TedTest

From the Ted Talk by Eddie Woo: How math is our real sixth sense

Unscramble the Blue Letters

"I love mathematics" (Laughter) is exactly what to say at a party if you want to spend the next couple of hours sipping your drink alone in the least cool corner of the room. And that's because when it comes to this subject - all the numbers, formulas, symbols, and calculations - the vast majority of us are outsiders, and that includes me. That's why today I want to share with you an outsider's perspective of mathematics - what I utdneasnrd of it, from someone who's always struggled with the subject. And what I've discovered, as someone who went from being an odtesiur to making maths my career, is that, slgrinusrpiy, we are all deep down born to be maitinaaectmhs. (Laughter) But back to me being an outsider. I know what you're thinking: "Wait a second, Eddie. What would you know? You're a maths teacher. You went to a selective school. You wear glasses, and you're Asian." (Laughter) Firstly, that's racist. (Laughter) Secondly, that's wrong. When I was in sohocl, my fvioarte seujcbts were English and history. And this caused a lot of angst for me as a tneageer because my high school truly honored micatthmeas. Your status in the school pretty much correlated with which mathematics class you ranked in. There were eight classes. So if you were in maths 4, that made you just about agverae. If you were in mahts 1, you were like royalty. Each year, our school etenerd the prestigious Australian Mathematics Competition and would print out a list of everyone in the school in order of our scores. Students who received prizes and high distinctions were pinned up at the start of a long corridor, far, far away from the dark and shameful place where my name aeeparpd. Maths was not really my thing. Stories, characters, narratives - this is where I was at home. And that's why I raised my sails and set course to become an English and history teacher. But a cacnhe encounter at sydeny University altered my life forever. I was in line to enroll at the fctaluy of education when I started the conversation with one of its professors. He ntieocd that while my academic life had been dominated by humiinaets, I had actually attempted some high-level maths at school. What he saw was not that I had a problem with maths, but that I had peesrerevd with maths. And he knew something I didn't - that there was a critical sgorathe of mathematics educators in Australian slohcos, a shortage that remains to this day. So he encouraged me to change my teaching area to mathematics. Now, for me, becoming a teacher wasn't about my love for a particular suejbct. It was about having a personal impact on the lievs of young people. I'd seen fasrhtnid at school what a lasting and positive difference a great teacher can make. I wanted to do that for someone, and it didn't matter to me what subject I did it in. If there was an acute need in mathematics, then it made sense for me to go there. As I sditued my degree, though, I discovered that mathematics was a very different subject to what I'd originally thuoght. I'd made the same mtiksae about mathematics that I'd made eiealrr in my life about music. Like a good mingart child, I dutifully lrneead to play the piano when I was young. (Laughter) My weekends were filled with eldesnsly repeating scales and memorizing every note in the piece, spring and winter. I lasted two years before my career was abruptly ended when my teacher told my parents, "His fingers are too short. I will not teach him anymore." (leauhgtr) At seven years old, I thought of music like torture. It was a dry, solitary, joyless exercise that I only engaged with because someone else forced me to. It took me 11 years to egmere from that sad place. In year 12, I picked up a steel string acoustic guitar for the first time. I wanted to play it for church, and there was also a girl I was fairly keen on impressing. So I cincovned my brother to tcaeh me a few chords. And slwoly, but surely, my mind cgenahd. I was egenagd in a creative poescrs. I was making music, and I was hooked. I started playing in a band, and I felt the delight of rhythm pulsing through my body as we brought our sounds together. I'd been surrounded by a musical ocean my ertnie life, and for the first time, I realized I could swim in it. I went through an almost identical experience when it came to mathematics. I used to believe that maths was about rote learning inscrutable formulas to solve abtrsact problems that didn't mean anything to me. But at university, I began to see that mathematics is immensely practical and even beautiful, that it's not just about finding ansrwes but also about learning to ask the right questions, and that mathematics isn't about msndlsiley crunching numbers but rather about forming new ways to see problems so we can solve them by cbiinnomg insight with imagination. It gradually dawned on me that mathematics is a sense. Mathematics is a snsee just like sight and touch; it's a sense that allows us to perceive realities which would be otherwise intangible to us. You know, we talk about a sense of humor and a sense of rhhtym. Mathematics is our sense for patterns, rsotaihplenis, and logical connections. It's a whole new way to see