Does math have a major flaw - Jacqueline Doan and Alex Kazachek
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Date: 2024-04-24
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Comments and reviews: 20
Martin-pb7ts
I am seeing this quite frequently with supposed paradoxesin Math and Physics that don't seem to require reality:
Step1: Make impossible propositions and postulates.
Step2: Show how those impossible propositions or postulates create a contradiction.
Step3: Amazement by everyone.
I will regard this paradox as something more than a steaming pile of turd if you can answer the following two questions:
1. Show me how a mathematician with a sharp knife (or some automated mechanism) can cut a circle an infinite amount of times within the timeframe of the universe (i. e. before the universe ends.
2. Show me how a mathematician can re-arrange an infinite amount of pieces within the timeframe of the universe (i. e. before the universe ends.
If you can show me that then I will be impressed. Until then stop pretending this is anything more than re-arranging some symbols and pretending they mean something.
This is a 2 step process which is not possible because it is not possible to end the first step. Infinity means carries on forever in this context. It is not possible to cut something into an infinite number of pieces and expect a pile of pieces at the end, because there is no end. If you want the person to re-assemble the pieces you are assuming that there is a point in time that the person cutting has finished but by the definition of infinite this will never happen. There will be no point in the future where the person cutting the circle will no longer be cutting the circle.
In context of this paradox, the answer is, no Math does not have a major flaw. Your flakey paradox does.
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I am seeing this quite frequently with supposed paradoxesin Math and Physics that don't seem to require reality:
Step1: Make impossible propositions and postulates.
Step2: Show how those impossible propositions or postulates create a contradiction.
Step3: Amazement by everyone.
I will regard this paradox as something more than a steaming pile of turd if you can answer the following two questions:
1. Show me how a mathematician with a sharp knife (or some automated mechanism) can cut a circle an infinite amount of times within the timeframe of the universe (i. e. before the universe ends.
2. Show me how a mathematician can re-arrange an infinite amount of pieces within the timeframe of the universe (i. e. before the universe ends.
If you can show me that then I will be impressed. Until then stop pretending this is anything more than re-arranging some symbols and pretending they mean something.
This is a 2 step process which is not possible because it is not possible to end the first step. Infinity means carries on forever in this context. It is not possible to cut something into an infinite number of pieces and expect a pile of pieces at the end, because there is no end. If you want the person to re-assemble the pieces you are assuming that there is a point in time that the person cutting has finished but by the definition of infinite this will never happen. There will be no point in the future where the person cutting the circle will no longer be cutting the circle.
In context of this paradox, the answer is, no Math does not have a major flaw. Your flakey paradox does.
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TLguitar
Because math is a man-made tool rather than a natural science, it can contain such examples that likely have no parallel in the physical world.
To my understanding this paradox stems down to being able to break down a set of values (i. e. ones that represent a sphere) into an infinite series of an infinitely-high resolution.
The unobservable universe may very well be infinite, but applied physical situations within our observable reality don't seem to be infinite. If a physical sphere is made of a finite number of subatomic particles, and space as well may be of a finite resolution, we can't section a physical one an infinite number of times to make use of the mathematical phenomenon which is =-1=-2.
Point being, this paradox breaks our brain because it applies to a mathematical sphere values that don't exist in a physical sphere.
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Because math is a man-made tool rather than a natural science, it can contain such examples that likely have no parallel in the physical world.
To my understanding this paradox stems down to being able to break down a set of values (i. e. ones that represent a sphere) into an infinite series of an infinitely-high resolution.
The unobservable universe may very well be infinite, but applied physical situations within our observable reality don't seem to be infinite. If a physical sphere is made of a finite number of subatomic particles, and space as well may be of a finite resolution, we can't section a physical one an infinite number of times to make use of the mathematical phenomenon which is =-1=-2.
Point being, this paradox breaks our brain because it applies to a mathematical sphere values that don't exist in a physical sphere.
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madskristiansen
In my experience, this paradox is what happens when theoretical frameworks of infinite energy meet the laws of physics and thermodynamics. Math is a system to measure and calculate the world around us. It is a language for the world, born from our abstract intellect and logic, thus only a part of the world BECAUSE we defined it so. The universe doesn't care for math.
In our minds, the logic can be as sound as possible and have infinite energy, but the real world has finite energy. Matter cannot be destroyed or created, only changed. This is our formulation of a universal fact, and though we invented the laws of physics, they still exist and are completely independent of us to exist.
Therefore, pure and perfect logic can create new matter from a perfect sphere, whereas the real world cannot.
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In my experience, this paradox is what happens when theoretical frameworks of infinite energy meet the laws of physics and thermodynamics. Math is a system to measure and calculate the world around us. It is a language for the world, born from our abstract intellect and logic, thus only a part of the world BECAUSE we defined it so. The universe doesn't care for math.
