As an American, I love BBC documentaries...been watching them for decades...always have to listen carefully because of the accent😆 and always thorough and engaging
The BBC used to be known for requiring the highest standard of diction in the world of broadcasting in the English language. It still sets the standard, yet you make it sound as if they aren't doing it right.
@@rjlchristie no, I was merely saying that although it is English, a British accent and dialog can sometimes seem like a more foreign language if I try to multi-task while listening 😆
For the average person, this is perhaps the best series ever produced depicting the origins, foundations, and beauty of mathematics. It is truly wonderful.
@Fried Bananas Thank you for sharing your feelings and be aware that there is no need to feel guilty since many young boys fall in love with older women in their 30's who are married and have children.
but where did mathematics really originate? Greece?, Egypt?, China?, Persia?, any other pre-historic civilisation or does the beeb only have enough funds to employ a gcse history teacher whose bored with the national curriculum?
@@richtmason3792 Read "A History of Mathematics" by Merzbach and Boyer...if you get through that book, then you will know more about where "mathematics really" originated than most people!
@@64batsalex As a Brit myself I would quite happily call her a lady - the word is used as a polite way of saying 'woman' - it's the female form of 'gentleman'.
I love this format of science, I don't understand why youtube has taken 2 years to serve it up to me...I'd watch and learn way more if there was more of this kind of content.
perhaps not useful in day to day life, but it does make one think and notice patterns and get one interested in mathematics altogether, added wisdom is always useful imo, even if just on a fun or philosophical level@@rabmcnair4488
Finally. A great educational documentary. But not many views as most UA-camrs are affected with ADD, and rather watch ridiculous 5 minute videos that make them an...expert.
it makes sense that humans discover the already existing laws of maths, as we call it, and invent human systems to describe the discoveries. enjoyed watching. thank you
@@thetessellater9163 To correct your preferences of life, it is "Focus more on social aspects and topic related dues" not, trying to correct irrelevant issues compared to the current topic. Trying to accomplish perfection where no perfection can be accomplished nor is it needed to be flawless. Adapting to different ways of language while still trying to understand and comprehend the complete meaning of things. Good luck, heal well, it will help.
She didn't try to teach any mathematics in this video. just discuss the meta-aspects of it (a little reduced history, philosophical distinction between discovered and invented, and such). very little math was there. However, I'd still really like her to be my teacher. She's enchanting, and sexy, and red-hot interesting
I am thankful because this video has taught me Dodecahedron(s). I have made many of my own dodecahedrons by printing the papers of them, writing on them, cutting the unneeded parts and sticking them together. I am happy of my own dodecahedrons thank you.
Teacher: "Johnny - what's five add five?" Johnny: "Err... that's ten Miss" Teacher: "That's very good Johnny! Johnny: "Very good Miss? It's bloody perfect"
@@TAYLORHWALL - Actually there is a slightly naughtier one:- "Now Johnny, I saw you counting your fingers there! This time, put your hands in your pockets, and add five and five" "Err... Okay Miss" _Shuffles and fidgets for a minute_ ... Err ... That's eleven Miss" ...
26:13 In the background to the right, there's Carl Sagan’s book »COSMOS« in the shelf. Parts of his work here go back to ancient Greece and the Platonists as well. I recommend the TV series »Cosmos«, still a great watch. Cheers!
I wish I could be as enthusiastic about, well, anything as this lady is about math. Maybe cheese. I might be able to work up this amount of enthusiasm over cheese.
I love this lady. She is more than just a presenter and a mathematician; she is a genius-a very good-looking genius. And I could listen to her all day.
@@whirledpeas3477 Dude that is not ok. You can have your taste for sure, but actually saying that is just rude. Also I think she is a beautiful woman and many people think this way.
@@whirledpeas3477 Everyone with a bit sense should realize that you should not just make rude statements about someone's appearance. You can have your opinion, that's fine, but being like this to someone who hasn't done any harm to you is just not ok. But listen: I didn't say that you are not allowed to say that. You just shouldn't do it for obvious reasons.
Holy crap! That gimble system on the camera during that roller coaster ride was amazing! That camera turned and rotated on every axis and I could only just make out the one horizontal rod it was riding on. I'd love to see how that thing is built. Ok, on to the rest of the show.
37:50. It's more likely that we developed the basic addition/subtraction ability as an essential preservation awareness. If we see three enemies approaching and then we see only two it might be useful to be able to deduce that the third one has concealed itself ... perhaps for nefarious reasons.
If you watch her many videos -- she often hides her ring with her other hand. She might be married -- but she is open to options ;) (I wrote this above, but it might fit better under your comment ;) )
yes exactly, this is the problem with the world - everything is either - or.. false choices... what was invented was simply the language describing these relationships
We are all supporting in various different ways from the negative and or positive and their combinations by comparing the binary nature of energy itself.
I have always considered Beethoven to be a fantastic genius of a mathematician, even more so than a musician for he wrote his greatest piece after he was tone deaf. He must have known how the numbers fit together.
He "listened" by perceiving the vibrations through contact instead of using his ears. Maybe he was aware of the mathematical patterns within music as well, either way extremely impressive.
Ontological Mathematics answer's everything in this documentary. There are some great books written on this topic. For example, see the: ''Truth series by Dr. Thomas Stark'' or ''Ontological Mathematics for the Curious: An Introduction to Ontological Thinking by Dr. Cody Newman'' is also a great read. :)
I find it very interesting that Hanna's right brain lights up when she thinks about math. But she *is* a mathematician - she's very very skilled at math, and may have made it "part of her" in a way that allows her to engage her "creativity engines" when working with math. I don't think it's a "given" at all that everyone's right brain would light up in response to math. One of my "high skills" was doing digital logic design back in the late 1980's and 1990's - I was very good at it, and could do large amounts of it "in my head" before I ever started to right anything down. I wonder if my right brain would have lit up when doing that. It could be that becoming expert in some field actually MEANS "getting your right brain in on the game," so that you can just "flow the stuff." BTW, I *absolutely love* Hanna's voice. Just fabulous. :-)
I longingly WISH I had the interest and fascination with math, numbers, and learning that I do now, back when I was in like 7th-9th grade! But I remind myself that it's never to late, and now more than ever there is more access to free educational material online than ever before!
I knew I was finally a computer programmer when I realized there was nothing special about the number system I used. I knew I was finally a mathematician when I realized there was nothing special about the symbols themselves. There is an abstract idea of a pencil separate from the physical object, just as numbers have an essential quality separate from their usage. Mathematical objects just have a lot less entropy than something like a pencil. It doesn't surprise me that we see these patterns in biology since things like the number of petals on a flower are just an expression of the highly compressed information stored on a lot simpler structure called DNA. A lot of time this has to do with nature 'liking' to minimize energy usage. It could also have something to do with building 2-dimensional objects in a 3d world.
This lady asks the question: How do we know these maths work? From my point of view I just look at the buildings behind her. They're still standing because some engineer was able to calculate the loads and stresses that would have to be overcome if the building was to serve the purpose for which it was being constructed.
@11:09 fun fact the half circular divisions in between the segments are actually called involute of circle that is the only shape in geometry that is capable of being stacked inside a circle or a spiral
"I get that there are people who really buy into this other 'realm of reality' and especially if your days and nights are spent thinking about and investigating and researching this realm - that doesn't mean that it's real." - Brian Greene. That's so true in so many different fields, starting with religion and philosophy.
Everything we see and do not see except the creator and the created objects: space and what fills it planets (Earth) stars satellites (moons) nebulas galaxies all forms of life including us (humans and all forms of life on earth) quite literally come from our thoughts, those same thoughts come from a realm called the mind. Our bodies purpose is to protect the brain right to hold the brain? Well we don't at all hold onto with our hands thoughts until they become manifest through the act of creation. Before any of these objects become manifest they are only held in one place the realm of the mind. A very real realm that while appears to be only held by the brain can't be held with the hands. Just because we can't see it or hold it with our hands before the act of creation does not mean it does not exist. Like gravity or oxygen. We can't see either of them yet they do exist gravity holds us down and oxygen allows us to live and without either we would float away or suffocate. And Technically if the object exists in your mind before it exists in this world it is real. As real as the realm it came from. Why or how you might ask? Because before you see it in your hands you first see it in your mind using what some people refer to as the minds eye. -JC The day science begins to study non-physical phenomena, it will make more progress in one decade than in all the previous centuries of its existence -Nikola Tesla
@@archonofthelivinggod7091 Ah, the ever-invisible deity that never shows up, and needs YOU to tell us about him/her/it. "space and what fills it planets (Earth) stars satellites (moons) nebulas galaxies all forms of life including us (humans and all forms of life on earth) quite literally come from our thoughts, those same thoughts come from a realm called the mind" How did the moon create tides and the impact of those tides on the geological/fossil record before there was any mind to conceive of these things? Your post is nothing more than unfalsifiable and meaningless word salad dressed up to seem profound.
