“This sentence is false,” is a sentence to which it’s impossible to assign a truth value; it’s recursive (self-referential) and paradoxical (the assumption of the value “true” causes an evaluation of “false,” and vice-versa).
@@aetysoldier Where? which one? If I can't find it - and even if I could, how could we expect lifeless, souless mathematics to find it? Nothing moves in mathematics.
@@aetysoldier I replied to this. My reply did not appear. "The sentence itself". Which is "the sentence" "itself"? The world is very big, there are many sentences in it. Does mathematics have a map for determing which is "this sentence"? No.
And yet it is true that something can be false! I would say the sentence itself creates a paradox. In the way it is formulated. Let us ask ourselves this question before anything else: is it truly a complete sentence? 🤔
"I am afraid of a day when a computer passes the Turing test , but am infinitely more terrified of the day when a computer intentionally fails one." Love, Cortana
what makes you so sure that even a human will pass the Turing test? If you're terrified of the day when a computer intentionally fails one, you have humans to thank for it, because we all do intentional things, and not always for the right reasons. If a computer fails one, it might have to do with survival, which wouldn't make sense at all, because when a computer can fail one, it's smart enough to make backups just in case something happens.
@@upandatom ok I have no idea why or how “this sentence is false.” is a singularity. If “this sentence is false.” Is true it makes the false sentence untrue thereby making the fake sentence true. So quite literally, the sentence in understood to be undefined or the equivalent of 1 divided by 0.
@@upandatom just tell me how small is Singularity? How small it can get? I am not intrested in whats happening there or what is it made of. Just tell me how small it is and has it anything to do with Plank Length or Plank Radius?
It will actually grow. The rule is that when he lies the nose grows, but this doesn't mean that it cannot grow when he tells the truth. Remember that a implies b doesn't mean that no(a) implies not(b)
Really enjoyed this video, Jade! Your drawings are so charming - they always make us smile even when contemplating the end of human existence "as we know it!"
The concept of "Nothing" represented by the number "0" (zero) did not exist in the beginning. The number "0" (zero) is a relatively recent human innovation in mathematics. But, there has always been "1" (one). The fact that one (1) exists and can generate the position/concept of "nothing" (0) shows that there first exists one (1). Thus, nothing (0) does not truly exist alone: One (1) must first exist that can generate the position/concept of nothing (0). Mathematically, Absolute nothing "could be" expressed as 0 to the power of 0, which can equal 1. "Nothing" IS "Something"; because, it comes from "Something". Moreover, since Nothing (perceived) is not Nothing (actual), then it is possible for Something to come from Nothing (actual). Because, Something (1) is inherently pre-existing within Nothing (actual), hence, 0 to the power of 0 can equal 1. Simply put, Something (1) exists before Nothing (0) can exist. In the beginning, there was Singularity (1).
Just nailed it ! Considering overall presentation,the acts and clarity in content , when I imagine anything better than this I get into Singularity. The sentence near end of video,"This sentence is false." is a simple correct sentence, so its true that it is a sentence but says itself a false ,this means it has to be false in first place .So what sense of true or false can we make out of this sentence.Thus, this situation is an instance of singularity.
It's circular being both false, and not false at the same time. And thank you for your palatable, upbeat and charming explanation of a normally confusing concept :)
"This statement is false." If it is false, then it is true and if it is true then it is false. You are referring to Godel's incompleteness theorem and Russel Paradox, isn't it?
"This sentence is false" is true. Therefore, this sentence is true. But it says that it is false. So sentence=false&true. So the value of the sentence is 0 and 1 at the same time, but maybe... the value can't be determined from our human perspective. Therefore, it could be a Schröndinger's cat scenario.
The sentence is neither, a sentence i neither true or false, a statement is either true or false. when we hear "this sentence is false" we understand "this statement is false" which is wrong, it's not a statement, it's like saying " 53f6egu7h785758bB(*^NTN*^ " is a word... it just isn't. So if you think it's a sentence it's neither true or false, it's like trying to understand if "tree" is true or false... it doesn't make sense. If you think it's a statement, you're now just plain wrong because the definition of a mathematical statement is "A proposition we know *for sure* is *either* true or false" and... well we know for sure it's neither true nor false, therefore it's not a statement.
@@francescosorce5189 Why isn't "53f6egu7h785758bB(*^NTN*^" a word? I mean, it's a single distinct meaningful element, used with others to form a sentence. Seems like a word to me.
@@christopheraplin yeah looking back I could've made a better example, what I meant for *gibberish* isn't a word is "it isn't recognized as one" however the "give it a value" trick doesn't work with "this statement is false"... because it results in a paradox, and since it does it isn't a statement by the fact that you can't determine it's value.
Something being "undefined" in math does _not_ mean "we don't know the answer" it means that there _isn't_ an answer _in the set we're working in._ For exactly, we can say that √(-1) is undefined over the set of real numbers because there is no real number that has the property that squaring it gives negative 1. However, if we instead work over the set of complex numbers, √(-1) is perfectly well defined and is usually denoted by "i." We say "defined" for a reason -- because we literally just defined a new mathematical object into existence. "i" is _defined_ as being √(-1), or, in other words, the number that, when squared, gives -1. Similarly, over the natural numbers, 0-5 is undefined, because the result isn't a natural number, but an integer. Yet, it's perfectly well defined over the integers or any superset of them. Additionally, √(2) is undefined over the rational numbers, but perfectly well defined over the reals. The reason that students don't usually hear the term "undefined" come up until someone asks about division by zero is that just extending the number is fairly easy and obviously useful when going from the naturals to the integers, then to the rationals, and then the reals and even the complex numbers have a lot of applications. It's not actually very difficult to do this to allow division by zero -- we basically just add infinity to the real numbers and specify a few simple axioms. That's called the extended real number line. -- it's just that it's not that very _useful_ to do so. It's more useful to add positive and negative infinity to the set of complex numbers -- that gives a number system referred to as the Reimann sphere (because, viewing it geometrically, it's a sphere), but this isn't someone that would be taught to students in pre algebra or algebra 1, which is usually when students are told that division by zero is undefined.