In our minds, the logic can be as sound as possible and have infinite energy, but the real world has finite energy. Matter cannot be destroyed or created, only changed. This is our formulation of a universal fact, and though we invented the laws of physics, they still exist and are completely independent of us to exist.
Therefore, pure and perfect logic can create new matter from a perfect sphere, whereas the real world cannot.
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lrwerewolf
Does mathematics have a major flaw Yes. Over 90% of mathematicians are mathematical platonists who think they're dealing with real existing objects, even if those real existing objects are abstracta. The universe is not governed by math, math is simply the language we invented to model the universe. As is pointed out in this video, we select the axioms arbitrarily to suit our goal, they're neither true nor false, they're what justify other claims. The real flaw is that most mathematicians don't actually delve into philosophy of math and thus fail to understand they're just playing a Wittgensteinian language game with formal systems.
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Does mathematics have a major flaw Yes. Over 90% of mathematicians are mathematical platonists who think they're dealing with real existing objects, even if those real existing objects are abstracta. The universe is not governed by math, math is simply the language we invented to model the universe. As is pointed out in this video, we select the axioms arbitrarily to suit our goal, they're neither true nor false, they're what justify other claims. The real flaw is that most mathematicians don't actually delve into philosophy of math and thus fail to understand they're just playing a Wittgensteinian language game with formal systems.
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whatisdis
Not sure if right, but I think I came up with a version of Banach-Tarski Paradox of my own.
Take a series of whole numbers from 1 to infinity. Now take all the odd numbers in the series and add it up. You'll find that the total is infinity. Now do the same with even numbers. Add all the even numbers up and you'll get infinity too.
In the end you get two infinities from one infinity. Which doesn't seem right considering the odd version of infinity doesn't have all the whole numbers yet it still totals to infinity.
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Not sure if right, but I think I came up with a version of Banach-Tarski Paradox of my own.
Take a series of whole numbers from 1 to infinity. Now take all the odd numbers in the series and add it up. You'll find that the total is infinity. Now do the same with even numbers. Add all the even numbers up and you'll get infinity too.
In the end you get two infinities from one infinity. Which doesn't seem right considering the odd version of infinity doesn't have all the whole numbers yet it still totals to infinity.
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JaybeePenaflor
I first encountered the Banach-Tarski paradox in my subject for mathematical proof. When we discussed certain set-theoretical concepts, we naturally covered the Axiom of Choice. Our teacher introduced us to the Banach-Tarski paradox and promised we would eventually learn its proof as we attended higher mathematical classes. I needed to learn concepts from mathematical analysis and topology to actually understand the proof.
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I first encountered the Banach-Tarski paradox in my subject for mathematical proof. When we discussed certain set-theoretical concepts, we naturally covered the Axiom of Choice. Our teacher introduced us to the Banach-Tarski paradox and promised we would eventually learn its proof as we attended higher mathematical classes. I needed to learn concepts from mathematical analysis and topology to actually understand the proof.
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evanlucas8914
Sometimes you can follow all the rules and come to an unexpected result. This is like California declaring the bee a fish because it meets all the criteria. No it's not actually a fish but according to the rules we established it is legally a fish.
The same goes for this. It's not technically possible in reality (as far as we know, however according to the rules we have established it's possible.
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Sometimes you can follow all the rules and come to an unexpected result. This is like California declaring the bee a fish because it meets all the criteria. No it's not actually a fish but according to the rules we established it is legally a fish.
The same goes for this. It's not technically possible in reality (as far as we know, however according to the rules we have established it's possible.
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igoikeni
It's like creating the natural numbers twice from themselves: split them in evens and odds. Half all the evens, increment and half all the odds: you have the original numbers, but twice. How paradoxical
It's not puzzling or in tension with intuition at all. In fact I find it mundane or boring.
Essentially Bannach-Tarsky relies on the ssme concpt with some added geometrical fluff.
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It's like creating the natural numbers twice from themselves: split them in evens and odds. Half all the evens, increment and half all the odds: you have the original numbers, but twice. How paradoxical
It's not puzzling or in tension with intuition at all. In fact I find it mundane or boring.
Essentially Bannach-Tarsky relies on the ssme concpt with some added geometrical fluff.
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sai_beo
The spheres (circles) are constructed via an infinite process. Using that same infinite process one could have constructed two identical spheres (circles, instead. If I'm not mistaken, that is the idea behind the theorem. It is not saying that if you have two oranges, you can theoretically slice it up and combine the pieces into two identical oranges.