@@annoyed707 You know it's funny that you call what I said "word salad" because all you did was state the exact opposite of what I said. The atom was first defined in between 450 and 535 BC by a Greek philosopher named Democritus. The atom wasn't proven to exist until 2000 years later simply because people like you didn't have the instruments to prove Democrituses findings during his time. And that's a fact. Care to tell me how Democritus knew the atom existed before there was an instrument to prove it? Sir Isaac Newton claimed the atom did not exist but did believe a creator exists. Your the exact opposite of him. You believe an atom exists but you don't believe a creator can and/or does exist. It "Annoys" me that you argue against what should be considered common sense. Building blocks don't assemble themselves. You would do well to research what a (self organized) system is. All of the wisest men in history knew what a self organized system is. And they all knew the creator as the self organized system. Self organized meaning: without a creator to create said creator unless it be the one single creator in and of itself. The creator in and of itself created all things including itself without any outside intervention. So as to say the creater was and is now and always will be both; 1 and 0 True and false Real and imaginary Chicken and egg Alpha and omega Male and female Positive and negative Symmetrical and asymmetrical And I'm sure you know where this is going. All things we see do come from human thoughts. Except any and all forms of life and the Earth and space along with whatever fills it. We are... along with all other things both living and not that arent created by human thoughts, thoughts made manifest by the only one authentic binary force know as "God" or the creator. Jesus christ Sir Isaac Newton Nikola Tesla Albert Einstein Buckminster Fuller Earnest Rutherford And the list goes on. Every one of these men knew the very words I'm speaking now. Whether or not their faith was as solid as the philosopher stone. A creator exists whether or not said creator makes an appearance.
@@annoyed707 And to answer your question. The creator has existed since the beginning of time. In fact the creator is responsible for time. So if there is any reason our universe is shaped the way that it is. It's because the creator made it so. I wasn't saying humans created the universe. I said the creator did. I said that any and all human creations came from the realm of the mind. I hope this makes sense. If it was my lack of punctuation that confused you than for that I apologise. I will start addressing proper punctuation more effectively.
Invention vs Discovery brings us back to perspective. If it were invented, there was a possibility of its existence; therefore, if it is invented, it is also discovered.
"Mathematics" - man made or ... Patterns are all around us. They are the relationships that exists in the universe. Math is just the way these patterns / relationships are described. We sense a pattern / relationship, explain it to each other via what we call mathematics. So, "Mathematics" is how we communicate about the patterns and relationships. As we discover patterns and relationships, mathematics is unfolding like words to a poet or linguist, one who fines a new way to express themself! Because of logic, our ability to imagine and our desires: mathematics, like thoughts, may predict unknown patterns and relationships. All this is just to say: the universe doesn't "speak mathematically;" nor are we the creators of mathematics. Instead we discover and create "patterns and relationships." And we explore and explain them in mathematical terms.
@@vicbonett7772 animals in general are curious, and being driven by desire we seek satisfaction. So what is desire driving us to ... The mind naturally sees patterns and relationships. From them we are guided to potential forefillment, i.e. desire satisfied, may be. It could be argued that, we started looking for patterns and relationships because of the search for food, safety and water.
@@mantoniol24 I'd say it has always been there. But the question is, what is "it." I believe that math itself does not really exist. It is simply our way of trying to understand the characteristics and logic of the universe.
@@charlesdacosta2446 It's the mind of the predator to look for patterns and relationships, to find what stands out or doesn't belong, in the search for food...... or prey. In the long hours of searching for prey, humans discovered their fascination for patterns and developed the language of mathematics to describe them, and copy them, for his/her own needs and/or uses.
I cannot recall a time when I disliked math. Studies, yes. Homework, yes. Math, no. I understand that a lot of what Plato said is clearly mystical religiosity. But it does not follow that all math is therefore invented. In fact, I believe that the place Plato spoke of, where mathematical objects exist is simply this: the sentient mind. They exist there in potentiality, and they exist in the universe itself in potentiality, as well. That 'place' is just the realm of the possible. There are, without doubt, mathematical properties built into the fabric and very existence of the universe; the speed of light in a vacuum; the charges of the electron & of the quark; the Planck length, time & mass, etc. These are all, inescapably mathematical, whether you like Plato's ideas or not. What we "discover" is the quantities & relationships in the universe itself; what we "invent" is what to call them & what to do with them. We are like children watching a game they don't understand, which has rules they also don't understand. What we do is figure out the rules. That's what we're discovering: what the rules are, whether they ever happen in objective reality (whatever that is!) is secondary to the fact that they are rules. They are, at least possibilities. That's all it is. No mystery; no religion involved. Now, that wasn't so hard, was it? Rikki Tikki.
Humans invented language in order to communicate ideas and descriptions, I see Maths in the exactly the same way ie a language to better describe the world and the universe.
But that could not be done, unless the "world and universe" were yielding... unless our experiences (pre-described) were expressing so much symmetry and rules.
@@MottiShneor i get that they r expressing so many rules and symmetry and patterns, but I feel like those patterns are there so that the things we see today look the way they are, and constant rates need to be made otherwise how will be see the same thing. Otherwise how can we have multiple trees looking similar, flowers, anything else. There is a particular structure that we see (that is constant) that helps us form everyrhing we see today, created naturally but because of the mathematical side of the human mind we see these patterns too but the way we express it is through mathematical symbols and ideas.
@@MottiShneor almost like in English you have personification. U see something doing something but as humans, we have seen It and have developed language over the years and we can describe it in a human context.
I love the golden ratio,,, Can't wait to see where we will journey to ,,, Please keep your arms in the ride at all times and remain seated and enjoy the ride,, I know I will.
The ancient Egyptians were already aware of Maths way before the Greeks. The Maths are all over the ancient pyramids and other buildings in ancient Egypt. There's a theory that assumes the ancient Egyptians discovered/invented the a feasible and more accurate unit of measure which we now call Metre, which many other measures the derived from. Apparently the Egyptians might have discovered the Metre by measuring the constant size of drops of water from the river Nile. It is very much known that Pythagoras, Plato, Euclid and others did visit ancient Egypt at some point and probably took back (and probably claimed for themselves) a lot of new info back to Greece
Intelligent, conversationalist, beautiful, lovely voice, humorous, wonderfully freckled, and adventurous, the only thing preventing you from being the perfect woman is you're not a redhead... Oh, wait, you actually are one! As I said, literally perfect! Try and convince me otherwise.
Math is the abstract representation of patterns in nature which encompasses both quantities and their relationships. It started with simple observations like two rocks are more than one. Four rocks are twice as many as two. Humans developed language and writing to express these relationships and this evolved over time. I don't see a conflict here. I think people sometimes become overawed by abstractions and mix up semantic arguments for substantive ones.
exactly. I hate when almost everyone speaks of maths (or any other subject) as something abstract that explains to US something, when it's just some way that we have devised to describe and communicate the reality/matter/patterns/etc we see around us. Like at the beginning she says ''we look for math deep inside our brain''. No we don't, we try to understand how the brain works, and we can attempt to describe and communicate our findings by expressing them in different modes. We can do that mathematically (with numbers, equations, etc), literally (with words), chemically (by explaining the chemical processes/etc), and such. It is not that literature or mathematics or chemistry explains to US something, it's the other way around. I hate this angle that 99% of lecturers, videos, books, etc take.
Amen! No one would ever say, "Did you invent your amazing verbal description of a tree, or just discover it?" The very question makes no sense. 3 (and therefore any other quantity!) clearly existed before humans, we just invented the language called math that's so good at describing nature's patterns (because it's a PART of nature's patterns! Way too much is made over Platonism. Rikki Tikki.
