Is Math a Feature of the Universe or a Feature of Human Creation? | Idea Channel | PBS
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Durata: 8 minuti 45 secondi
Autore: PBS Idea Channel
Data pubblicazione: 03/06/2013
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Math is invisible. Unlike physics, chemistry, and biology we can't see it, smell it, or even directly observe it in the universe. And so that has made a lot of really smart people ask, does it actually even EXIST?!?! Similar to the tree falling in the forest, there are people who believe that if no person existed to count, math wouldn't be around . .at ALL!!!! But is this true? Do we live in a mathless universe? Or if math is a real entity that exists, are there formulas and mathematical concepts out there in the universe that are undiscovered? Or is it all fiction? Whew!! So many questions, so many theories... watch the episode and let us know what you think! All Time 10 Videos: Veritasium - ( Fast, Furious & Funny - ( The Brain Scoop - ( ASAPScience - ( The Royal Institute of Great Britain - ( The Spangler Effect - ( Minute Physics - ( Head Squeeze - ( Vsauce - ( Episode Links: Weezy Waiter's "The Good Stuff" Awesome Math photos from Nikki Graziano Further Reading for the "Online/Offline" Episode: Nathan Jurgenson: EA and Guns Article Sources: Eugene Wigner Velocity of an Unladen Swallow Alain Badiou Briefings on Existence Lakoff / Nunez Where Does Math Comes From? Mark Colyvan An Introduction to the Philosophy of Mathematics Tweet of the Week: Music: "Europe" by Roglok ( "Carry on Carillon" by Roglok ( "Bouncy Castle" by Roglok ( ":P" by Roglok ( Level 5: Room for the Homeless Binarpilot Clockwork - Titan (geometry remix) Let us know what sorts of crazy ideas you have, about this episode and otherwise: Tweet at us! @pbsideachannel (yes, the longest twitter username ever) Email us! pbsideachannel [at] gmail [dot] com Idea Channel Facebook! Hosted by Mike Rugnetta (@mikerugnetta) Made by Kornhaber Brown ( Want some more Idea Channel? Here's Last Week's episode: "Is Developing Artificial Intelligence (AI) Ethical?" Want another one? Here ya go: "Is Sad Music Actually Sad?" Here's Some More: "Is Buying Call of Duty a Moral Choice?"

Math does not exist ...
Math does not exist "out in the universe". At the same time, it does not simply "exist in our brain". It is actually in a layer that is beyond the universe. Math is not in the universe, the universe is in Math. This may sound strange, awfully philosophical, or perhaps even meaningless, until you understand model theory. The idea behind model theory is that mathematical rules can "map" into real-world concepts. Like, similar to the example already given, 2+2=4 can map into the real-world take 2 cats, add 2 more cats, get 4 cats. But the main premise of model theory is that you can map the same mathematical concept into several different elements. For example, 2+2 doesn't have to be about cats. In fact, it doesn't even have to be about physical objects. If you've waited 2 seconds, and immediately after you've waited 2 more seconds, then you've waited for 4 seconds. In the eyes of model theory, then, math is about finding out what's common to different models. It starts by trying to find a minimal list of observable facts that a certain model has to fulfill in order to be "sufficiently similar" to other models. For example, in the case of addition, we require that we don't care about the order of the objects. For instance, if you put 2 black cats right of 2 white cats, then while you have 4 cats, this doesn't represent the fact that you have, right to left, black-black-white-white cats. Only if you decide this latter detail is unimportant, does the model fit. On the other hand, if color does matter, than taking the black cats first, and then putting the white cats right of them, changes the group of cats. The next step is then to figure out what can be inferred based only on these observable facts, without relying on the observations themselves. For instance, 2+2=4 is actually a direct result of 1+1=2, 2+1=3, 3+1=4 and order of operations not mattering. The first 3 can be seen simply as definitions of 2, 3 and 4 (As what happens to the group when you add one more of the smallest group). They are giving names to concepts. The last one is the thing that must be true for a model to fit. Any aspect of this universe, or any other, that fits this requirement, would also fulfill 2+2=4. The ultimate result of model theory lies in Godel's completeness theorem. It states that: 1. If something is true in a purely mathematical sense, then it is true for all models that satisfy the basic required observations. This means that math can be used to reason about the real universe. Another way to look at it, is that math can be used to show that certain types of things cannot exist, in any universe, simply because, in mathematical form, they would result in a contradiction. A good example is that the laws of thermodynamics (conservation of energy) can't be violated without first violating one of the basic laws of mechanics (e.g. every action has an equal and opposite reaction) that mathematically cause them. So long as the basic observations hold, the conclusions must also hold. Conversely, if an observation shows that the conclusion was violated, it implies that one of the basic rules on which it was based was violated as well. 2. If something is true for all models, then there is a finite mathematical proof for it. Or, conversely, if there is no finite mathematical proof for something, then there is a theoretical model in which it is not true. While this fact may not directly relate to this universe, as the "model in which it is not true" may simply be a theoretical universe that doesn't actually exist, it does give us a way to limit the things that must be absolutely true for all possible universes. All of those must have FINITE proof, that is, the proof can be written using mathematical symbols on a finite number of pages. At the same time, every time mathematicians think they've found a model that could only exist in theory, the universe has shown that if it's mathematically possible, then there's some aspect of the universe in which it physically exists. That's not to say that this is always the case, simply that mathematicians are still in search of the case in which it isn't.