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The spheres (circles) are constructed via an infinite process. Using that same infinite process one could have constructed two identical spheres (circles, instead. If I'm not mistaken, that is the idea behind the theorem. It is not saying that if you have two oranges, you can theoretically slice it up and combine the pieces into two identical oranges.
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nerd26373
Math is supposed to be abstract. One thing that strikes people about it is that it can never be completely understood. Even when you look at it in a different angle, there's still some areas that need analysis on. Equations are anything but perfect. People spend years just looking for the 'correct' answers when they probably aren't the best answers.
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Math is supposed to be abstract. One thing that strikes people about it is that it can never be completely understood. Even when you look at it in a different angle, there's still some areas that need analysis on. Equations are anything but perfect. People spend years just looking for the 'correct' answers when they probably aren't the best answers.
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henriquecardoso45
TED-Ed math videos are always impeccable. There's a great ending quote on Spivak's Calculus from Jonathan Swift, when he lays the definitions of the reals:
There was a most ingenious Architect
who had contrived a new Method
for building Houses,
by beginning at the Roof, and working
downwards to the Foundation.
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TED-Ed math videos are always impeccable. There's a great ending quote on Spivak's Calculus from Jonathan Swift, when he lays the definitions of the reals:
There was a most ingenious Architect
who had contrived a new Method
for building Houses,
by beginning at the Roof, and working
downwards to the Foundation.
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eshelsh1905
Great video, but your explanation for the axiom of choice (2: 20) was rather unclear - I’m already familiar with the aoc and still got lost in the metaphor.
It might have been better to explain what the axiom actually is, before saying when a choice is valid and telling the story about the omniscient chooser.
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Great video, but your explanation for the axiom of choice (2: 20) was rather unclear - I’m already familiar with the aoc and still got lost in the metaphor.
It might have been better to explain what the axiom actually is, before saying when a choice is valid and telling the story about the omniscient chooser.
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tharagleb
Not an infinite number (at 0: 15, a finite number. From Wik: Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball.
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Not an infinite number (at 0: 15, a finite number. From Wik: Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball.
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Shatterverse
Just because something is logically correct in mathematics doesn't mean that it's actually useful in real life. If it wad, then we'd have negative mass and backwards time and if this exist, which there's no proof of. Don't even get me started on why dividing by zero pisses me off.
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Just because something is logically correct in mathematics doesn't mean that it's actually useful in real life. If it wad, then we'd have negative mass and backwards time and if this exist, which there's no proof of. Don't even get me started on why dividing by zero pisses me off.
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Moomoo0013
Wait, I actually was able to follow through with this! Basically, math itself is pretty abstract but it becomes concrete once we apply it in a practical situation (a. k. a. reality. And there are alot of alternate truths, I guess, that would lead to different realities. Cool stuff.
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Wait, I actually was able to follow through with this! Basically, math itself is pretty abstract but it becomes concrete once we apply it in a practical situation (a. k. a. reality. And there are alot of alternate truths, I guess, that would lead to different realities. Cool stuff.
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Nictator42
Not really a good explanation of the paradoxm tbh. This essay reads more like an intro to the existence of the paradox itself without actually getting into any of the important details. Basically, the essay essentially says nothing about the problem whatsoever.
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Not really a good explanation of the paradoxm tbh. This essay reads more like an intro to the existence of the paradox itself without actually getting into any of the important details. Basically, the essay essentially says nothing about the problem whatsoever.
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xiaohuwang4173
Let's not forget during the Banach-Tarski construction, the pieces the ball is cut into are in fact non-measurable, meaning there's no consistent way to assign a volume to each of them, making it even less realistic
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Let's not forget during the Banach-Tarski construction, the pieces the ball is cut into are in fact non-measurable, meaning there's no consistent way to assign a volume to each of them, making it even less realistic
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joanhoffman3702
I was following along, then I got lost partway through. It’s a good thing I understand the math needed for everyday life! Not that I was terrible at math in school, it’s just not something I need day to day.
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I was following along, then I got lost partway through. It’s a good thing I understand the math needed for everyday life! Not that I was terrible at math in school, it’s just not something I need day to day.
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earthling_parth
I'll sorry but your video did not explain the Banach-Tarski paradox to me. I did not understand this video at all. Probably one of the few Ted-Ed videos where I've had this experience.
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I'll sorry but your video did not explain the Banach-Tarski paradox to me. I did not understand this video at all. Probably one of the few Ted-Ed videos where I've had this experience.
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dianeyoung8130
So basically they were like this axiom has some logic problems and a bunch of mathmaticians were like yeah. but we are not going to re-proof everything. so it stays.
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So basically they were like this axiom has some logic problems and a bunch of mathmaticians were like yeah. but we are not going to re-proof everything. so it stays.
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