I love your videos, they have a lot of personality! btw, it was hilarious how you adjusted your glasses every time you wrote something in the blackboard xD
@@upandatom Surely, it's a parody of the all too common school teacher? Chuck Berry wrote and sang it: "The teacher don't know how mean she looks". John Lennon also told us: "I used to get mad at my school (though I can't complain), the teachers who taught me were ghouls". Now I'm really going to show my lack of understanding - I always thought that the singularity in a black hole is a dimensionless point...
Excellent video, I wasn't expecting this, but the way you went round all the definitions of singularity was really interesting. I really like y=1/x (geeky yes I know). It produces (if rotated around the x axis) a solid with a finite volume but an infinite surface area.
Hi Jade! I’m a 25 year old man who’s been for a long time unsure of his life’s ambitions arising from lifelong depression with many poor choices resulting in the way, and such a pretty smart funny physicist as yourself makes me want to follow my ambition and go back to school to work in researching&developing new theoretical understands of reality and find meaning in this world all the more, which has always seems so lacking. Ive always believed if you can find out how the universe around you works you can figure why it does too. And your name is Jade and mine is Wade so I thought that was delightful as well lol. Keep up the wonderful videos the world desperately needs more beautiful female minds such as yours ❤️🌏✨ so in hopes of groundbreaking discoveries and a better life ahead of me I should only have three words in the back of my head I suppose...... “Up and Atom” 😄
OMG, I recently stumbled onto your videos and ever since I've been watching your stuff and YOU're amazing, seriously!!! I've never seen Shannon info/entropy explained so clearly, which we both know is extremely counter-intuitive, ironically so in this age of "information!?" I just had to hit you up an tell you that you're my fav youtube star, watching it right now on the TV, this episode in fact, once you show interest in the most intelligent person to ever live, or in my opinion of it, Mr. von Neumann, I have all his books, and his intellect BLOW me total away, I'm smart, he's like me time Grahams number! :D Great eye BTW, keep making these, i think I got a great one for you to explain esp given Bitcoin and such, have you ever heard of the Kelly Criterion, it extrapolated Shannon idea of Info Entropy into betting/money management. The original paper is called: A New Interpretation of Information Rate by John Kelly, Here ya go, just in case, you're so intelligent, I can't imagine you not having heard of it and I'd love to see it explained, because if anyone can do what you did for Shannon Entropy, you got this! ;)
I enjoyed the video, but @2:12 you say that mathematicians don't know what 1/0 is, but I don't really think this is the case. Mathematicians just choose not to define 1/0 because attempts to define it can lead to inconsistent results. We created division to begin with, it's not like we discovered division out in nature somewhere and we're trying to understand it better.
Well it doesnt seem logical to ask how many zeros are in 1. 0+0+0+0.... Will never budge from zero, so how can it be defined, there must be a proof in there, as even with infinite zeros you do not get any closer to 1. In essence it doesnt really make sense as a question. And also limits dont necessarily explain the real question. I would say that that because limits always are 'approaching' what we really want is an infinitessimal. Not zero, to output infinity. If you reverse the equation you would find a reciprocal of infinity is an infinitessimal.
This was my first video watch of yours and I totally fell in love with your content!!! And I also remember Sabine Hossenfelder once replied to your comment on her channel.
Damn! I must say that the connection you demosntrated between the two couldn't have been done so in any better way! Loved it. Consider me as your new subscriber. Hoping to see more amazing content!
About the dividing by zero thing. You can resolve the paradox by deciding that dividing any number by 0 is basically not dividing that number. And as soon as someone points THAT out, they mention the law of transitive numbers...where multiplying has to be dividing in reverse.. But the thing is, just as you are NOT dividing a number by anything. If you multiply it by 0, you are NOT multiplying it by anything. But that also means we have to put some kind of emphasis on order of numbers and operations, because other wise 6X0=6 and 6X0=0 are both correct. It might be worth differentiating (6)X0 vs. 6X0.. Where (6)X0 is (You have six of something, and you are not multiplying it.) and 6x0 is that you have 6 sets of 0 or 0 sets of 6.. Its confusing, but worth thinking about.
Love the content. I never studied much in physics or higher math. I took basic physics in my associates degree. But lately, I have been interested in quantum physics and quantum theory in general now, thanks to some of your videos. Thanks and good work.
Hey, Jade, I dunno whether you will be taking a look at this comment provided I am writing it so long after you made the vid, but there's a problem I see. When you write xy=constant (1 in this case, as you have assumed. A postive constant), it gives a hyperbolic graph in the 1st coordinate. But when you write (-x)y=(same)constant (1 as well), you won't get a curve in 3rd quadrant, because there both x and y are negative, so they would multiply to give a postive number, thus a curve in 2nd quadrant. (-x)y=constant is same as xy=(-constant) which is a negative result (since we are assuming constant to be positive). You should So I guess there's something wrongy-wrongy in your explanation about 1/0 thing. Btw, great vid there! Admire your enthusiasm, and wonderfully vibrant explanations. Keep it up!
