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.
I think numbers are ...
I think numbers are like adjectives that describe real, physical things. Red apples exist just as much as six apples exist, but it wouldn't make sense to say that red exists on its own. And math is more like a verb because any mathematical operation involves a transformation to numbers. Or rather, math transforms the things that numbers describe. Math exists through patterns. For example, when you go to the beach and see waves, all you really see is water. But the pattern the water follows creates a wave. That pattern is math. So, math and numbers cannot exist independent of matter and energy, but they do in fact exist.
Wait, are we sure ...
Wait, are we sure we can see "physics"? We can see objects (kinda) and we describe those objects with equations and principles of physics, but we can't see Newton's first law. We can see objects (kinda) that obey the first law, but we can't see the first law. We can see objects that obey mathematical correlations too so I guess I don't see the difference clearly.
We Are Showboat14/02/2015
"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
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
I believe it falls ...
I believe it falls onto the math realists to explain whether or not that math exists. *They* are the one making a claim that math exists, so *they* have to prove it. (I'm hoping you notice that this is an analogy of another hot topic...)
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?
Another reason math ...
Another reason math can exist without us is because of the very things that make up the universe, they are purely mathematical subatomic particles, they just have quantities for their properties, e.g mass, spin, charge, etc.. Humans couldnt have created math if by doing so will mean it creates all of the very objects that make up the universe, as they are already in the universe long before us, possibly created by the theoretical big bang
Look at the ...
Look at the universe. Look at everything around you. It can all be described by math. Of course we don't know everything yet, but look at how the universe is governed by forces between fundamental particles that can all be neatly described by math. The universe is entirely mathematical, which people have a hard time believing. The thing is that the math that we use in paper is just the laws of the universe being translated to another language. Much like how we can convey 3d perspectives on a 2d sheet of paper. We could create another way of writing math, but it would all be fundamentally the same. Our brains just came up with a way of describing the laws in an other language, but there was a language there to begin with. In nothing else in science you get all this perfect descriptions of what happens in the world. How a simple function like f(x)=x^2 describes the parabolic path on an object moving forward and falling under a gravitational field. It is too accurate to be just human creation. If I could I would bet that if we found intelligent life like us they would have the same concepts in math but in a different way because of how they decided to denote numbers and operators. They could describe sums in a totally different way, not just different symbols, but it would be just a sum. 
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
Ben Bogart26/10/2014
Mathematics is the ...
Mathematics is the language of universe... read this : :-D
Anubhav Balodhi16/02/2015
This video hit me ...
This video hit me like a pop song that I can't get out of my head. I guess I've always thought math was a language used to describe things, but now I'm not so sure. I hope maybe +Artem Kaznatcheev will pick up on this and write something.
Kirk M26/10/2014
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
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
This was all spoken ...
This was all spoken about in metaphors in the movie Lucy. Where they challenged what the human brain makes up compared to what to what it actually knows, aside from what humans make up so that we can understand the Time, and Math.
I believe that ...
I believe that mathematics is a conceptual, logical construct of the human mind. It's analytic in the sense that mathematical equations are true by definition. However, unlike say, Alice in Wonderland, it can effectively be applied to the real world to good effect. I'm not really sure why. Maybe it's like measurement. A physical body has various real properties that can be quantified and measured by humans, although what units of measurement we use are mere human constructs. There are no "inches" or "meters" in the world--those are just the concepts we created to quantify and measure distance or length. One thing I learned from computer programming is the need to abstract real world stuff into data and variables that the computer can work with. A maze program turns a maze into a grid, a 2 dimensional array of 'walls' (ones) and "no-walls" (zeroes). The computer doesn't know what a wall is, but it knows how to deal with ones and zeroes. The player cannot move through 1's (walls), but can move through 0's (no-walls). Perhaps mathematics is not merely an internally consistent logical construct, but a particular type of abstraction of reality, which would explain why it can be applied to reality. 
If math only exists ...
If math only exists inside our brain, why do we DISCOVER it? We can't discover something if we knew it all along...or is that a stupid question?
Philip J. Fry19/02/2015
There is a term ...
There is a term that describes the condition that math works in 10s. I can't think of the term, but the concept pushes me toward the conclusion that math does not exist outside of our heads... at least not as we know it. Does the external world know, after 9, to go back to 1 and tag a 0 on the end (10)? The same applies to 19-20, 99-100, etc. It seems to me that the most thorough understanding of which we are capable thus far is that math has an external existence, AND we, collectively as a specie, have an internal, subjective perception of it--sort of like how we perceive color whereas a rock only absorbs or reflects certain wavelengths of light, I suppose. The external existence of math is not math, but something else, just as the external existence of color is not color. I guess I side with the guys who say math only exists in our heads.
Philipp Wells14/02/2015
Hey PBS Idea ...
Hey PBS Idea Channel: The Alain Badiou quote in this video is presented disastrously out of context. You present Badiou as endorsing what, in the original context (Briefings on Existence, SUNY Press 2006), he is merely describing in order to refute. Badiou does not believe that math is "a fiction of intelligible consistency;" that is his characterization of Aristotlean philosophy of math. Badiou rejects fictionalism in favor of his own, idiosyncratic Platonism which holds that mathematics is ontology itself.
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?
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 
it's just a way for ...
it's just a way for us to make sense of things...that's all it is really. We try and make it something so grand mysterious, but we've created everything we do in math. It's like an easier way of counting things and putting things in numerical perspective.
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