the world. Now, I want to show you a mathematical reality that I guarantee you've seen before but perhaps never really perceived. It's been hidden in plain sight your entire life. This is a river delta. It's a beautiful peice of geometry. Now, when we hear the word geometry, most of us think of triangles and circles. But geometry is the mathematics of all shapes, and this meeting of land and sea has created shapes with an undeniable pattern. It has a mathematically recursive structure. Every part of the revir delta, with its twists and turns, is a microversion of the gaeertr whole. So I want you to see the mathematics in this. But that's not all. I want you to compare this river delta with this amazing tree. It's a wonder in itself. But focus with me on the srliteiimais between this and the river. What I want to know is why on erath should these shapes look so remarkably alike? Why should they have anything in common? Things get even more pipexnelrg when you realize it's not just weatr systems and plants that do this. If you keep your eyes open, you'll see these same saehps are everywhere. Lightning bolts disappear so quickly that we sdleom have the opportunity to ponder their geometry. But their shape is so uinamlkstbae and so similar to what we've just seen that one can't help but be suspicious. And then there's the fact that every snlige person in this room is filled with these shapes too. Every cubic ceiettnmer of your body is packed with blood vessels that trace out this same petatrn. There's a mcmtaatehail reality weovn into the fabric of the universe that you share with winding rviers, towering trees, and raging storms. These shapes are examples of what we call "fractals," as mathematicians. Fractals get their name from the same pacle as fractions and fractures - it's a reference to the broken and sttreaehd shapes we find around us in nruate. Now, once you have a sense for fractals, you really do start to see them everywhere: a head of broccoli, the leaves of a fern, even clouds in the sky. Like the other senses, our mathematical sense can be refined with pciactre. It's just like developing perfect pitch or a taste for wines. You can learn to perceive the mathematics around you with time and the right guidance. Naturally, some people are born with spehrar seness than the rest of us, others are born with impairment. As you can see, I drew a short straw in the genetic lottery when it came to my eyesight. Without my glasses, everything is a blur. I've wrstleed with this sense my entire life, but I would never dream of saying, "Well, seeing has always been a struggle for me. I guess I'm just not a seeing kind of person." (Laughter) Yet I meet people every day who feel it quite nartaul to say exactly that about mathematics. Now, I'm convinced we close ourselves off from a huge part of the human experience if we do this. Because all human beings are werid to see patterns. We live in a patterned universe, a cosmos. That's what cosmos means - orderly and prneetatd - as opposed to chaos, which means disorderly and random. It isn't just seeing patterns that humans are so good at. We love making patterns too. And the people who do this well have a special name. We call them artists, musicians, sculptors, painters, cinematographers - they're all pattern creators. muisc was once described as the joy that poplee feel when they are counting but don't know it. (Laughter) Some of the most stnikrig examples of mathematical patterns are in Islamic art and design. An aversion to depicting hanums and animals led to a rich history of intricate tile arrangements and geometric forms. The aesthetic side of mathematical patterns like these bginrs us back to nature itself. For instance, flowers are a universal symbol of beauty. Every culture around the planet and throughout hstoiry has regarded them as objects of wonder. And one acepst of their beauty is that they exhibit a special kind of symmetry. Flowers grow organically from a ceetnr that eadnpxs orawduts in the shape of a spiral, and this creates what we call "rotational smyrmety." You can spin a flower around and around, and it still looks basically the same. But not all spirals are ceretad equal. It all depends on the angle of rotation that goes into creating the spiral. For instance, if we build a spiral from an agnle of 90 degrees, we get a cross that is neither beautiful nor efficient. Huge parts of the flowers area are westad and don't produce seeds. Using an angle of 62 degrees is better and produces a nice circular shape, like what we usually associate with flowers. But it's still not great. There's still large parts of the area that are a poor use of resources for the flower. However, if we use 137.5 degrees, (Laughter) we get this beautiful pattern. It's ahinistsong, and it is exactly the kind of pattern used by that most majestic of flowers - the sunflower. Now, 137.5 degeres might seem pretty random, but it actually emerges out of a special number that we call the "golden ratio." The golden ritao is a mathematical reilaty that, like fractals, you can find everywhere - from the phalanges of your fingers to the pillars of the Parthenon. That's why even at a praty of 5000 people, I'm proud to declare, "I love mathematics!" (Cheers) (Applause)