Mathematics is a study of patterns by humans. The study is invention, the patterns are discovered. The patterns ‘exist’ whether humans discover them or not. Some, myself included, like MIT physicist Max Tegmark, suspect that these patterns are foundational, as in the foundations of the ‘physical’ world. Because (abstract) patterns exist independently of our physical world, e.g. pi is (IS!) precisely the same whether the world exists or not, patterns therefore provide a possible foundation for all of existence. Some worry that this contradicts religious principles, but it does so no more than other ideas about how the world works. Furthermore, since abstract pattern, our limited human studies not withstanding, is both ultimately infinitely infinite, and “perfect”, characteristics usually attributed to deity, perhaps it is no wonder the Pythagoreans saw it as a religion.
@@tjthreadgood818 you only really have to look at crystals (salt being a common example) to realise there is some fundamental shapes that govern the shapes in the macroscopic world. Most materials are simply too complex to easily recognise that. I don't see them as perfect in the real world though, as they almost always have flaws and too complex shapes. Attributing this to deities, seems to me more a point of lack of understanding at that time, than simply the shapes. Stars (and other natural phenomenon) were seen as deities at one time. Not so much because they were perfect, but inexplicable. I'm actually a little surprised at Pythagoreans (and others) not spotting the difference between the abstract versions made by human hands, and the examples found in nature. Which approximate some shapes, and are governed by them, but almost never are perfect. So, in a way, the greek mathematicians were able to make shapes more perfect than those found in nature, and thus improving upon creation? It seems to be contradictory to their beliefs. All that doesn't take away from that being intriguing though.
And the various collective shrug at the misuse of plurality (it's Math - short for Mathematics) is equally as astonishing. It's not like you're ignorant, you're aware and do it anyway.
@@make.and.believe We (not just the UK, so dial in your ethnocentric neck) prefer maths; mathematics is plural because it covers many disciplines, maths is simply short for that and does not denote a lack of plurality, so why drop the 'S'?
It's amazing that to hear about the most beautiful structures in nature from someone who is clearly one of the most beautiful forms nature has manifested on the visual spectrum.
As a child I love to stare at the sun with my eyes closed and would often go into states of trance and would see mathematical formulas scrolling around in 3d space just like in the movie the Matrix, only this one was in the late 60s, so maybe it is a part of the fabric that has our world is made of.
These programs are not aimed at the Know it All’s for after all they know it all. They are aimed at intelligent ordinary people who are interested to learn more and as such do an excellent job. Thank you BBC for occasionally getting it right.
In the beginning we discovered the relationships between the objects that make up the universe, we invented mathematics as a language to describe these relationships. The very same statement can be applied to music, we discovered music within our minds and hearts, the notes on the pages are the language we invented to describe the music.
Note that Hannah pronounces it "maths", the correct abbreviation of the plural word mathematics. Also, just like maths, physics is plural. [Aussie in BC]
@@PLecN Pants, glasses etc are also only in plural, while Messias only exist in singular. But I think it comes more from the context "the field of mathematics" rather than being a plural form; like when I say I study Genetics, I can't say "Genetic". The field of Physics etc.
I love math as an adult! the tragedy is that the potential interest in math that is in all of us is supressed by math teachers from whom roughly 90% suck.
50:23 >Euler's Formula comes out like 3 times >Logarithm product rules But they're not even the active component in calculating the differential equations of air flow (mildly triggered)
Let's rotate the board! I was waiting for the episode where she explains Numberwang, but she totally avoided the subject. I suppose it's just a BBC show so we cannot expect them to get into the really difficult stuff.
Producer: Hey Dr. Fry, we'd like you to host a BBC documentary about maths Fry: Only if I get to walk through a lot of hilly grassy fields Producer: Deal!
This is really interesting! Thank you for sharing :) ps. For further maths videos, after this series ;) Terry Jones presents a fun video on YT called The Story of 1.
21:50 Small pedantic correction, no the Platonic solids are not the only objects where every side is the same shape. There's the Kepler-Poinsot solids www.software3d.com/Kepler.php Or if we restrict ourselves to convex polyhedra, there's the Catalan solids, www.software3d.com/Archimedean.php duals of the Archimedean solids. Any deltahedron would also suffice, eg the Snub Disphenoid www.software3d.com/J84.php Also the dual of any prism, such as the pentagonal dipyramid www.software3d.com/Dipyramid5.php or the dual of any antiprism, such as the pentagonal deltohedron www.software3d.com/Delto5.php The Platonic solids are the regular convex polyhedra. To be regular, all faces must be the same regular polygon, AND all vertices must be surrounded in the same regular way. That is, the cross-section through any vertex must also give a regular polygon, and all must give the same regular polygon.
Always surprised at how close objective and subjective topics crossover, the further and deeper you delve into science and mathematics the more it begins to be Philosophy and Religion, and vice versa of course.
I know it’s free here, but I support Curiosity Stream. I suggest you do too, it’s a way for more docs like this to be made. They need money to make them you guys! Curiosity Stream is like $20 a year. We need more minds that love docs!
I think the universe is in us as well as us being the universe so mathematics in its pure unwritten form is the universe but by writing out numbers and equations is like deciphering hieroglyphics and translating that into a language we can understand
I agree. Neither invented now discovered. A hunter gatherer or MLB outfielder knows where the projectile is going to land even if neither of them took a calculus course. As with Newton and calculus it would appear to me that maths are innate in the way we think and perceive our environment. So mathematical symbols are a means to articulate what the brain was doing anyway, whether we paid attention to it or not.
@@pfreddyp in a weird way "the universe we live in is a simulation like the matrix" is plausible looking at it purely from a mathematical standpoint because it's all information ones and zeros if you will running calculations from how planets orbit to how our DNA replicates and quantum fluctuations keeps us on our toes lol
Math(s) is there as the superstructure behind our universe. The most fundamental concept of math is "1" or "wholeness" I think, and I think "MATH" singular is more precise the term. I think math, like the Mandelbrot, is contiguous--all connected--one thing. But to describe math as plural is to give math a godlike treatment, as we call God Elohim (a plural Hebrew word used to describe one thing) and that is not so bad, because math is very close to the sacred. How each culture describes, explores and exploits math(s) (or simply enjoys them) says a lot about their pursuit of noble, abstract ideas, which is a function of humanity. Math is beautiful! Great video.
Very well made documentary, but i am bothered by the misinterpretation regarding USING imaginary numbers. There are many many fields of mathematics that use the 2nd dimension of the number line (the up-down part), and that mathematics is the same as the mathematics of imaginary numbers. But the scope is viewed backwards, and should be : " mathematics with 2nd dimension on the number line is the general scope, and mathematics using imaginary numbers is a special case of that scope where the unit for up-down has the special property of i*i=--1". In other words, if mathematics involving imaginary numbers does not use the property i*i=-1, it is mathematics of Two-dimensional space.
Hannah did address what you are talking about. The "two-dimensional space" you refer to is the Cartesian plane. This is distinctly different from the complex plane (with imaginary numbers in one axis). It's not so much that the Cartesian plane is the "general scope" (or usual case, as you stated) and the complex plane is the "special case." They are really describing two different things. You can view the complex plane as the "full" representation of the number line, whereas the Cartesian plane is used to represent relations between variables.
An Indian mathematician Aacharya Hemchandra Samvat 1088-1173 discovered a sequence of an addition ie 1+2+3+... this combination still can be found in the Indian music Tabla based on a number of beats and its graduation in the number of segments or groups. Birth of Fibonacci 1170-1250 his book Liber Abaci, in 1202 hence the info she presenting outdated or copied.
I love it when science and beauty goes hand in hand :) Animals are also aware of numbers. For example, 3 hyenas will not attack one single lioness. But as soon as they are 4 or more hyenas, they will attack a single lioness.. And 1 lioness will not try to take the food away from 4 hyenas, but will easy try to take it away from 3 hyenas.. :) As i am no mathematician i must admit that this video gave me 3 WOW experiences, The Platonic Solids, The history about the number zero and the number i. (The number "i" is completely new to me, so i have to search on it now to learn more, and i blame you if this drives me crazy) ;)
"... why mathematical rules and patterns seem to infiltrate everything around us." We invented mathematics to model the world around us, and then we act surprised that it seems to infiltrate everything around us.
you know you´re a nerd when a woman who you already find attractive on first sight doubles in attractiveness once she tells you that she´s a scientist.... Keep in mind that even at 13:28, it´s still about maths....
