
I honestly don't see much in common, they seem more like the opposite ends of the spectrum.
@@AlexanderShamov the one who cannot transcend illusion of “Duality” does tend to complicate things.
@@AlexanderShamov well to me its like art is in the realm of the subjective to which the mathematics if there are any are still unknown. Its related to the unsolved question of consciousness and qualia.
But look at the medium of any art its all things that are subject to the laws of physics which are mathematical. Also if you look at the technique of any artist they use mathematical concepts like rhythm, proportion, and tempo among others. So to me there is a connection but I see mathematics as objective while art in the realm of the subjective.
It's a matter of perspective.
Inventing a steam engine is also a form of discovery - you discover that if you turn water into steam it expands, so if you combine mechanical elements in such and such way, you can convert thermal energy into kinetic energy etc.
You could write your reasoning down on a piece of paper, never constructing a physical steam engine, only proving the validity of the concept in theory.
Have you invented it? Or have you only discovered certain possibilities that have always been part of the fabric of reality?
It's only a matter of convention which word you decide to use.
Carl Sagan's book Contact contained a crazy idea, that the random digits of pi contained a message that explained how to build a machine that could access an ancient stargate system of wormholes to travel between the planets. That's pretty radical for a scientist since there's no logical way to explain how a "picture" could exist in an abstract constant, as if the ratio of a circumference of a cylinder to radius would have to be changed to store that picture!
Carl Sagan was probably referring to the idea of _rich numbers_ i.e. numbers whose decimal expansion contain every possible sequence of digits. It's not proven that pi is a rich number, but it wouldn't be surprising, since _almost all_ real numbers are rich numbers.
@@ferdinandkraft857 Good attempt, but actually not. That would be the only explanation, except impossibly far up to find. They were unlikely sequential 0,1 digits, base 11, embedded perhaps some millions of digits down, which made a bitmap picture.
kasmana.people.cofc.edu/MATHFICT/mf55-spoiler.html
I think that Sagan was trying to find something that would give even a skeptic like himself that numinous feeling of amazement that goes beyond being impressed with an alien being's advanced technology. We can all imagine scientific advancements that could alter the physical universe, but to alter a constant derivable from Euclidean geometry itself seems, well, god-like! As "Nils Tycho" points out: "That is what makes the conclusion so spectacular."
Just a footnote: the digits in PI (π) aren't random. They just seem that way.
@@jeancorriveau8686 You mean "not random since deterministic" but in practice such irrational numbers can be the best random number generator you can get.
Universe/ reality has patterns and math is just our translation of those patterns.
Life is just matter forced to exchange energy. :) Math is it's numerical expression.
@@mindofmayhem. dumb reductionism.
@@JustinHerchel More like adjective holism. {(-_-)}
@@mindofmayhem. That's a moronic statement. Life is not just matter forced to exchange energy, everybody knows that. Are your emotions just matter forced to exchange energy? How about conscienceness? How about thoughts and ideas? How about choices? How about skepticism, determinism, and realism... So many -ism's in life. Life can be as simple as possible, yet can be so complex at the same time. Well that's just a tiny fraction of life for you buddy, something that the most intelligent species in the universe is still trying to fathom. Alright buddy.
@@ultrainstinctgoku2509 Are your emotions just matter forced to exchange energy? Yes, they are complex chemistry common to all mammals. How about thoughts and ideas? Artifacts or neural networks that can be simulated in algorithms. How about choices? Illusions. There is only observable behaviour that can be simulated by algorithms. Ask social media companies. How about skepticism, determinism, and realism...? These are just thoughts and ideas.
Urantia: 15:14.9 Your planet is a member of an enormous cosmos; you belong to a well-nigh infinite family of worlds, but your sphere is just as precisely administered and just as lovingly fostered as if it were the only inhabited world in all existence.
It's a language mankind has developed to relate to all four realms. Think, what good is a fossil to the granite when it is man that can put that fossil in a geological time frame and imagine the beast within the granite. It's man's creative ability to relate to the environment one chooses to 'study'.
I wish I was better at mathematics. It just feels peculiar that we have to be conscious to discover mathematics
Well, you can't conclude that Mathematics brings us closer to truth if we are not sure whether it was invented or discovered.
Neither the answer, I'm still stuck of the question of why they made it so damn hard.
Because life is hard and so does the world , the universe
Invented subjectively to interpret what human can observe
The number systems with the concepts of zero and infinity, imaginary values , trescandental numbers are a typical example of human subjective interpretation of what they can observe in the universe