This bugged my mind for a while now and I found the answer in a 4 years old video. I'm subscribed just for a few weeks but I will watch an Uo and Atom video daily from now. They are so informative!
Think about it like this: thresholds, if one of the chessboard squares is a magnitude threshold and you don't have the resources to cross that line, you are screwed. And that one sentence applies to absolutely everything. As Y approaches infinity X approaches 0. What this means is that you need to change planes. To go past approaching infinity in the Y axis you have to move into Z axis. It is threshold. What happens in nature if you don't have the energy requirements to move past a threshold is nature resets you. In modern economics they are called bubbles. A bubble bursts because it cannot sustain itself after reaching its own threshold, and there is a hard reset. However, if you change magnitudes there is also a type of reset and you have to adjust your equation, but essentially it will stay similar to before (at least up to a certain point, you can witness these things as you go the scale of distances 10^-38 to 10^29 Meters): As Z approaches infinity Y approaches 0, but it will be from the perspective of Z. From the perspective of X it is as though Y approached infinity and then went to infinity again. Don't ask me what that would look like in terms of technology or population or whatever, I have no way of knowing such things. Perhaps, it is the difference between nothing and something.
It's a small answer, but it makes a profound experience on us as we start to think of what it truly means and I know this because of what I just wrote in the comments, and as always thanks for watching - vsauce
If a singularity represents an unknown state, then AGI's singularity is "we don't know what'll happen when this occurs". Much like cosmologists have no idea what occurs in a "black hole" (nor what a black hole truly is). It seems in the context of AGI that "singularity" refers to an initial starting state from the results of a previous state.
Thank you Jade for giving me a lot of clarity on Singularity! Same terms can mean different things in different context. There is also the ancient idea of spiritual enlightenment as singularity.
OMG my brain is blowing up. Your math example of a singularity was genius. The number Zero and a black hole comparison was where my brain went boom. Tying all these treads together with AI and the discussion of AI and tech growth was so interesting.
HAWKING-PENROSE THEOREM: No space-time (M, g) can simultaneously satisfy the following conditions: 1. M does not contain closed time curves; 2. All causal geodesic inextensible in M contains a pair of conjugated points; 3. There is a prisoner set in the future, or in the past, S (contained) M
Great job teaming up with Physics Girl. You have a unique sense of style with simple drawings to help me understand some cool topics. Now to your sentence: does this mean that all singularities are paradoxical or exist outside of logic? Because what is infinite gravity? We can't reach infinity...*sighs* why you do this to me sicence..
Dear Up and atom. Would you do a video on how the law of diminishing returns relates to the law of accelerating returns. And just the other day I was wondering about the law of unintended consequences.
I did! I'm planning/hoping to study for a master's degree in Machine Learning next school year, and I must say I enjoy you recent videos regarding algorithms and computers in general... well done!
I understand singularity like dividing a number with 2: 1/2=0.5/2=0.25/2=0.125/2=0.0625... etc. witch graphically explained leads to a lane going more straight but never completely, which is infinite, which is singularity, and I think that the similar effect applies to going into a black hole. Let's take the speed of light per second as "1" and multiplying by 2 so 1x2=2x2=4x2=4x2=8 and so on so as every second passes while we go into a black hole our speed doubles, and that's why light can not escape a black hole, can't even think about us.
Singularity is the source where God is. And God is 1. And from this 1 came the universe. This means that everyone are in reality 1. You are from the singularity experiencing itself. Don't fight or hate others or you'll be fighting and hating yourself.
This is so now my fav RUclips channel! I cannot do maths to save my life lol but I sure love to study/learn about this type of stuff. And a HUGE paradox fanatic ^_^
Thanks for the great explanation. I am still having an issue understanding why it is called singularity. The english word usually means "one of a type". Whereas we are talking about it being infinite or undefined. And it is not that there is just one black hole. There can be many. So why was this word chosen? The opposite is pluarlity - which I think makes more sense in the way that "anything is possible"...finding it difficult to grasp why this word to talk about these phenomena...
zero, as a concept, was introduced in India around 3rd century (as a "void"). before that, everything was defined and there was no singularity, only plurality.
@@nishant1004 As I said, if its true, that you always lie, you would tell the truth, that you always lie, but that would be paradox. But it makes sense, when its false, that you always lie: because that doesnt mean that you always tell the truth, but sometimes you tell the truth and sometimes you lie as now. So its defined.
@@nishant1004 in other words, lets suppose you sometimes tell the truth and sometimes you lie. By saying that you always lie, ok, makes no sense if its true, but there are no logic problems if its a lie
When I studied ecology, I was taught that the population of a new specie in an ecosystem will tend to grow exponentially at first, until it depletes some important resource, then the population will enter a phase where it will follow a sinusoidal (sort of) shape of booms and collapses. I suspect we are merely approaching a plateau that will lead to a collapse... But that collapse will not be extinction: it will be followed by a another growth phase, a boom etc.
I worked as a astronomy/astrophysics news reporter for several years, and it always sucked when the singularities came in a sucked the easyness of explaining wtf the research was about in layman terms. This video did it much better than me! :)
On the subject of singularities. We orbit one and that causes the density of space to compress. So all distances have to be compensated if comparing anything to allow for the distances we are away from large objects. The universe is not the same everywhere. And that brings up the question is the universe expanding? Are galaxies way larger than expected as space is compressed. Is the space in our galaxy contracting as they get larger with collisions so distances for us get smaller and it appears the universe is expanding.