2021's Biggest breakthrough in Mathematics. String theorist Brian Greene was looking at this problem for all his life but nothing clicked. Well somebody had to do it, so I stepped up the plate, here it is, hot off the presses : We can pair every positive floating point number using up only about 20% of the integers Algorithm #1 : Convert a float with a zero whole part into an integer 1. Reverse the character sequence representing this float 2. Remove the decimal point to obtain the desired integer Example : Convert the float 0.002743 into its integer equivalent 1. Reverse the float string to obtain 347200.0 2. Remove the decimal point to obtain the integer 3472000 3. Note : All corresponding integers will be terminated by the character “0” Algorithm #2 : Convert a float with a non-zero whole part into an integer 1. Count the number of whole digits or NWD (those preceding the decimal point ) 2. Append a number of “0” digits equal to NWD to the float. 3. Append a digit “1” to the resulting float 4. Remove the decimal point to obtain the desired integer Example : Convert the float 1230.0098 into its integer equivalent 1. Count the number of whole digits : NWD = 4 2. Append NWD = 4 “0” digits to obtain 1230.00980000 3. Append a digit “1” to obtain 1230.009800001 4. Remove the decimal point : this gives us the final integer of 1230009800001 Note : We append a digit “1” to distinguish the integers derived from floats with non-zero whole parts from integers generated by floats with zero whole parts . This can be done for every float [whole.fraction] where whole > 0 !!! AMAZING!!! We just came up with a scheme which pairs each positive float with a positive integer. Note : .
As a woman of science I find it strange how Platon looked at the irregular and imperfect. When he brings up his analogy I ask, but what causes the blurring of these shadows? Those fundamental aspects of the world have to be far more interesting. Than perfect shapes. Platon feels shallow minded when he didn't look at the dept of his ideas.
For me, a thing that is invented depends on who invented it. Take the airplane for example. There were several competing designs for the first airplane. The Wright Flyer happened to be the first successful design, but after that other built airplanes with radically different designs. Today airplanes don't look anything like the first airplane. A discovery however, has nothing to do with who discovers it. It will be the same regardless of who finds it, and it will stay the same even after it is discovered. Mathematics is the same no matter who invents it. An alien living in the Andromeda Galaxy will have "invented" Calculus that is identical to what Newton "invented". They will use rules for Algebra that are identical to the rules we have. It will know that Pi is about (but not quite exactly) 3.14. This to me suggests a discovery, not an invention.
I kinda wonder why it's so hard to think that there are patterns in the real world that we discover and maths is the language we invent to express what we find, at the same time. Of course there is a relationship between what you discover and how you describe it, but that's true for natural languages, too. The words you use influence the way you think about things. 2 + 3 is only 5 if you're thinking in a decimal system. Maybe irrational numbers wouldn't be special, if we didn't. Physical laws are real, reality is real. Once you start discovering natural laws and describe them, you start finding them all over the place, surprise, surprise. And still mathematics are a system to model reality in our heads, just like anything else we understand. Because the only reality is out there. As soon as we start thinking about stuff, what we deal with is a model of reality in our heads. But oh well.
A delightfully imaginative documentary. Maths as a discovery or an invention. As someone who actually likes mathematical ideas and ideals, I decided to give this a try. The question I finally focused on, was the issue of the imaginary numbers. This was the bit of evidence that convinced me that maths are a discovery the we invented a language around. Things such as the Fibonacci scale, actually exist in the natural world without the invention of the language to understand it, therefore, maths exist as a real thing to deal with, but man has a need to understand and prove, and play with things he likes. Enter the general creation of the language of mathematics. Zero/0, for example, is nothing more than a word/symbol, to describe the idea/reality of nothing. Negative numbers are a construct used as an aid to help us understand the universe, such as wave events and the like. I'm not sure, but I have a difficult time understanding why this isn't apparent to anyone who looks at mathematics. I am not a mathematician, just someone who enjoys and loves to play with math.
As an American, I love BBC documentaries...been watching them for decades...always have to listen carefully because of the accent😆 and always thorough and engaging
The BBC used to be known for requiring the highest standard of diction in the world of broadcasting in the English language.
It still sets the standard, yet you make it sound as if they aren't doing it right.
@@rjlchristie no, I was merely saying that although it is English, a British accent and dialog can sometimes seem like a more foreign language if I try to multi-task while listening 😆
For the average person, this is perhaps the best series ever produced depicting the origins, foundations, and beauty of mathematics. It is truly wonderful.
For someone more than average mathematically...it's boring.
@Fried Bananas Thank you for sharing your feelings and be aware that there is no need to feel guilty since many young boys fall in love with older women in their 30's who are married and have children.
but where did mathematics really originate? Greece?, Egypt?, China?, Persia?, any other pre-historic civilisation or does the beeb only have enough funds to employ a gcse history teacher whose bored with the national curriculum?
@@richtmason3792 Read "A History of Mathematics" by Merzbach and Boyer...if you get through that book, then you will know more about where "mathematics really" originated than most people!
Not as boring as you im sure. @@Veggamattic
Utterly brilliant . I could listen to this lady all day.
That's Dr Hannah Fry. She has more videos on youtube for Numberphile, Ted Talks and The Royal Institution
She is not a lady, which is a title - like lord - just a woman.
@@thetessellater9163 a man's lady
It's an american thing
@@64batsalex As a Brit myself I would quite happily call her a lady - the word is used as a polite way of saying 'woman' - it's the female form of 'gentleman'.
I love this format of science, I don't understand why youtube has taken 2 years to serve it up to me...I'd watch and learn way more if there was more of this kind of content.
WHat have you actually learned that is useful? Don't get me wrong I found the programme very interesting as well.
perhaps not useful in day to day life, but it does make one think and notice patterns and get one interested in mathematics altogether, added wisdom is always useful imo, even if just on a fun or philosophical level@@rabmcnair4488
It took 6 years for me the have this in my feed 😮
This is such a lovely introduction to the philosophy of maths!
OMG, three hours of Hannah Fry's voice; excuse me while I quietly melt.
Finally. A great educational documentary. But not many views as most UA-camrs are affected with ADD, and rather watch ridiculous 5 minute videos that make them an...expert.
I have ADHD lol
. I bet your an apostrophe.
it makes sense that humans discover the already existing laws of maths, as we call it, and invent human systems to describe the discoveries. enjoyed watching. thank you
I wish I could of had her teaching in my math class, she makes it understandable. Enjoyable.
Daniel, to correct your grammar, it is "...could have.." not "..could of.." if it helps.
@@thetessellater9163 To correct your preferences of life, it is "Focus more on social aspects and topic related dues" not, trying to correct irrelevant issues compared to the current topic. Trying to accomplish perfection where no perfection can be accomplished nor is it needed to be flawless. Adapting to different ways of language while still trying to understand and comprehend the complete meaning of things.
Good luck, heal well, it will help.
She didn't try to teach any mathematics in this video. just discuss the meta-aspects of it (a little reduced history, philosophical distinction between discovered and invented, and such). very little math was there. However, I'd still really like her to be my teacher. She's enchanting, and sexy, and red-hot interesting
She must be loved at restaurants. (9:00)
Waitress: "That redhead is writing on the windows again."
Haha!
"Tell 'er to write the specials when she's done her 'thing'; red and green only! "..
dont worry it can be easily wiped... whiteboard markers on glass can be easily wiped with even hands and leave no marks
@@vinitvsankhe You do realize that it was meant to be funny, right?
Henry Tjernlund he's a terrible heckler!!
@@jimknox8720 I sure am.
Wow, that smart woman, that red hair, that skin like marble and the eyes to sink in ... I fell in love...
you forgot her beautiful voice
I can dig it. You should check out her colleague (sorta), Dr. Holly Kreiger. She's another lovely redhead math whiz with beautiful skin.
This is a wonderful documentary that allows and average person to understand about the vastness of Mathematics
I could watch and listen to Hannah Fry talk about anything. Even math, especially math.
Maths
Why do Americans abbreviate MATHEMATICS to MATH, and not MATHS ??
@@thetessellater9163 Because it's one shorter.
I am thankful because this video has taught me Dodecahedron(s). I have made many of my own dodecahedrons by printing the papers of them, writing on them, cutting the unneeded parts and sticking them together. I am happy of my own dodecahedrons thank you.
There's something special about the combination of math, freckles and British accents
It's Hannah Fry!
I couldn't say it better
and red hair...
way to make it creepy!
She's smokin' hot.
Teacher: "Johnny - what's five add five?"
Johnny: "Err... that's ten Miss"
Teacher: "That's very good Johnny!