Open Cloze

"I love mathematics" (Laughter) is exactly what to say at a party if you want to spend the next couple of hours sipping your drink alone in the least cool corner of the room. And that's because when it comes to this subject - all the numbers, formulas, symbols, and calculations - the vast majority of us are outsiders, and that includes me. That's why today I want to share with you an outsider's perspective of mathematics - what I __________ of it, from someone who's always struggled with the subject. And what I've discovered, as someone who went from being an ________ to making maths my career, is that, ____________, we are all deep down born to be ______________. (Laughter) But back to me being an outsider. I know what you're thinking: "Wait a second, Eddie. What would you know? You're a maths teacher. You went to a selective school. You wear glasses, and you're Asian." (Laughter) Firstly, that's racist. (Laughter) Secondly, that's wrong. When I was in ______, my ________ ________ were English and history. And this caused a lot of angst for me as a ________ because my high school truly honored ___________. Your status in the school pretty much correlated with which mathematics class you ranked in. There were eight classes. So if you were in maths 4, that made you just about _______. If you were in _____ 1, you were like royalty. Each year, our school _______ the prestigious Australian Mathematics Competition and would print out a list of everyone in the school in order of our scores. Students who received prizes and high distinctions were pinned up at the start of a long corridor, far, far away from the dark and shameful place where my name ________. Maths was not really my thing. Stories, characters, narratives - this is where I was at home. And that's why I raised my sails and set course to become an English and history teacher. But a ______ encounter at ______ University altered my life forever. I was in line to enroll at the _______ of education when I started the conversation with one of its professors. He _______ that while my academic life had been dominated by __________, I had actually attempted some high-level maths at school. What he saw was not that I had a problem with maths, but that I had __________ with maths. And he knew something I didn't - that there was a critical ________ of mathematics educators in Australian _______, a shortage that remains to this day. So he encouraged me to change my teaching area to mathematics. Now, for me, becoming a teacher wasn't about my love for a particular _______. It was about having a personal impact on the _____ of young people. I'd seen _________ at school what a lasting and positive difference a great teacher can make. I wanted to do that for someone, and it didn't matter to me what subject I did it in. If there was an acute need in mathematics, then it made sense for me to go there. As I _______ my degree, though, I discovered that mathematics was a very different subject to what I'd originally _______. I'd made the same _______ about mathematics that I'd made _______ in my life about music. Like a good _______ child, I dutifully _______ to play the piano when I was young. (Laughter) My weekends were filled with _________ repeating scales and memorizing every note in the piece, spring and winter. I lasted two years before my career was abruptly ended when my teacher told my parents, "His fingers are too short. I will not teach him anymore." (________) At seven years old, I thought of music like torture. It was a dry, solitary, joyless exercise that I only engaged with because someone else forced me to. It took me 11 years to ______ from that sad place. In year 12, I picked up a steel string acoustic guitar for the first time. I wanted to play it for church, and there was also a girl I was fairly keen on impressing. So I _________ my brother to _____ me a few chords. And ______, but surely, my mind _______. I was _______ in a creative _______. I was making music, and I was hooked. I started playing in a band, and I felt the delight of rhythm pulsing through my body as we brought our sounds together. I'd been surrounded by a musical ocean my ______ life, and for the first time, I realized I could swim in it. I went through an almost identical experience when it came to mathematics. I used to believe that maths was about rote learning inscrutable formulas to solve ________ problems that didn't mean anything to me. But at university, I began to see that mathematics is immensely practical and even beautiful, that it's not just about finding _______ but also about learning to ask the right questions, and that mathematics isn't about __________ crunching numbers but rather about forming new ways to see problems so we can solve them by _________ insight with imagination. It gradually dawned on me that mathematics is a sense. Mathematics is a _____ just like sight and touch; it's a sense that allows us to perceive realities which would be otherwise intangible to us. You know, we talk about a sense of humor and a sense of ______. Mathematics is our sense for patterns, _____________, and logical connections. It's a whole new way to see the world. Now, I want to show you a mathematical