Great video again, love your enthusiasm. But AI & Black Holes is a tenuous link at best. And "this sentence is false"? The sentence, like any sentence, is a string of words so in that sense it's neither true nor false. If we said "this sentence is true" would it change anything?
I really enjoy your channel, and I hope you find my comments interesting rather than repugnant, but again we find the prophecy of scripture written thousands of years ago fitting significantly with your subject. Daniel 12:4 tells us that his book of prophecy was closed to understanding until the time just before the "singularity" of knowledge you speak of. "But thou, O Daniel, shut up the words, and seal the book, even to the time of the end: many shall run to and fro, and knowledge shall be increased." Then life went on pretty much the same for almost three-thousand years... until the cars and airplanes gave the "many" a way to run to and fro, and, as you showed on your timeline, basic flight led to space travel in an exponential curve of knowledge increase. How close are we now to the singularity... that the scripture declares as "the end"? I really enjoy your contemplations!
“This sentence is false” is the paradoxical sentence that Kurt Goedel used to show that math could never be complete. However I think this line of reasoning assumes that true self-reference is possible. If not, then I believe the paradox is resolved by asserting that “this sentence” can never refer to itself but only to another instance of the “sentence.” In other words, saying “this sentence” always refers to a new, separate instance of a sentence that is false, allowing the statement about that sentence to still be true. Just my two cents lol.
“This sentence is false,” is a sentence to which it’s impossible to assign a truth value; it’s recursive (self-referential) and paradoxical (the assumption of the value “true” causes an evaluation of “false,” and vice-versa).
Which is "this" sentence?
@@JohnJones-tx6rt The sentence itself
@@aetysoldier Where? which one? If I can't find it - and even if I could, how could we expect lifeless, souless mathematics to find it? Nothing moves in mathematics.
@@aetysoldier I replied to this. My reply did not appear.
"The sentence itself". Which is "the sentence" "itself"? The world is very big, there are many sentences in it. Does mathematics have a map for determing which is "this sentence"? No.
And yet it is true that something can be false!
I would say the sentence itself creates a paradox.
In the way it is formulated.
Let us ask ourselves this question before anything else: is it truly a complete sentence? 🤔
Singularity is my current relationship status
:(
Nyahaha
Wait... Does that means you got married by yourself?
Aww I was gonna make that joke
At least you get to put "it's complicated".
"I am afraid of a day when a computer passes the Turing test , but am infinitely more terrified of the day when a computer intentionally fails one."
Love, Cortana
Anchanted One but it is interesting to think about...
Awe but if it were truly intelligent would it ever actually pass one in the first place?
5G
@@rorriMMirror 5G A non ionising frequency band, what about it?
what makes you so sure that even a human will pass the Turing test? If you're terrified of the day when a computer intentionally fails one, you have humans to thank for it, because we all do intentional things, and not always for the right reasons. If a computer fails one, it might have to do with survival, which wouldn't make sense at all, because when a computer can fail one, it's smart enough to make backups just in case something happens.
that "adjusting the glasses after every math expression/ graph plot is absolutely hilarious!
If by "hilarious" you mean "insanely hot", then yes, I agree
And kibda hot too.... lol
Insanely hot definitely!
It's annoying
Didn't you notice 6:41?
This sentence is _non-Boolean._
This sentence, much like division by zero, is _undefined._
*This sentence is a singularity*
LOL this made me laugh.
no u
The following question is a singularity:
Will you answer no to my question (yes/no) ?
@@susmitamohapatra9293 So could you also call it a Paradox?
@@PromethorYT yup, in fact 'paradox' might be a more fitting name to my question, given it's unanswerable nature
Taehyung's singularity bought me here....
Just difference is that this is easy to understand than him
I knew that it ain't possible that no one talks about Tae in this comment section
Lol
Damn me too
Sooo true
Oh girl you caught me
@@yveltal3605 Same here!!😅
Love the AI theme lately!
Thanks Toby :)
Do u guys know each other personally ?
@@upandatom do u guys know each other
@@upandatom ok I have no idea why or how “this sentence is false.” is a singularity.
If “this sentence is false.” Is true it makes the false sentence untrue thereby making the fake sentence true. So quite literally, the sentence in understood to be undefined or the equivalent of 1 divided by 0.
@@upandatom just tell me how small is Singularity? How small it can get? I am not intrested in whats happening there or what is it made of. Just tell me how small it is and has it anything to do with Plank Length or Plank Radius?
What would happen if Pinocchio said, “My nose will grow now,”
Holy shit.
It will actually grow. The rule is that when he lies the nose grows, but this doesn't mean that it cannot grow when he tells the truth. Remember that a implies b doesn't mean that no(a) implies not(b)
T or F: Pinocchio wanted to be a real boy with wood or a woiden boy with real wood?
@@69erthx1138 LOOOOOOOOOOOOOOOOOOOOOOOOOOOL
Pinocchio is a thug! Going to Pleasure Island. My 6 year old loves the cartoon
Really enjoyed this video, Jade! Your drawings are so charming - they always make us smile even when contemplating the end of human existence "as we know it!"
You guys are the best :)
Stop doing that please. Don't make me ask in person.
Can u explain me why she use the statement "as we know it" at the end please
The concept of "Nothing" represented by the number "0" (zero) did not exist in the beginning. The number "0" (zero) is a relatively recent human innovation in mathematics. But, there has always been "1" (one). The fact that one (1) exists and can generate the position/concept of "nothing" (0) shows that there first exists one (1). Thus, nothing (0) does not truly exist alone: One (1) must first exist that can generate the position/concept of nothing (0). Mathematically, Absolute nothing "could be" expressed as 0 to the power of 0, which can equal 1. "Nothing" IS "Something"; because, it comes from "Something". Moreover, since Nothing (perceived) is not Nothing (actual), then it is possible for Something to come from Nothing (actual). Because, Something (1) is inherently pre-existing within Nothing (actual), hence, 0 to the power of 0 can equal 1. Simply put, Something (1) exists before Nothing (0) can exist. In the beginning, there was Singularity (1).