Johnny: "Very good Miss? It's bloody perfect"
WTF XD
i roared at this! you just made my day!
@@TAYLORHWALL :0)
@@TAYLORHWALL - Actually there is a slightly naughtier one:- "Now Johnny, I saw you counting your fingers there! This time, put your hands in your pockets, and add five and five"
"Err... Okay Miss" _Shuffles and fidgets for a minute_ ... Err ... That's eleven Miss" ...
@@glutinousmaximus hahahahahahahaha!
I think I can get my 12 year old son interested in Math this way.
and girls.
I think you can get a 100 year dead eunuch interested in math this way.
@@lazaruslong697 That would be Lazarus without the long...
GOD Will Guide
26:13 In the background to the right, there's Carl Sagan’s book »COSMOS« in the shelf. Parts of his work here go back to ancient Greece and the Platonists as well. I recommend the TV series »Cosmos«, still a great watch. Cheers!
I wish I could be as enthusiastic about, well, anything as this lady is about math. Maybe cheese. I might be able to work up this amount of enthusiasm over cheese.
maths
@@bettyswollocks1670 Brits call it maths, Americans call it math. Look it up. There's a whole hubbub about it online and even on YT.
@@riggs20 never fails
Something about a sketch set in a cheese shop...
😅😅 Hannah Fry goes *crazy* over maths in all her interviews, podcasts etc especially fluid dynamics which she's a professor of
I love this lady. She is more than just a presenter and a mathematician; she is a genius-a very good-looking genius. And I could listen to her all day.
I just love her voice. Could listen to her all day.
Much better than looking at her 🤮
@@whirledpeas3477 Dude that is not ok. You can have your taste for sure, but actually saying that is just rude.
Also I think she is a beautiful woman and many people think this way.
@@digitalesklassenzimmer7278 so you decide what is okay, you must love North Korea 🇰🇵?
@@whirledpeas3477 Everyone with a bit sense should realize that you should not just make rude statements about someone's appearance. You can have your opinion, that's fine, but being like this to someone who hasn't done any harm to you is just not ok.
But listen: I didn't say that you are not allowed to say that. You just shouldn't do it for obvious reasons.
@@whirledpeas3477 - You're nuts. She is lovely.
Holy crap! That gimble system on the camera during that roller coaster ride was amazing! That camera turned and rotated on every axis and I could only just make out the one horizontal rod it was riding on. I'd love to see how that thing is built.
Ok, on to the rest of the show.
I think that might be a 360 degree camera and the rotation is digital, possibly edited that way after the fact.
She is so beautiful and intelligent. Perfect combo!
and redhead!!
Inna-lect and beauty, a dangerous combination, last thing you want is a woman with a mind of her own, "these are words to live by" peace out bros.
You ever wanna go back and delete a comment you made while drunk? Yes, that's what happened here.
@Mr Scratch She has some good qualities. she looks good.
she can make a man horny, you kind of just want her.
37:50. It's more likely that we developed the basic addition/subtraction ability as an essential preservation awareness. If we see three enemies approaching and then we see only two it might be useful to be able to deduce that the third one has concealed itself ... perhaps for nefarious reasons.
I'm definitely in love with Hannah Fry
Yup. Me too
Haha I was opening my pringles and this comment caught my eye ...
I actually laughed pretty hard
Was funny that pal
If you watch her many videos -- she often hides her ring with her other hand. She might be married -- but she is open to options ;)
(I wrote this above, but it might fit better under your comment ;) )
@@octaviusvanzandt3695 simp
I was going to say that I wish I had a maths teacher like Hannah Fry, but then I realized that I would never pay any attention to the actual maths.
I came from the up and atom video.
Nice and entertaining documentary. 😀
They didn't do her justice with the thumbnail
Can we take a moment to recognize the AMAZING CAMERA WORK?!?!
Relationships are discovered. Notation, algorithms and techniques are invented.
yes exactly, this is the problem with the world - everything is either - or.. false choices... what was invented was simply the language describing these relationships
We are all supporting in various different ways from the negative and or positive and their combinations by comparing the binary nature of energy itself.
@Roger Loquitur The number it self always, only when the symbol and definition of the symbol is manipulated.
I have always considered Beethoven to be a fantastic genius of a mathematician, even more so than a musician for he wrote his greatest piece after he was tone deaf. He must have known how the numbers fit together.
He "listened" by perceiving the vibrations through contact instead of using his ears. Maybe he was aware of the mathematical patterns within music as well, either way extremely impressive.
Just now realised before Rene Descartes we didn't know we can definitely tell the location of point with coordinates on x-axis and y axis
Beautiful presentation. Just wow. Seen all the series. Wonderful presentation. Mine is 1000th comment. 999 also done by me.
Ontological Mathematics answer's everything in this documentary. There are some great books written on this topic. For example, see the: ''Truth series by Dr. Thomas Stark'' or ''Ontological Mathematics for the Curious: An Introduction to Ontological Thinking by Dr. Cody Newman'' is also a great read. :)
Or Why Beauty Is Truth: A History of Symmetry by Ian Stewart.
Are you both saying the beautiful host is misleading her followers? Maybe?
@@nextchannelnext8890 No, The books I suggested explain everything where she talks about in this documentary.
@@vivablasfemia7604 hmmm ... brb
I have watched BBC i didcnot see this six years ago although thank goodness uploaded on UA-cam
I find it very interesting that Hanna's right brain lights up when she thinks about math. But she *is* a mathematician - she's very very skilled at math, and may have made it "part of her" in a way that allows her to engage her "creativity engines" when working with math. I don't think it's a "given" at all that everyone's right brain would light up in response to math. One of my "high skills" was doing digital logic design back in the late 1980's and 1990's - I was very good at it, and could do large amounts of it "in my head" before I ever started to right anything down. I wonder if my right brain would have lit up when doing that. It could be that becoming expert in some field actually MEANS "getting your right brain in on the game," so that you can just "flow the stuff."
BTW, I *absolutely love* Hanna's voice. Just fabulous. :-)
have you ever questioned what "lights up" actually means - we can measure something but have no idea how it relates to actual thinking
I mean in the video they did mention that it's the same for most people on the experiment right?
I longingly WISH I had the interest and fascination with math, numbers, and learning that I do now, back when I was in like 7th-9th grade! But I remind myself that it's never to late, and now more than ever there is more access to free educational material online than ever before!
I knew I was finally a computer programmer when I realized there was nothing special about the number system I used. I knew I was finally a mathematician when I realized there was nothing special about the symbols themselves. There is an abstract idea of a pencil separate from the physical object, just as numbers have an essential quality separate from their usage. Mathematical objects just have a lot less entropy than something like a pencil. It doesn't surprise me that we see these patterns in biology since things like the number of petals on a flower are just an expression of the highly compressed information stored on a lot simpler structure called DNA. A lot of time this has to do with nature 'liking' to minimize energy usage. It could also have something to do with building 2-dimensional objects in a 3d world.
I wonder the detailed stand point about Math & Fibonacci numbers series.
That was really excellent, Dr. Fry.
This lady asks the question: How do we know these maths work? From my point of view I just look at the buildings behind her. They're still standing because some engineer was able to calculate the loads and stresses that would have to be overcome if the building was to serve the purpose for which it was being constructed.
Watching this girl cut up a ball painted to look like Earth to explain Riemann sums was the start of one of the best mushroom trips ever! Sooo nice
@11:09 fun fact the half circular divisions in between the segments are actually called involute of circle that is the only shape in geometry that is capable of being stacked inside a circle or a spiral
"I get that there are people who really buy into this other 'realm of reality' and especially if your days and nights are spent thinking about and investigating and researching this realm - that doesn't mean that it's real." - Brian Greene.
That's so true in so many different fields, starting with religion and philosophy.
Everything we see and do not see except the creator and the created objects: space and what fills it planets (Earth) stars satellites (moons) nebulas galaxies all forms of life including us (humans and all forms of life on earth) quite literally come from our thoughts, those same thoughts come from a realm called the mind. Our bodies purpose is to protect the brain right to hold the brain? Well we don't at all hold onto with our hands thoughts until they become manifest through the act of creation. Before any of these objects become manifest they are only held in one place the realm of the mind. A very real realm that while appears to be only held by the brain can't be held with the hands.