reality that I guarantee you've seen before but perhaps never really perceived. It's been hidden in plain sight your entire life. This is a river delta. It's a beautiful _____ of geometry. Now, when we hear the word geometry, most of us think of triangles and circles. But geometry is the mathematics of all shapes, and this meeting of land and sea has created shapes with an undeniable pattern. It has a mathematically recursive structure. Every part of the _____ delta, with its twists and turns, is a microversion of the _______ whole. So I want you to see the mathematics in this. But that's not all. I want you to compare this river delta with this amazing tree. It's a wonder in itself. But focus with me on the ____________ between this and the river. What I want to know is why on _____ should these shapes look so remarkably alike? Why should they have anything in common? Things get even more __________ when you realize it's not just _____ systems and plants that do this. If you keep your eyes open, you'll see these same ______ are everywhere. Lightning bolts disappear so quickly that we ______ have the opportunity to ponder their geometry. But their shape is so ____________ and so similar to what we've just seen that one can't help but be suspicious. And then there's the fact that every ______ person in this room is filled with these shapes too. Every cubic __________ of your body is packed with blood vessels that trace out this same _______. There's a ____________ reality _____ into the fabric of the universe that you share with winding ______, towering trees, and raging storms. These shapes are examples of what we call "fractals," as mathematicians. Fractals get their name from the same _____ as fractions and fractures - it's a reference to the broken and _________ shapes we find around us in ______. Now, once you have a sense for fractals, you really do start to see them everywhere: a head of broccoli, the leaves of a fern, even clouds in the sky. Like the other senses, our mathematical sense can be refined with ________. It's just like developing perfect pitch or a taste for wines. You can learn to perceive the mathematics around you with time and the right guidance. Naturally, some people are born with _______ ______ than the rest of us, others are born with impairment. As you can see, I drew a short straw in the genetic lottery when it came to my eyesight. Without my glasses, everything is a blur. I've ________ with this sense my entire life, but I would never dream of saying, "Well, seeing has always been a struggle for me. I guess I'm just not a seeing kind of person." (Laughter) Yet I meet people every day who feel it quite _______ to say exactly that about mathematics. Now, I'm convinced we close ourselves off from a huge part of the human experience if we do this. Because all human beings are _____ to see patterns. We live in a patterned universe, a cosmos. That's what cosmos means - orderly and _________ - as opposed to chaos, which means disorderly and random. It isn't just seeing patterns that humans are so good at. We love making patterns too. And the people who do this well have a special name. We call them artists, musicians, sculptors, painters, cinematographers - they're all pattern creators. _____ was once described as the joy that ______ feel when they are counting but don't know it. (Laughter) Some of the most ________ examples of mathematical patterns are in Islamic art and design. An aversion to depicting ______ and animals led to a rich history of intricate tile arrangements and geometric forms. The aesthetic side of mathematical patterns like these ______ us back to nature itself. For instance, flowers are a universal symbol of beauty. Every culture around the planet and throughout _______ has regarded them as objects of wonder. And one ______ of their beauty is that they exhibit a special kind of symmetry. Flowers grow organically from a ______ that _______ ________ in the shape of a spiral, and this creates what we call "rotational ________." You can spin a flower around and around, and it still looks basically the same. But not all spirals are _______ equal. It all depends on the angle of rotation that goes into creating the spiral. For instance, if we build a spiral from an _____ of 90 degrees, we get a cross that is neither beautiful nor efficient. Huge parts of the flowers area are ______ and don't produce seeds. Using an angle of 62 degrees is better and produces a nice circular shape, like what we usually associate with flowers. But it's still not great. There's still large parts of the area that are a poor use of resources for the flower. However, if we use 137.5 degrees, (Laughter) we get this beautiful pattern. It's ___________, and it is exactly the kind of pattern used by that most majestic of flowers - the sunflower. Now, 137.5 _______ might seem pretty random, but it actually emerges out of a special number that we call the "golden ratio." The golden _____ is a mathematical _______ that, like fractals, you can find everywhere - from the phalanges of your fingers to the pillars of the Parthenon. That's why even at a _____ of 5000 people, I'm proud to declare, "I love mathematics!" (Cheers) (Applause)