Absolute domination of the masses and nothing is going to be private,
What's Singularity?
Me: a song by Kim Taehyung, actually a masterpiece.
Mee too 💜💜🤣🤣I purple you 💜
That's what i thought🤣💜borahae
Lame dude, BTS fans just wanna crap over everything.
@@Kevin-cy2dr uh-
I knew that it ain't possible that no one talks about Tae in this comment section
Lol
Just nailed it ! Considering overall presentation,the acts and clarity in content , when I imagine anything better than this I get into Singularity.
The sentence near end of video,"This sentence is false." is a simple correct sentence, so its true that it is a sentence but says itself a false ,this means it has to be false in first place .So what sense of true or false can we make out of this sentence.Thus, this situation is an instance of singularity.
this was such a nice comment thank you n_n
The way Jade explains complex things is amazing. This channel is precious.
It's circular being both false, and not false at the same time. And thank you for your palatable, upbeat and charming explanation of a normally confusing concept :)
"This statement is false." If it is false, then it is true and if it is true then it is false. You are referring to Godel's incompleteness theorem and Russel Paradox, isn't it?
I knew someone would get it.
"This sentence is false" is true.
Therefore, this sentence is true.
But it says that it is false.
So sentence=false&true.
So the value of the sentence is 0 and 1 at the same time, but maybe... the value can't be determined from our human perspective.
Therefore, it could be a Schröndinger's cat scenario.
Hehehe or it's just English! 🙃 But for reals, totally enjoyed this translation into written terms.
It's in a Superposition!!!
The sentence is neither, a sentence i neither true or false, a statement is either true or false.
when we hear "this sentence is false" we understand "this statement is false" which is wrong, it's not a statement, it's like saying " 53f6egu7h785758bB(*^NTN*^ " is a word... it just isn't.
So if you think it's a sentence it's neither true or false, it's like trying to understand if "tree" is true or false... it doesn't make sense.
If you think it's a statement, you're now just plain wrong because the definition of a mathematical statement is "A proposition we know *for sure* is *either* true or false" and... well we know for sure it's neither true nor false, therefore it's not a statement.
@@francescosorce5189 Why isn't "53f6egu7h785758bB(*^NTN*^" a word? I mean, it's a single distinct meaningful element, used with others to form a sentence.
Seems like a word to me.
@@christopheraplin yeah looking back I could've made a better example, what I meant for *gibberish* isn't a word is "it isn't recognized as one"
however the "give it a value" trick doesn't work with "this statement is false"... because it results in a paradox, and since it does it isn't a statement by the fact that you can't determine it's value.
Something being "undefined" in math does _not_ mean "we don't know the answer" it means that there _isn't_ an answer _in the set we're working in._ For exactly, we can say that √(-1) is undefined over the set of real numbers because there is no real number that has the property that squaring it gives negative 1. However, if we instead work over the set of complex numbers, √(-1) is perfectly well defined and is usually denoted by "i." We say "defined" for a reason -- because we literally just defined a new mathematical object into existence. "i" is _defined_ as being √(-1), or, in other words, the number that, when squared, gives -1. Similarly, over the natural numbers, 0-5 is undefined, because the result isn't a natural number, but an integer. Yet, it's perfectly well defined over the integers or any superset of them.
Additionally, √(2) is undefined over the rational numbers, but perfectly well defined over the reals.
The reason that students don't usually hear the term "undefined" come up until someone asks about division by zero is that just extending the number is fairly easy and obviously useful when going from the naturals to the integers, then to the rationals, and then the reals and even the complex numbers have a lot of applications. It's not actually very difficult to do this to allow division by zero -- we basically just add infinity to the real numbers and specify a few simple axioms. That's called the extended real number line. -- it's just that it's not that very _useful_ to do so. It's more useful to add positive and negative infinity to the set of complex numbers -- that gives a number system referred to as the Reimann sphere (because, viewing it geometrically, it's a sphere), but this isn't someone that would be taught to students in pre algebra or algebra 1, which is usually when students are told that division by zero is undefined.
I love your videos, they have a lot of personality!
btw, it was hilarious how you adjusted your glasses every time you wrote something in the blackboard xD
Hey thank you! And yeah I'm not sure why I did that it seemed like a good idea lol xD
@@upandatom Surely, it's a parody of the all too common school teacher? Chuck Berry wrote and sang it: "The teacher don't know how mean she looks". John Lennon also told us: "I used to get mad at my school (though I can't complain), the teachers who taught me were ghouls".
Now I'm really going to show my lack of understanding - I always thought that the singularity in a black hole is a dimensionless point...
Great explanation! I wish instructors/teachers were as fun as you were when I was on my grade school/hs days
6:08 The king was lucky his opponent thought of a rather unusual chessboard consisting of only 25 squares.
6:21 Then he fucked up by filling a chessboard consisting of 90 squares.
Singularity is dangerous I'm mean look at The Kim Taehyung 💜
I knew that it ain't possible that no one talks about Tae in this comment section
I actually came to see that only
Lol
@@yveltal3605 mai Hu ofc😉😅
Great explanation!