Saar Korren17/12/2014
I think maths does ...
I think maths does exist outside of the human brain. My evidence for this belief is with cicadas. Cicadas have an interesting life-cycle which helps them avoid being eaten by predators. They only pupate at prime number intervals. They do this to avoid syncing their life-cycles with those of their predators, which give birth at regular (more divisible) intervals. In conclusion, evolution has helped the cicadas with a fundamental property of the universe - prime numbers. (In addition, prime numbers appear naturally in the vibrations of crystals.) So, unless you think cicadas (and crystals) are pure figments of the human mind, you should probably accept maths as an inherent property of the universe. "The primes are the atoms of the arithmetic. The hydrogen and oxygen of the world of numbers." - Marcus du Sautoy
Everything Changes03/01/2015
An important ( ...
An important (philosophical) question... My worry: Fictional or real, it is a fact that logic (math) is compatible with the functions in the universe to an immense range of scales that surpass human experience (hence, I believe, evolution is not enough to give a satisfactory answer given that this knowledge became available a few hundred years ago - give or take). An this range is reasonable to expect that will become much wider in the next few hundred years. So, what is the relation of the human brain function to the function of physical phenomena that are describable in terms of math (and many of them lie beyond the everyday experience)? Is Math a Feature of the Universe or a Feature of Human Creation? | Idea Channel | PBS
Konstantinos Anagnostopoulos25/10/2014
Good thing I found ...
Good thing I found this video. I've been telling this to people for a long time. Math is not proven empirically, but logically, it's proven in itself. Therefore it's not science, it's philosophy.
"Jesus, can you ...
"Jesus, can you heal my sick baby?" "Do you believe I am the LORD come to save you from sin?" "Idunno what that means but if it means healing my baby, sure why the hell not!" "Congratulations, your baby is healed! Stop sinning and tell everyone the truth about the universe!" "Thanks Jesus, you my bro!" *fist pound* -Somewhere in the new testament, Holy Bible
I think to say that ...
I think to say that math isn't real is like saying that red isn't real. Red is a construct of the human mind, and our perception of reality filtered through our eyes and brain, but since a more of less objective universe exists outside of us, it's super useful when describing red things to other people. Calculus was a math that was invented by Newton in order to describe the motions of the planets and the moon when standard mathematics didn't work. So I would have to say that math is probably not fundamentally true, but is useful in describing the universe. Newton basically invented the word "red." But for math. There is a problem of infinity being an answer in quantum physics. Since that's a useless answer for equations, or for knowing anything about how the universe works, people say that it can't be the actual answer. But if the answers really are infinity, that means that there are certain things we just can't know until we develop a better system of understanding that can account for the stupid useless answers that the universe gives (maybe). But that new thing could be the next calculus.
Punk Patriot31/12/2014
if i have a ball. i ...
if i have a ball. i have one ball i break it in half then i have 2. Math works. No matter what language u say it in it's the same concepts no mater how you found out about it or figured it out on your own cause it's pretty freakin obvious if ur a functioning intelligent lifeform, it all is the same everywhere. It's universal. If something has one something somewhere across the other side of the universe than that something has one of something and if that something breaks that one of something in half, then there will be 2 of it. Cause math is universal and that's all that matters. Whatever can acknowledge it, can make it. Discussing all this crap he's jerking off to is irrelevant to math and more relevant to human perception.
Ying Chee21/01/2015
Mathematics is real ...
Mathematics is real and exists independent of the human mind. Anyone who thinks otherwise doesn't understand math, and is likely getting confused by the human symbols, terms (names), and definitions that we invent in order to comprehend math.
Dagobah 35921/08/2014
Obviously this is ...
Obviously this is my opinion, but I firmly believe math is a creation of us, humans, to describe ourself, and I say ourself, because we are a part of the universe, we are the universe, but still.. I mean, until us, we humans, came into existence, it was like the universe didn't exist, because there was no one to ponder about it, but the universe as science (and math too) has proven, came into existence a looooong long time before "us", and until very recently, no one cared if electrons, protons, neutrons had this or that spin, mass or electrical charge... no one cared if light was a wave and particule, the knowledge of the existance of black holes, if the big bang happend or not, the universe just was... and even now, the universe just is, and even though math can describe the whole universe it whole randomness, that will still be a creation of us, of the universe, looking itself in the mirror, so yeah... the fact that we can give values to the observations of our subjetive expereinces that can be labelled as "objective! because they truly are, again, that's just us... giving funny names and symblos to abstract parts of the universe 
I would say maths ...
