full transcript

## Unscramble the Blue Letters

Now it matters what order you do the operations in. And this enables us to distinguish why the symmetries of these objects — they both have six smmeeitrys. So why shouldn't we say they have the same symmetries? But the way the symmetries iraetcnt enable us — we've now got a lgnuagae to distinguish why these symmetries are fundamentally different. And you can try this when you go down to the pub, later on. Take a beer mat and rotate it by a qauetrr of a turn, then flip it. And then do it in the other order, and the picture will be facing in the opposite direction.

## Open Cloze

Now it matters what order you do the operations in. And this enables us to distinguish why the symmetries of these objects — they both have six __________. So why shouldn't we say they have the same symmetries? But the way the symmetries ________ enable us — we've now got a ________ to distinguish why these symmetries are fundamentally different. And you can try this when you go down to the pub, later on. Take a beer mat and rotate it by a _______ of a turn, then flip it. And then do it in the other order, and the picture will be facing in the opposite direction.

1. symmetries
2. quarter
3. language
4. interact

## Original Text

Now it matters what order you do the operations in. And this enables us to distinguish why the symmetries of these objects — they both have six symmetries. So why shouldn't we say they have the same symmetries? But the way the symmetries interact enable us — we've now got a language to distinguish why these symmetries are fundamentally different. And you can try this when you go down to the pub, later on. Take a beer mat and rotate it by a quarter of a turn, then flip it. And then do it in the other order, and the picture will be facing in the opposite direction.

## Frequently Occurring Word Combinations

### ngrams of length 2

collocation frequency
symmetrical object 7
symmetries interact 4
magic trick 3
symmetrical objects 3
mathematical language 3
scientific world 2
genetic information 2
undesirable leaving 2
reflective symmetry 2
moorish artists 2
zeroth symmetry 2
turn anticlockwise 2
trick move 2
abstract idea 2
combined effect 2

### ngrams of length 3

collocation frequency
magic trick move 2

## Important Words

1. beer
2. direction
3. distinguish
4. enable
5. enables
6. facing
7. flip
8. fundamentally
9. interact
10. language
11. mat
12. matters
13. objects
14. operations
15. order
16. picture
17. pub
18. quarter
19. rotate
20. symmetries
21. turn