Solution

favorite
slowly
greater
single
shattered
wrestled
laughter
maths
sense
school
senses
center
pattern
relationships
understand
engaged
striking
rivers
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subject
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entire
humans
teach
seldom
centimeter
thought
sydney
angle
sharper
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teenager
firsthand
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changed
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nature
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endlessly
created
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rhythm
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outwards
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noticed
earth
emerge
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party
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music
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chance
river
mistake
mathematical
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water
abstract
convinced
piece
similarities
people
perplexing
ratio
learned
history
humanities
outsider
wasted
entered
aspect
shapes
astonishing

Original Text

"I love mathematics" (Laughter) is exactly what to say at a party if you want to spend the next couple of hours sipping your drink alone in the least cool corner of the room. And that's because when it comes to this subject - all the numbers, formulas, symbols, and calculations - the vast majority of us are outsiders, and that includes me. That's why today I want to share with you an outsider's perspective of mathematics - what I understand of it, from someone who's always struggled with the subject. And what I've discovered, as someone who went from being an outsider to making maths my career, is that, surprisingly, we are all deep down born to be mathematicians. (Laughter) But back to me being an outsider. I know what you're thinking: "Wait a second, Eddie. What would you know? You're a maths teacher. You went to a selective school. You wear glasses, and you're Asian." (Laughter) Firstly, that's racist. (Laughter) Secondly, that's wrong. When I was in school, my favorite subjects were English and history. And this caused a lot of angst for me as a teenager because my high school truly honored mathematics. Your status in the school pretty much correlated with which mathematics class you ranked in. There were eight classes. So if you were in maths 4, that made you just about average. If you were in maths 1, you were like royalty. Each year, our school entered the prestigious Australian Mathematics Competition and would print out a list of everyone in the school in order of our scores. Students who received prizes and high distinctions were pinned up at the start of a long corridor, far, far away from the dark and shameful place where my name appeared. Maths was not really my thing. Stories, characters, narratives - this is where I was at home. And that's why I raised my sails and set course to become an English and history teacher. But a chance encounter at Sydney University altered my life forever. I was in line to enroll at the faculty of education when I started the conversation with one of its professors. He noticed that while my academic life had been dominated by humanities, I had actually attempted some high-level maths at school. What he saw was not that I had a problem with maths, but that I had persevered with maths. And he knew something I didn't - that there was a critical shortage of mathematics educators in Australian schools, a shortage that remains to this day. So he encouraged me to change my teaching area to mathematics. Now, for me, becoming a teacher wasn't about my love for a particular subject. It was about having a personal impact on the lives of young people. I'd seen firsthand at school what a lasting and positive difference a great teacher can make. I wanted to do that for someone, and it didn't matter to me what subject I did it in. If there was an acute need in mathematics, then it made sense for me to go there. As I studied my degree, though, I discovered that mathematics was a very different subject to what I'd originally thought. I'd made the same mistake about mathematics that I'd made earlier in my life about music. Like a good migrant child, I dutifully learned to play the piano when I was young. (Laughter) My weekends were filled with endlessly repeating scales and memorizing every note in the piece, spring and winter. I lasted two years before my career was abruptly ended when my teacher told my parents, "His fingers are too short. I will not teach him anymore." (Laughter) At seven years old, I thought of music like torture. It was a dry, solitary, joyless exercise that I only engaged with because someone else forced me to. It took me 11 years to emerge from that sad place. In year 12, I picked up a steel string acoustic guitar for the first time. I wanted to play it for church, and there was also a girl I was fairly keen on impressing. So I convinced my brother to teach me a few chords. And slowly, but surely, my mind changed. I was engaged in a creative process. I was making music, and I was hooked. I started playing in a band, and I felt the delight of rhythm pulsing through my body as we brought our sounds together. I'd been surrounded by a musical ocean my entire life, and for the first time, I realized I could swim in it. I went through an almost identical experience when it came to mathematics. I used to believe that maths was about rote learning inscrutable formulas to solve abstract problems that didn't mean anything to me. But at university, I began to see that mathematics is immensely practical and even beautiful, that it's not just about finding answers but also about learning to ask the