Just because we can't see it or hold it with our hands before the act of creation does not mean it does not exist. Like gravity or oxygen. We can't see either of them yet they do exist gravity holds us down and oxygen allows us to live and without either we would float away or suffocate. And Technically if the object exists in your mind before it exists in this world it is real. As real as the realm it came from. Why or how you might ask? Because before you see it in your hands you first see it in your mind using what some people refer to as the minds eye. -JC
The day science begins to study non-physical phenomena, it will make more progress in one decade than in all the previous centuries of its existence
-Nikola Tesla
@@archonofthelivinggod7091 Ah, the ever-invisible deity that never shows up, and needs YOU to tell us about him/her/it.
"space and what fills it planets (Earth) stars satellites (moons) nebulas galaxies all forms of life including us (humans and all forms of life on earth) quite literally come from our thoughts, those same thoughts come from a realm called the mind"
How did the moon create tides and the impact of those tides on the geological/fossil record before there was any mind to conceive of these things? Your post is nothing more than unfalsifiable and meaningless word salad dressed up to seem profound.
@@annoyed707 You know it's funny that you call what I said "word salad" because all you did was state the exact opposite of what I said. The atom was first defined in between 450 and 535 BC by a Greek philosopher named Democritus. The atom wasn't proven to exist until 2000 years later simply because people like you didn't have the instruments to prove Democrituses findings during his time. And that's a fact. Care to tell me how Democritus knew the atom existed before there was an instrument to prove it? Sir Isaac Newton claimed the atom did not exist but did believe a creator exists. Your the exact opposite of him. You believe an atom exists but you don't believe a creator can and/or does exist. It "Annoys" me that you argue against what should be considered common sense. Building blocks don't assemble themselves. You would do well to research what a (self organized) system is. All of the wisest men in history knew what a self organized system is. And they all knew the creator as the self organized system. Self organized meaning: without a creator to create said creator unless it be the one single creator in and of itself. The creator in and of itself created all things including itself without any outside intervention. So as to say the creater was and is now and always will be both;
1 and 0
True and false
Real and imaginary
Chicken and egg
Alpha and omega
Male and female
Positive and negative
Symmetrical and asymmetrical
And I'm sure you know where this is going. All things we see do come from human thoughts. Except any and all forms of life and the Earth and space along with whatever fills it. We are... along with all other things both living and not that arent created by human thoughts, thoughts made manifest by the only one authentic binary force know as "God" or the creator.
Jesus christ
Sir Isaac Newton
Nikola Tesla
Albert Einstein
Buckminster Fuller
Earnest Rutherford
And the list goes on. Every one of these men knew the very words I'm speaking now. Whether or not their faith was as solid as the philosopher stone. A creator exists whether or not said creator makes an appearance.
@@annoyed707 And to answer your question. The creator has existed since the beginning of time. In fact the creator is responsible for time. So if there is any reason our universe is shaped the way that it is. It's because the creator made it so. I wasn't saying humans created the universe. I said the creator did. I said that any and all human creations came from the realm of the mind. I hope this makes sense. If it was my lack of punctuation that confused you than for that I apologise. I will start addressing proper punctuation more effectively.
Invention vs Discovery brings us back to perspective. If it were invented, there was a possibility of its existence; therefore, if it is invented, it is also discovered.
originalgospel.blog
"Mathematics" - man made or ...
Patterns are all around us. They are the relationships that exists in the universe. Math is just the way these patterns / relationships are described.
We sense a pattern / relationship, explain it to each other via what we call mathematics.
So, "Mathematics" is how we communicate about the patterns and relationships.
As we discover patterns and relationships, mathematics is unfolding like words to a poet or linguist, one who fines a new way to express themself!
Because of logic, our ability to imagine and our desires: mathematics, like thoughts, may predict unknown patterns and relationships.
All this is just to say: the universe doesn't "speak mathematically;" nor are we the creators of mathematics. Instead we discover and create "patterns and relationships." And we explore and explain them in mathematical terms.
Why did we start looking at patterns and relationships ?
@@vicbonett7772 animals in general are curious, and being driven by desire we seek satisfaction. So what is desire driving us to ... The mind naturally sees patterns and relationships. From them we are guided to potential forefillment, i.e. desire satisfied, may be.
It could be argued that, we started looking for patterns and relationships because of the search for food, safety and water.
The question is whether we created math or has math always been there and we are discovering it.
@@mantoniol24 I'd say it has always been there. But the question is, what is "it." I believe that math itself does not really exist. It is simply our way of trying to understand the characteristics and logic of the universe.
@@charlesdacosta2446 It's the mind of the predator to look for patterns and relationships, to find what stands out or doesn't belong, in the search for food...... or prey. In the long hours of searching for prey, humans discovered their fascination for patterns and developed the language of mathematics to describe them, and copy them, for his/her own needs and/or uses.
Funny choice of thumbnail image...
I cannot recall a time when I disliked math. Studies, yes. Homework, yes. Math, no. I understand that a lot of what Plato said is clearly mystical religiosity. But it does not follow that all math is therefore invented. In fact, I believe that the place Plato spoke of, where mathematical objects exist is simply this: the sentient mind. They exist there in potentiality, and they exist in the universe itself in potentiality, as well. That 'place' is just the realm of the possible. There are, without doubt, mathematical properties built into the fabric and very existence of the universe; the speed of light in a vacuum; the charges of the electron & of the quark; the Planck length, time & mass, etc. These are all, inescapably mathematical, whether you like Plato's ideas or not. What we "discover" is the quantities & relationships in the universe itself; what we "invent" is what to call them & what to do with them. We are like children watching a game they don't understand, which has rules they also don't understand. What we do is figure out the rules. That's what we're discovering: what the rules are, whether they ever happen in objective reality (whatever that is!) is secondary to the fact that they are rules. They are, at least possibilities. That's all it is. No mystery; no religion involved. Now, that wasn't so hard, was it? Rikki Tikki.
Eloquently said, sir.
Who made the rules?
Humans invented language in order to communicate ideas and descriptions, I see Maths in the exactly the same way ie a language to better describe the world and the universe.
And to leave messages in the construction of the buildings
But that could not be done, unless the "world and universe" were yielding... unless our experiences (pre-described) were expressing so much symmetry and rules.
@@MottiShneor i get that they r expressing so many rules and symmetry and patterns, but I feel like those patterns are there so that the things we see today look the way they are, and constant rates need to be made otherwise how will be see the same thing. Otherwise how can we have multiple trees looking similar, flowers, anything else. There is a particular structure that we see (that is constant) that helps us form everyrhing we see today, created naturally but because of the mathematical side of the human mind we see these patterns too but the way we express it is through mathematical symbols and ideas.
@@MottiShneor almost like in English you have personification. U see something doing something but as humans, we have seen It and have developed language over the years and we can describe it in a human context.
1 minute 48 seconds and I am in love with this woman. Gorgeous redhead who is a maths genius... can't beat that in my book
I love the golden ratio,,, Can't wait to see where we will journey to ,,, Please keep your arms in the ride at all times and remain seated and enjoy the ride,, I know I will.
The ancient Egyptians were already aware of Maths way before the Greeks. The Maths are all over the ancient pyramids and other buildings in ancient Egypt. There's a theory that assumes the ancient Egyptians discovered/invented the a feasible and more accurate unit of measure which we now call Metre, which many other measures the derived from. Apparently the Egyptians might have discovered the Metre by measuring the constant size of drops of water from the river Nile. It is very much known that Pythagoras, Plato, Euclid and others did visit ancient Egypt at some point and probably took back (and probably claimed for themselves) a lot of new info back to Greece
If you like math, follow us on instagram.
instagram.com/raremathbooks/
Intelligent, conversationalist, beautiful, lovely voice, humorous, wonderfully freckled, and adventurous, the only thing preventing you from being the perfect woman is you're not a redhead... Oh, wait, you actually are one! As I said, literally perfect! Try and convince me otherwise.
Math is the abstract representation of patterns in nature which encompasses both quantities and their relationships. It started with simple observations like two rocks are more than one. Four rocks are twice as many as two. Humans developed language and writing to express these relationships and this evolved over time. I don't see a conflict here. I think people sometimes become overawed by abstractions and mix up semantic arguments for substantive ones.
exactly. I hate when almost everyone speaks of maths (or any other subject) as something abstract that explains to US something, when it's just some way that we have devised to describe and communicate the reality/matter/patterns/etc we see around us. Like at the beginning she says ''we look for math deep inside our brain''. No we don't, we try to understand how the brain works, and we can attempt to describe and communicate our findings by expressing them in different modes. We can do that mathematically (with numbers, equations, etc), literally (with words), chemically (by explaining the chemical processes/etc), and such. It is not that literature or mathematics or chemistry explains to US something, it's the other way around. I hate this angle that 99% of lecturers, videos, books, etc take.