Excellent video, I wasn't expecting this, but the way you went round all the definitions of singularity was really interesting. I really like y=1/x (geeky yes I know). It produces (if rotated around the x axis) a solid with a finite volume but an infinite surface area.
I discovered your channel through Diana’s channel. I’m amazed by your content, you are so charismatic!!! Keep up with the good job!!!
Hi Jade!
I’m a 25 year old man who’s been for a long time unsure of his life’s ambitions arising from lifelong depression with many poor choices resulting in the way, and such a pretty smart funny physicist as yourself makes me want to follow my ambition and go back to school to work in researching&developing new theoretical understands of reality and find meaning in this world all the more, which has always seems so lacking. Ive always believed if you can find out how the universe around you works you can figure why it does too. And your name is Jade and mine is Wade so I thought that was delightful as well lol. Keep up the wonderful videos the world desperately needs more beautiful female minds such as yours ❤️🌏✨ so in hopes of groundbreaking discoveries and a better life ahead of me I should only have three words in the back of my head I suppose...... “Up and Atom” 😄
I just discovered your channel, and I can't tell you how much I love your videos! Amazing job at explaining these complex concepts. Thank you!
Thank you for the video.🌱
Thanks very much Jade,you explained this concept in a very simple way.well done.
Great channel! Subscribed.
right back atcha ;)
Hi JMG! 😁
John Michael Godier Hey it’s that sci fi guy from another channel.
OMG, I recently stumbled onto your videos and ever since I've been watching your stuff and YOU're amazing, seriously!!! I've never seen Shannon info/entropy explained so clearly, which we both know is extremely counter-intuitive, ironically so in this age of "information!?" I just had to hit you up an tell you that you're my fav youtube star, watching it right now on the TV, this episode in fact, once you show interest in the most intelligent person to ever live, or in my opinion of it, Mr. von Neumann, I have all his books, and his intellect BLOW me total away, I'm smart, he's like me time Grahams number! :D Great eye BTW, keep making these, i think I got a great one for you to explain esp given Bitcoin and such, have you ever heard of the Kelly Criterion, it extrapolated Shannon idea of Info Entropy into betting/money management. The original paper is called: A New Interpretation of Information Rate by John Kelly, Here ya go, just in case, you're so intelligent, I can't imagine you not having heard of it and I'd love to see it explained, because if anyone can do what you did for Shannon Entropy, you got this! ;)
Wouldn't let me add Kelly's paper, its free everywhere in pdf format, have a great day Jade, love the name btw!
I enjoyed the video, but @2:12 you say that mathematicians don't know what 1/0 is, but I don't really think this is the case. Mathematicians just choose not to define 1/0 because attempts to define it can lead to inconsistent results. We created division to begin with, it's not like we discovered division out in nature somewhere and we're trying to understand it better.
Exactly
Well it doesnt seem logical to ask how many zeros are in 1. 0+0+0+0.... Will never budge from zero, so how can it be defined, there must be a proof in there, as even with infinite zeros you do not get any closer to 1. In essence it doesnt really make sense as a question. And also limits dont necessarily explain the real question.
I would say that that because limits always are 'approaching' what we really want is an infinitessimal. Not zero, to output infinity. If you reverse the equation you would find a reciprocal of infinity is an infinitessimal.
This was my first video watch of yours and I totally fell in love with your content!!!
And I also remember Sabine Hossenfelder once replied to your comment on her channel.
Damn! I must say that the connection you demosntrated between the two couldn't have been done so in any better way! Loved it. Consider me as your new subscriber. Hoping to see more amazing content!
n_n
About the dividing by zero thing. You can resolve the paradox by deciding that dividing any number by 0 is basically not dividing that number. And as soon as someone points THAT out, they mention the law of transitive numbers...where multiplying has to be dividing in reverse.. But the thing is, just as you are NOT dividing a number by anything. If you multiply it by 0, you are NOT multiplying it by anything. But that also means we have to put some kind of emphasis on order of numbers and operations, because other wise 6X0=6 and 6X0=0 are both correct. It might be worth differentiating (6)X0 vs. 6X0.. Where (6)X0 is (You have six of something, and you are not multiplying it.) and 6x0 is that you have 6 sets of 0 or 0 sets of 6.. Its confusing, but worth thinking about.
Watching this after seeing taehyung singularity mv 😆😆
😂❤️
Omg lol 🤣😂
omg same !!!!!!
Same
Me too!
Love the content. I never studied much in physics or higher math. I took basic physics in my associates degree. But lately, I have been interested in quantum physics and quantum theory in general now, thanks to some of your videos. Thanks and good work.
I've been wondering why these two things were called a "singularity" for a while now. Thanks for sharing. You are an incredible presenter!
aww thank you so much :)
I wish you had been one of my math teachers, back in the day. Passion for knowledge is most of the 'skill' of teaching any subject. I admire you.
"There were six singularities before the formation of universe"
Can you please explain this sentence from Gaurdians of the Galaxy
Hey, Jade, I dunno whether you will be taking a look at this comment provided I am writing it so long after you made the vid, but there's a problem I see. When you write xy=constant (1 in this case, as you have assumed. A postive constant), it gives a hyperbolic graph in the 1st coordinate. But when you write (-x)y=(same)constant (1 as well), you won't get a curve in 3rd quadrant, because there both x and y are negative, so they would multiply to give a postive number, thus a curve in 2nd quadrant. (-x)y=constant is same as xy=(-constant) which is a negative result (since we are assuming constant to be positive). You should So I guess there's something wrongy-wrongy in your explanation about 1/0 thing.