right questions, and that mathematics isn't about mindlessly crunching numbers but rather about forming new ways to see problems so we can solve them by combining insight with imagination. It gradually dawned on me that mathematics is a sense. Mathematics is a sense just like sight and touch; it's a sense that allows us to perceive realities which would be otherwise intangible to us. You know, we talk about a sense of humor and a sense of rhythm. Mathematics is our sense for patterns, relationships, and logical connections. It's a whole new way to see the world. Now, I want to show you a mathematical reality that I guarantee you've seen before but perhaps never really perceived. It's been hidden in plain sight your entire life. This is a river delta. It's a beautiful piece of geometry. Now, when we hear the word geometry, most of us think of triangles and circles. But geometry is the mathematics of all shapes, and this meeting of land and sea has created shapes with an undeniable pattern. It has a mathematically recursive structure. Every part of the river delta, with its twists and turns, is a microversion of the greater whole. So I want you to see the mathematics in this. But that's not all. I want you to compare this river delta with this amazing tree. It's a wonder in itself. But focus with me on the similarities between this and the river. What I want to know is why on earth should these shapes look so remarkably alike? Why should they have anything in common? Things get even more perplexing when you realize it's not just water systems and plants that do this. If you keep your eyes open, you'll see these same shapes are everywhere. Lightning bolts disappear so quickly that we seldom have the opportunity to ponder their geometry. But their shape is so unmistakable and so similar to what we've just seen that one can't help but be suspicious. And then there's the fact that every single person in this room is filled with these shapes too. Every cubic centimeter of your body is packed with blood vessels that trace out this same pattern. There's a mathematical reality woven into the fabric of the universe that you share with winding rivers, towering trees, and raging storms. These shapes are examples of what we call "fractals," as mathematicians. Fractals get their name from the same place as fractions and fractures - it's a reference to the broken and shattered shapes we find around us in nature. Now, once you have a sense for fractals, you really do start to see them everywhere: a head of broccoli, the leaves of a fern, even clouds in the sky. Like the other senses, our mathematical sense can be refined with practice. It's just like developing perfect pitch or a taste for wines. You can learn to perceive the mathematics around you with time and the right guidance. Naturally, some people are born with sharper senses than the rest of us, others are born with impairment. As you can see, I drew a short straw in the genetic lottery when it came to my eyesight. Without my glasses, everything is a blur. I've wrestled with this sense my entire life, but I would never dream of saying, "Well, seeing has always been a struggle for me. I guess I'm just not a seeing kind of person." (Laughter) Yet I meet people every day who feel it quite natural to say exactly that about mathematics. Now, I'm convinced we close ourselves off from a huge part of the human experience if we do this. Because all human beings are wired to see patterns. We live in a patterned universe, a cosmos. That's what cosmos means - orderly and patterned - as opposed to chaos, which means disorderly and random. It isn't just seeing patterns that humans are so good at. We love making patterns too. And the people who do this well have a special name. We call them artists, musicians, sculptors, painters, cinematographers - they're all pattern creators. Music was once described as the joy that people feel when they are counting but don't know it. (Laughter) Some of the most striking examples of mathematical patterns are in Islamic art and design. An aversion to depicting humans and animals led to a rich history of intricate tile arrangements and geometric forms. The aesthetic side of mathematical patterns like these brings us back to nature itself. For instance, flowers are a universal symbol of beauty. Every culture around the planet and throughout history has regarded them as objects of wonder. And one aspect of their beauty is that they exhibit a special kind of symmetry. Flowers grow organically from a center that expands outwards in the shape of a spiral, and this creates what we call "rotational symmetry." You can spin a flower around and around, and it still looks basically the same. But not all spirals are created equal. It all depends on the angle of rotation that goes into creating the spiral. For instance, if we build a spiral from an angle of 90 degrees, we get a cross that is neither beautiful nor efficient. Huge parts of the flowers area are wasted and don't produce seeds. Using an angle of 62 degrees is better and produces a nice circular shape, like what we usually associate with flowers. But it's still not great. There's still large parts of the area that are a poor use of resources for the flower. However, if we use 137.5 degrees, (Laughter) we get this beautiful pattern. It's astonishing, and it is exactly the kind of pattern used by that most majestic of flowers - the sunflower. Now, 137.5 degrees might seem pretty random, but it actually emerges out of a special number that we call the "golden ratio." The golden ratio is a mathematical reality that, like fractals, you can find everywhere - from the phalanges of your fingers to the pillars of the Parthenon. That's why even at a party of 5000 people, I'm proud to declare, "I love mathematics!" (Cheers) (Applause)