Amen! No one would ever say, "Did you invent your amazing verbal description of a tree, or just discover it?" The very question makes no sense. 3 (and therefore any other quantity!) clearly existed before humans, we just invented the language called math that's so good at describing nature's patterns (because it's a PART of nature's patterns! Way too much is made over Platonism. Rikki Tikki.
Mathematics is a study of patterns by humans. The study is invention, the patterns are discovered. The patterns ‘exist’ whether humans discover them or not. Some, myself included, like MIT physicist Max Tegmark, suspect that these patterns are foundational, as in the foundations of the ‘physical’ world. Because (abstract) patterns exist independently of our physical world, e.g. pi is (IS!) precisely the same whether the world exists or not, patterns therefore provide a possible foundation for all of existence. Some worry that this contradicts religious principles, but it does so no more than other ideas about how the world works. Furthermore, since abstract pattern, our limited human studies not withstanding, is both ultimately infinitely infinite, and “perfect”, characteristics usually attributed to deity, perhaps it is no wonder the Pythagoreans saw it as a religion.
@@tjthreadgood818 yes to everything you said.
@@tjthreadgood818 you only really have to look at crystals (salt being a common example) to realise there is some fundamental shapes that govern the shapes in the macroscopic world. Most materials are simply too complex to easily recognise that. I don't see them as perfect in the real world though, as they almost always have flaws and too complex shapes. Attributing this to deities, seems to me more a point of lack of understanding at that time, than simply the shapes. Stars (and other natural phenomenon) were seen as deities at one time. Not so much because they were perfect, but inexplicable. I'm actually a little surprised at Pythagoreans (and others) not spotting the difference between the abstract versions made by human hands, and the examples found in nature. Which approximate some shapes, and are governed by them, but almost never are perfect. So, in a way, the greek mathematicians were able to make shapes more perfect than those found in nature, and thus improving upon creation? It seems to be contradictory to their beliefs.
All that doesn't take away from that being intriguing though.
thank you so much such a brilliant show !
The seething hatred in the comments (variously for women, maths, and/or the BBC) is really quite astonishing.
And the various collective shrug at the misuse of plurality (it's Math - short for Mathematics) is equally as astonishing. It's not like you're ignorant, you're aware and do it anyway.
That (the below for some reason UA-cam?) being said, the BBC and Women are awesome things.
It's like all the crazy people on UA-cam suddenly decided to comment on this video.
@@make.and.believe Wrong, the Commonwealth Nations such as UK, NZ, Australia, South Africa all say "Maths".
@@make.and.believe We (not just the UK, so dial in your ethnocentric neck) prefer maths; mathematics is plural because it covers many disciplines, maths is simply short for that and does not denote a lack of plurality, so why drop the 'S'?
Mvgroup , now that's a name I haven't come across in years!
It's amazing that to hear about the most beautiful structures in nature from someone who is clearly one of the most beautiful forms nature has manifested on the visual spectrum.
And sound spectrum.
As a child I love to stare at the sun with my eyes closed and would often go into states of trance and would see mathematical formulas scrolling around in 3d space just like in the movie the Matrix, only this one was in the late 60s, so maybe it is a part of the fabric that has our world is made of.
I just got sent here from my math teacher 💀
Omfg mine did half an hour ago
same!!! 8th?
@@aggieledwell you are in fact, in my math class
These programs are not aimed at the Know it All’s for after all they know it all. They are aimed at intelligent ordinary people who are interested to learn more and as such do an excellent job. Thank you BBC for occasionally getting it right.
02:14 - So Agent Mulder retired and became a mathematician. Makes sense.
Lmao!
In the beginning we discovered the relationships between the objects that make up the universe, we invented mathematics as a language to describe these relationships. The very same statement can be applied to music, we discovered music within our minds and hearts, the notes on the pages are the language we invented to describe the music.
Oh Hannah, model like beauty, genius level intelligence and so far out of my league she might as well be on another planet
Oh she could only have like 5 or 6 kids with those hips.
@@jason1440 Looks like someone is trying to multiply.
@Peter Lustig yes, narrating a bbc documentary makes you pretty basic 😏
@@BradCozine Exponentially.
Great content. Thanks Oscar for had posted it on YouTUBE.
Note that Hannah pronounces it "maths", the correct abbreviation of the plural word mathematics. Also, just like maths, physics is plural. [Aussie in BC]
@@CPLWeeks data comes from the latin word data and it is plural, the singular version is datum. Cheers.
Is 'mathematics' plural? If so, what exactly is one mathematic?
@@PLecN Pants, glasses etc are also only in plural, while Messias only exist in singular. But I think it comes more from the context "the field of mathematics" rather than being a plural form; like when I say I study Genetics, I can't say "Genetic". The field of Physics etc.
I love math as an adult! the tragedy is that the potential interest in math that is in all of us is supressed by math teachers from whom roughly 90% suck.
I love her voice so much.
The beauty of mathematics is unbounded
thanks for uploading this
50:23
>Euler's Formula comes out like 3 times
>Logarithm product rules
But they're not even the active component in calculating the differential equations of air flow (mildly triggered)
Never knew Madhuri Dixit is a Mathematician, wow!
When I saw that second line of imaginary numbers, all I could think was "That's Numberwang!"
Let's rotate the board! I was waiting for the episode where she explains Numberwang, but she totally avoided the subject. I suppose it's just a BBC show so we cannot expect them to get into the really difficult stuff.
HUMANS DISCOVERED THE CONCEPTS AND IDEAS OF MATHS. THEN INVENTED THE SYMBOLS AND LANGUAGE OF IT TO MAKE IT MORE RELATABLE TO US HUMANS.
Math and Mindfulness Come From PERFECTION (SPIRIT) Alive and Active
But maths itself was always there else there would have been nothing to discover, perhaps no discoverer either.
Producer: Hey Dr. Fry, we'd like you to host a BBC documentary about maths
Fry: Only if I get to walk through a lot of hilly grassy fields
Producer: Deal!
Probably the other way round, if you know anything about TV producers!
That wink at 8:43
Yep she has me in the palm of her hand.
I'm melting under her amazingness O.O
Kristina Chausheva
Naughty, naughty girl... you 😝😘😍😉 ‼️
@@MegaBanne O.~
it's cringe worthy
This is really interesting! Thank you for sharing :) ps. For further maths videos, after this series ;) Terry Jones presents a fun video on YT called The Story of 1.
11:40 All this talk of Fibonacci is making me hungry for Italian food.
21:50 Small pedantic correction, no the Platonic solids are not the only objects where every side is the same shape. There's the Kepler-Poinsot solids www.software3d.com/Kepler.php Or if we restrict ourselves to convex polyhedra, there's the Catalan solids, www.software3d.com/Archimedean.php duals of the Archimedean solids. Any deltahedron would also suffice, eg the Snub Disphenoid www.software3d.com/J84.php Also the dual of any prism, such as the pentagonal dipyramid www.software3d.com/Dipyramid5.php or the dual of any antiprism, such as the pentagonal deltohedron www.software3d.com/Delto5.php
The Platonic solids are the regular convex polyhedra. To be regular, all faces must be the same regular polygon, AND all vertices must be surrounded in the same regular way. That is, the cross-section through any vertex must also give a regular polygon, and all must give the same regular polygon.
like kun 1st yr taga west ka kg gina palantaw kja para sa synthesis paper
basta taga west, da best! hahaahhaah
Ay yawa HAHAHAHAHA
Hahaha yot
Grr
=) part of learning, though! =)
Always surprised at how close objective and subjective topics crossover, the further and deeper you delve into science and mathematics the more it begins to be Philosophy and Religion, and vice versa of course.
13:15 i just imagine the hulk from end game "so many stairs!".
😂
😀☺☺
I know it’s free here, but I support Curiosity Stream. I suggest you do too, it’s a way for more docs like this to be made. They need money to make them you guys! Curiosity Stream is like $20 a year. We need more minds that love docs!
I have watched this patiently, even, reverentially. But I've not learnt anything that fits my effort. Such are the doings of the BBC
I have. It fits mine perfectly.
Why did you not learn?