I would say maths as about the same properties as god has. Maths/god is considered to be invisible and immaterial and still everywhere and guiding everything. One can believe in it existence outside the human mind or just view it as some kind of projection we do. Both have deffinitions that rely on things that have to be assumed to be true (axioms or dogmata). What I find interesting is that the line between religious people and atheists are not the same as the one of mathematical realist and mathematical fictionalists.
I believe that ...
I believe that mathematics are a tool that humanity created for easier understanding of the Universe.
Mr. Nerd23/01/2015
How can math not ...
How can math not exist outside our minds? 3+1=4 has always been true, and will never stop being true. Even if space and time never existed, 3+1 would still equal 4. Numbers themselves are the same. 3=3 works the same way, so the value of 3 has always been 3, and would be without us. Am I wrong?
You have overlooked ...
You have overlooked one crucial thing. Science is faith as well, People used to think that the earth is the center of the universe. Most people had faith in it thus it was science. We all think that the Sun is the center now but that may not really be the case. Science may also be a creation of the human mind. In fact, if you think about it, nothing can be really said to be of the universe
Lindle Lee12/01/2015
Why not both. There ...
Why not both. There isn't a solid line between the inside and outside universe. Every feature our brains developed comes from something else, which is just as real. There is something in the invisible world i like to call the 4th dimension, the place where memes live, but it's not math. we just use math to study it.
Sadyh Von Schattig11/01/2015
Math is the mother ...
Math is the mother of all sciences. Except that would be philosophy... No, math is a simply part of our *language*! (it is "universal" in the sense that it exists in every developed language on the globe) But our math system have certain innate flaws. For example we cannot express the exact value of the transcendental numbers. (watch numberphile) In fact we can predict few patterns the digits of Pi. But how is this different from any other scientific concept? We constantly rethink and rework them, and we learn something new! So yes fundamentally I think math is a human creation. But with the possible excetion of natural constants; π (Pi), φ (Phi), e, √2, i, and so on... But as I already stated I math is language, and thus this debate is of semantic nature. Thus not that useful. (But still interesting)
I see math more as ...
I see math more as a meta language that helps us describe physics, geometry and other concepts. Somehow like XML?
As an electrical ...
As an electrical engineer I use a truck load of math, however though mathematical concepts are true and provable math is a human creation to explain quantities and their relation to other quantities especially related to zero. We are still creating different types of math to understand different scientific observations. We know that certain math was "created". Pythagoras the founder of the Pythagorean theorem and Issac Newton who "created" calculus.
Joseph Conard29/01/2015
For me math is just ...
For me math is just a description of things that sourrounds us. A creation, and explanation of features. It's something like a laguage that cannot be interpreted. A tool. Faith has nothing to do with that. You don't think of a laguage in terms of faith, because it is a judge (right or wrong), not an actual event that is real or not... Therefore I don't think it can be regarded as philosophy.
Math in my opinion ...
Math in my opinion is branch of logic. For example when it was first studied it was focused on geometry. 
We define the rules ...
We define the rules of math but we discover truths that arise out of those rules. Not necessarily truths about the universe, but truths about math
Math is simply a ...
Math is simply a very effective way one can model and describe existing things with. Its a tool created by men to help them think. Math just formalizes logic. I think the real question would be: does logic exist?
Johan 't Hart15/01/2015
My take is that, ...
My take is that, math is objective, but it only has any application when it's performed within subjective limits. so, while 2+2=4, objectively, it's up to humans to subjectively or arbitrarily define the space in which two of one object will be grouped together with two more of the same object, define the criteria by which those objects will be considered the same object, and the proceed to put them together. once the spaces have been defined, however, the objective reality of math will dictate that within those parameters, 2 of something plus two more of that thing will add to a total of 4. In reality as it exists with or without human observation, these parameters are also capable of existing, but are as big as the sphere of influence of objects, which is why, for example, we can use math to measure the pull of gravity on a planet with confidence enough that the gravity on a planet light-years away will only have a negligible influence on the results, if any at all. some things are just far enough from the sphere of influence of other things that math as a system can be isolated into these arbitrary areas for the purposes it needs to serve.
I liked this video ...
I liked this video just because of all the Python references... am I a bad person?
Lord Stronghold21/01/2015
It doesn't matter ...
It doesn't matter anyways. Our mathematicians are stumping themselves. Stay tuned guys because this is going to turn very comical. Well at least for those our us who are emotionally removed from the problem. 
Carrina Murphy06/01/2015
Have your mind ...
Have your mind blown. :D
KENNETH UDUT04/11/2014
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