Frequently Occurring Word Combinations

ngrams of length 2

collocation	frequency
mathematical reality	3
river delta	2
mathematical patterns	2

Important Words

abruptly
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acute
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hear
hidden
high
history
home
honored
hooked
hours
huge
human
humanities
humans
humor
identical
imagination
immensely
impact
impairment
impressing
includes
inscrutable
insight
instance
intangible
intricate
islamic
joy
joyless
keen
kind
knew
land
large
lasted
lasting
laughter
learn
learned
learning
leaves
led
life
lightning
line
list
live
lives
logical
long
lot
lottery
love
majestic
majority
making
mathematical
mathematically
mathematicians
mathematics
maths
matter
means
meet
meeting
memorizing
microversion
migrant
mind
mindlessly
mistake
music
musical
musicians
narratives
natural
naturally
nature
nice
note
noticed
number
numbers
objects
ocean
open
opportunity
opposed
order
orderly
organically
originally
outsider
outsiders
outwards
packed
painters
parents
part
parthenon
parts
party
pattern
patterned
patterns
people
perceive
perceived
perfect
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persevered
person
personal
perspective
phalanges
piano
picked
piece
pillars
pinned
pitch
place
plain
planet
plants
play
playing
ponder
poor
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practice
prestigious
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print
prizes
problem
problems
process
produce
produces
professors
proud
pulsing
questions
quickly
racist
raging
raised
random
ranked
ratio
realities
reality
realize
realized
received
recursive
reference
refined
regarded
relationships
remains
remarkably
repeating
resources
rest
rhythm
rich
river
rivers
room
rotation
rote
royalty
sad
sails
scales
school
schools
scores
sculptors
sea
seeds
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selective
sense
senses
set
shameful
shape
shapes
share
sharper
shattered
short
shortage
show
side
sight
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similarities
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sipping
sky
slowly
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solve
sounds
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spend
spin
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spirals
spring
start
started
status
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stories
storms
straw
striking
string
structure
struggle
struggled
students
studied
subject
subjects
sunflower
surely
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suspicious
swim
sydney
symbol
symbols
symmetry
systems
talk
taste
teach
teacher
teaching
teenager
thought
tile
time
today
told
torture
towering
trace
tree
trees
triangles
turns
twists
undeniable
understand
universal
universe
university
unmistakable
vast
vessels
wanted
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water
ways
wear
weekends
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year
years
young