This Series should be called math Philosophy for beginners or the simple-minded
I think the universe is in us as well as us being the universe so mathematics in its pure unwritten form is the universe but by writing out numbers and equations is like deciphering hieroglyphics and translating that into a language we can understand
I agree. Neither invented now discovered. A hunter gatherer or MLB outfielder knows where the projectile is going to land even if neither of them took a calculus course. As with Newton and calculus it would appear to me that maths are innate in the way we think and perceive our environment. So mathematical symbols are a means to articulate what the brain was doing anyway, whether we paid attention to it or not.
@@pfreddyp in a weird way "the universe we live in is a simulation like the matrix" is plausible looking at it purely from a mathematical standpoint because it's all information ones and zeros if you will running calculations from how planets orbit to how our DNA replicates and quantum fluctuations keeps us on our toes lol
With "such" a teacher... would have loved math classes!
we invent the symbology and apply it to what we discover
Agreed. It is quite ridiculous and arrogant to think humans invented math
Even so called "invented imaginary numbers" are only tools to help explain the discovery of that which already exists
@Roger Loquitur The human race F*ckwit
Math(s) is there as the superstructure behind our universe. The most fundamental concept of math is "1" or "wholeness" I think, and I think "MATH" singular is more precise the term. I think math, like the Mandelbrot, is contiguous--all connected--one thing. But to describe math as plural is to give math a godlike treatment, as we call God Elohim (a plural Hebrew word used to describe one thing) and that is not so bad, because math is very close to the sacred. How each culture describes, explores and exploits math(s) (or simply enjoys them) says a lot about their pursuit of noble, abstract ideas, which is a function of humanity. Math is beautiful! Great video.
Its full proper name is Mathematics which ends in 's'.
Very well made documentary, but i am bothered by the misinterpretation regarding USING imaginary numbers.
There are many many fields of mathematics that use the 2nd dimension of the number line (the up-down part), and that mathematics is the same as the mathematics of imaginary numbers. But the scope is viewed backwards, and should be :
" mathematics with 2nd dimension on the number line is the general scope, and mathematics using imaginary numbers is a special case of that scope where the unit for up-down has the special property of i*i=--1".
In other words, if mathematics involving imaginary numbers does not use the property i*i=-1, it is mathematics of Two-dimensional space.
Hannah did address what you are talking about. The "two-dimensional space" you refer to is the Cartesian plane. This is distinctly different from the complex plane (with imaginary numbers in one axis). It's not so much that the Cartesian plane is the "general scope" (or usual case, as you stated) and the complex plane is the "special case." They are really describing two different things. You can view the complex plane as the "full" representation of the number line, whereas the Cartesian plane is used to represent relations between variables.
An Indian mathematician Aacharya Hemchandra Samvat 1088-1173 discovered a sequence of an addition ie 1+2+3+... this combination still can be found in the Indian music Tabla based on a number of beats and its graduation in the number of segments or groups.
Birth of Fibonacci 1170-1250 his book Liber Abaci, in 1202 hence the info she presenting outdated or copied.
"This is not a maths lecture" -Hannah
What...?! Where am I? What is happening?!
I love it when science and beauty goes hand in hand :)
Animals are also aware of numbers.
For example, 3 hyenas will not attack one single lioness.
But as soon as they are 4 or more hyenas, they will attack a single lioness..
And 1 lioness will not try to take the food away from 4 hyenas, but will easy try to take it away from 3 hyenas.. :)
As i am no mathematician i must admit that this video gave me 3 WOW experiences, The Platonic Solids, The history about the number zero and the number i.
(The number "i" is completely new to me, so i have to search on it now to learn more, and i blame you if this drives me crazy) ;)
That might depend on how hungry the lion is!
"... why mathematical rules and patterns seem to infiltrate everything around us."
We invented mathematics to model the world around us, and then we act surprised that it seems to infiltrate everything around us.
If we never existed those mathematical rules would still exist.
@Roger Loquitur With the square root of -1.
@@DanEllis Nice *left finger on nose whilst pointing to you with right finger*
you know you´re a nerd when a woman who you already find attractive on first sight doubles in attractiveness once she tells you that she´s a scientist....
Keep in mind that even at 13:28, it´s still about maths....
a more relevant question is who or what could "discover" math but a conscious mind?
2021's Biggest breakthrough in Mathematics. String theorist Brian Greene was looking at this
problem for all his life but nothing clicked. Well somebody had to do it, so I stepped up the plate, here it is,
hot off the presses : We can pair every positive floating point number
using up only about 20% of the integers
Algorithm #1 : Convert a float with a zero whole part into an integer
1. Reverse the character sequence representing this float
2. Remove the decimal point to obtain the desired integer
Example : Convert the float 0.002743 into its integer equivalent
1. Reverse the float string to obtain 347200.0
2. Remove the decimal point to obtain the integer 3472000
3. Note : All corresponding integers will be terminated by the character “0”
Algorithm #2 : Convert a float with a non-zero whole part into an integer
1. Count the number of whole digits or NWD (those preceding the decimal point )
2. Append a number of “0” digits equal to NWD to the float.
3. Append a digit “1” to the resulting float
4. Remove the decimal point to obtain the desired integer
Example : Convert the float 1230.0098 into its integer equivalent
1. Count the number of whole digits : NWD = 4
2. Append NWD = 4 “0” digits to obtain 1230.00980000
3. Append a digit “1” to obtain 1230.009800001
4. Remove the decimal point : this gives us the final integer of 1230009800001
Note : We append a digit “1” to distinguish the integers derived from floats with
non-zero whole parts from integers generated by floats with zero whole parts .
This can be done for every float [whole.fraction] where whole > 0 !!! AMAZING!!!
We just came up with a scheme which pairs each positive float with a positive integer.
Note : .
Math is the language of Truth, the language of God -- or at least our best shot at it so far.
GOD is ONE EXPONENTIATION GOODNESS, PERFECTION (SPIRIT)
As a woman of science I find it strange how Platon looked at the irregular and imperfect. When he brings up his analogy I ask, but what causes the blurring of these shadows? Those fundamental aspects of the world have to be far more interesting. Than perfect shapes. Platon feels shallow minded when he didn't look at the dept of his ideas.
For me, a thing that is invented depends on who invented it. Take the airplane for example. There were several competing designs for the first airplane. The Wright Flyer happened to be the first successful design, but after that other built airplanes with radically different designs. Today airplanes don't look anything like the first airplane.
A discovery however, has nothing to do with who discovers it. It will be the same regardless of who finds it, and it will stay the same even after it is discovered.
Mathematics is the same no matter who invents it. An alien living in the Andromeda Galaxy will have "invented" Calculus that is identical to what Newton "invented". They will use rules for Algebra that are identical to the rules we have. It will know that Pi is about (but not quite exactly) 3.14.
This to me suggests a discovery, not an invention.
thx for uploading.
i love BBC docus.
I kinda wonder why it's so hard to think that there are patterns in the real world that we discover and maths is the language we invent to express what we find, at the same time. Of course there is a relationship between what you discover and how you describe it, but that's true for natural languages, too. The words you use influence the way you think about things. 2 + 3 is only 5 if you're thinking in a decimal system. Maybe irrational numbers wouldn't be special, if we didn't. Physical laws are real, reality is real. Once you start discovering natural laws and describe them, you start finding them all over the place, surprise, surprise. And still mathematics are a system to model reality in our heads, just like anything else we understand. Because the only reality is out there. As soon as we start thinking about stuff, what we deal with is a model of reality in our heads. But oh well.
How do you prove reality is real and not some perfectly put program? I think thats really what the video is about
A delightfully imaginative documentary. Maths as a discovery or an invention. As someone who actually likes mathematical ideas and ideals, I decided to give this a try. The question I finally focused on, was the issue of the imaginary numbers. This was the bit of evidence that convinced me that maths are a discovery the we invented a language around. Things such as the Fibonacci scale, actually exist in the natural world without the invention of the language to understand it, therefore, maths exist as a real thing to deal with, but man has a need to understand and prove, and play with things he likes. Enter the general creation of the language of mathematics. Zero/0, for example, is nothing more than a word/symbol, to describe the idea/reality of nothing. Negative numbers are a construct used as an aid to help us understand the universe, such as wave events and the like. I'm not sure, but I have a difficult time understanding why this isn't apparent to anyone who looks at mathematics. I am not a mathematician, just someone who enjoys and loves to play with math.