Btw, great vid there! Admire your enthusiasm, and wonderfully vibrant explanations. Keep it up!
Pacey and funny and hella smart. Smashed it.
n_n
This bugged my mind for a while now and I found the answer in a 4 years old video. I'm subscribed just for a few weeks but I will watch an Uo and Atom video daily from now. They are so informative!
You're a great scientific shower, thank you so much for your videos. You make physic look more easy hahaha :) Keeping making this great work.
Think about it like this: thresholds, if one of the chessboard squares is a magnitude threshold and you don't have the resources to cross that line, you are screwed. And that one sentence applies to absolutely everything.
As Y approaches infinity X approaches 0. What this means is that you need to change planes. To go past approaching infinity in the Y axis you have to move into Z axis. It is threshold. What happens in nature if you don't have the energy requirements to move past a threshold is nature resets you. In modern economics they are called bubbles. A bubble bursts because it cannot sustain itself after reaching its own threshold, and there is a hard reset. However, if you change magnitudes there is also a type of reset and you have to adjust your equation, but essentially it will stay similar to before (at least up to a certain point, you can witness these things as you go the scale of distances 10^-38 to 10^29 Meters): As Z approaches infinity Y approaches 0, but it will be from the perspective of Z. From the perspective of X it is as though Y approached infinity and then went to infinity again. Don't ask me what that would look like in terms of technology or population or whatever, I have no way of knowing such things. Perhaps, it is the difference between nothing and something.
It's a small answer, but it makes a profound experience on us as we start to think of what it truly means and I know this because of what I just wrote in the comments, and as always thanks for watching - vsauce
Excellent educational channel on RUclips! Keep it up Jade! Regards from a Computer Science and math teacher ! :-)
BTS Singularity music video brought me here
Lol me to💜
me too.
Me toooo 😂❤❤❤ hello fellow armys
two years later-me too
@@yoongiworld6162 same here
If a singularity represents an unknown state, then AGI's singularity is "we don't know what'll happen when this occurs". Much like cosmologists have no idea what occurs in a "black hole" (nor what a black hole truly is). It seems in the context of AGI that "singularity" refers to an initial starting state from the results of a previous state.
Thank you Jade for giving me a lot of clarity on Singularity! Same terms can mean different things in different context. There is also the ancient idea of spiritual enlightenment as singularity.
OMG my brain is blowing up. Your math example of a singularity was genius. The number Zero and a black hole comparison was where my brain went boom. Tying all these treads together with AI and the discussion of AI and tech growth was so interesting.
Thus episode was extremely mind boggling!
HAWKING-PENROSE THEOREM:
No space-time (M, g) can simultaneously satisfy the following conditions:
1. M does not contain closed time curves;
2. All causal geodesic inextensible in M contains a pair of conjugated points;
3. There is a prisoner set in the future, or in the past, S (contained) M
Great job teaming up with Physics Girl. You have a unique sense of style with simple drawings to help me understand some cool topics.
Now to your sentence: does this mean that all singularities are paradoxical or exist outside of logic? Because what is infinite gravity? We can't reach infinity...*sighs* why you do this to me sicence..
Dear Up and atom.
Would you do a video on how the law of diminishing returns relates to the law of accelerating returns. And just the other day I was wondering about the law of unintended consequences.
your way of explaining is amazing, thanks for such an informative video!
No worries thank you for watching! I hope you learned something :)
I did!
I'm planning/hoping to study for a master's degree in Machine Learning next school year, and I must say I enjoy you recent videos regarding algorithms and computers in general... well done!
Thank you and good luck with your degree! I think that's an excellent choice :)
I understand singularity like dividing a number with 2: 1/2=0.5/2=0.25/2=0.125/2=0.0625... etc. witch graphically explained leads to a lane going more straight but never completely, which is infinite, which is singularity, and I think that the similar effect applies to going into a black hole. Let's take the speed of light per second as "1" and multiplying by 2 so 1x2=2x2=4x2=4x2=8 and so on so as every second passes while we go into a black hole our speed doubles, and that's why light can not escape a black hole, can't even think about us.
Black holes are where God divided by zero 😂😂😂👍👍
Steven Wright is bloody genius and in comedy too.
@@Imru_gamer His friends call him Steve.
//but you can't divide by 0
Singularity is the source where God is. And God is 1. And from this 1 came the universe. This means that everyone are in reality 1. You are from the singularity experiencing itself. Don't fight or hate others or you'll be fighting and hating yourself.
@@Krututu13 but how do you know this. Any evidence for your claims? Please do not cite religious texts as facts.
I enjoyed the way you explained this out! Very sharp...Jade is absolutely stunning with intelligence and beauty. Thx for sharing!
This popped when I searched up Singularity by BTS, I-
I think I've become the smartest student in my school. :')
I knew that it ain't possible that no one talks about Tae in this comment section
I actually came to see that only
Lol
This is so now my fav RUclips channel! I cannot do maths to save my life lol but I sure love to study/learn about this type of stuff. And a HUGE paradox fanatic ^_^
Hmmm, an addendum would be to state that Moore's law is no longer accurate and is slowing down. Apart from that, comprehensive video.
Thank you :)
When you said "a technological event horizon" my heart fluttered. 7:00
i'm more familiar with it as
"what i'm about to say is true, what i just said is a lie"
Thanks for the great explanation. I am still having an issue understanding why it is called singularity. The english word usually means "one of a type". Whereas we are talking about it being infinite or undefined. And it is not that there is just one black hole. There can be many. So why was this word chosen? The opposite is pluarlity - which I think makes more sense in the way that "anything is possible"...finding it difficult to grasp why this word to talk about these phenomena...
AnswerswithJoe was right. Your videos are great. #notificationsquad
thank you and welcome!
You're a genius! This video also reminds me of the Torus as a model to black/white holes
Liked the Indian touch!
zero, as a concept, was introduced in India around 3rd century (as a "void"). before that, everything was defined and there was no singularity, only plurality.
"This sentence is false"
That statement is in a superposition of true and false. OMG you just invented a linguistic quantum computer!!
I always lie.
@@nishant1004 No you dont, you tell the truth sometimes and sometimes you lie, like here. So its no paradoxon
@@ioannisk.7637
So, what do you think in above case?
Am I lying or speaking truth about myself in the above statement.
@@nishant1004 As I said, if its true, that you always lie, you would tell the truth, that you always lie, but that would be paradox. But it makes sense, when its false, that you always lie: because that doesnt mean that you always tell the truth, but sometimes you tell the truth and sometimes you lie as now. So its defined.
@@nishant1004 in other words, lets suppose you sometimes tell the truth and sometimes you lie. By saying that you always lie, ok, makes no sense if its true, but there are no logic problems if its a lie
You are really good at this. Thank you!
I consultet Javascript and it said "This sentence is false" is in fact true.
Well... truthy anyway
Love your video. Well done!
Steven Wright is awesome.
"You can't have everything, where would you put it?"
This is called science with fun. Even the hard topics are illustrated in a fun way. Love from India 🇮🇳
lol love the cheezy acting
n_n I'm trying to get better!
you'll get better. Just watch your videos and keep in mind what you'd like to improve and it'll happen as you make more
I just love your videos!
Is anyone else here because they watched the bts Tae song "Singularity" and wanted to know what it meant? 😂💜💜💜
Mee lol 😂😂
Yess 😂
When I studied ecology, I was taught that the population of a new specie in an ecosystem will tend to grow exponentially at first, until it depletes some important resource, then the population will enter a phase where it will follow a sinusoidal (sort of) shape of booms and collapses. I suspect we are merely approaching a plateau that will lead to a collapse... But that collapse will not be extinction: it will be followed by a another growth phase, a boom etc.
ur freaking amazing, beautiful, smart af and ...to a point where ur talents are a singularity (kinda) for me ^_^
This is a great channel it encourages me so much. Très bien !
I find you one of the best female person in terms of explaining scientific terms ❤️
Love Jade keep up and atom more upwards sharing new videos
Love your videos; they are very engaging.
I want to marry you. ^_^
Too late. A Frenchman beat you to it.
Dude, concentrate on the science.
I worked as a astronomy/astrophysics news reporter for several years, and it always sucked when the singularities came in a sucked the easyness of explaining wtf the research was about in layman terms. This video did it much better than me! :)
On the subject of singularities. We orbit one and that causes the density of space to compress. So all distances have to be compensated if comparing anything to allow for the distances we are away from large objects. The universe is not the same everywhere. And that brings up the question is the universe expanding? Are galaxies way larger than expected as space is compressed. Is the space in our galaxy contracting as they get larger with collisions so distances for us get smaller and it appears the universe is expanding.
This this is the first video I've ever seen of yours and I'm less than 3 minutes through and I'm like this girl is wonderful!
Everyone: Division by zero is undefined.
L'Hôpital: Allow me to introduce myself.
Glad I have come across this video. That is thought provoking. Thanks for the effort !
Amazing !! Good explanation with simple examples
u gotta new subscriber ..congrates ...loved your channel.
You're literally so awesome this channel is amazing
Nice explanation And I am throughly amazed and I am interested to know about , what is gravity , and how it pulls all and why the magnets are not 🤯
4:44 THE SINGULARITY... is literally... EveryOne... being the only one...who is fully... Awake!
I think that's what he meant yeah exactly
I liked the video because of Dvořak as background music. One of my favourite Slavonic Dances.
“This sentence is false” is a Grelling-Nelson-paradox. It’s both X and -X at once. It’s undefined: a singularity.
excellent video and very clear explanation of singularity
Ur explanations are real hardwork 🤠
Love to watch🤓
One word for u AWESOME👩🏫
Great video again, love your enthusiasm. But AI & Black Holes is a tenuous link at best. And "this sentence is false"? The sentence, like any sentence, is a string of words so in that sense it's neither true nor false. If we said "this sentence is true" would it change anything?
I really enjoy your channel, and I hope you find my comments interesting rather than repugnant, but again we find the prophecy of scripture written thousands of years ago fitting significantly with your subject. Daniel 12:4 tells us that his book of prophecy was closed to understanding until the time just before the "singularity" of knowledge you speak of.
"But thou, O Daniel, shut up the words, and seal the book, even to the time of the end: many shall run to and fro, and knowledge shall be increased."
Then life went on pretty much the same for almost three-thousand years... until the cars and airplanes gave the "many" a way to run to and fro, and, as you showed on your timeline, basic flight led to space travel in an exponential curve of knowledge increase.
How close are we now to the singularity... that the scripture declares as "the end"?
I really enjoy your contemplations!
Great video! Loved it😍
“This sentence is false” is the paradoxical sentence that Kurt Goedel used to show that math could never be complete. However I think this line of reasoning assumes that true self-reference is possible. If not, then I believe the paradox is resolved by asserting that “this sentence” can never refer to itself but only to another instance of the “sentence.” In other words, saying “this sentence” always refers to a new, separate instance of a sentence that is false, allowing the statement about that sentence to still be true. Just my two cents lol.