My last semester in college is fast approaching and big changes are probably coming to my life soon. Hopefully I will have time to update this after i finish in May.
We are fascinated with symmetry
that's what we see in pretty faces, necessary but not sufficient, maybe not even necessary ask Cindy Crawford.
that's what we see in pretty faces, necessary but not sufficient, maybe not even necessary ask Cindy Crawford.
Symmetry can be any self similarity with respect to any of the dimensions of an object and a frame of reference.
I want to talk about a reflective symmetry.
Our right hand is the mirror image of our left hand. d is the mirror image of b (more or less graphically). Generally in order for mirror images to be constructed there must be a frame of reference or frame of symmetry.
Now let's talk about something not always associated with geometry: words, sentences, language.
Palindromes are sentences of 1d (like all sentences not in hyperfiction or madlibs) that express reflective symmetry.
I prefer pi.
reading it backwards we can see it says the same thing. the 0dimensional symmetry point is the 'f'.
race car
is also a palindrome. right hannah?
and the day before yesterday (do you know there's a single word for this in spanish) 01-02-2010 is a palindrome if you consider the string without any kind of separators. NOT ONLY THAT but it is a palindrome that could also be read as a base 3 number since only the digits 0 1 and 2 appear. In the next 100 years this will only happen in:
01022010, 11022011, 02022020, 12022021, 10122101. (5 times)
for 012 only.
and for general palindrome dates
01022010, 11022011, 02022020, 12022021, 03022030, 04022040, 05022050, 06022060, 07022070, 08022080, 09022090, 10122101. (12)
and almost 01122110 (8 days short).
but I know what you're thinking. "I don't live in America!/I dont write dates mm/dd/yyyy!" well there is an endless number of ways to write dates if you follow ddmmyyyy then there are even more palindromes because you are not restricted by the first two numbers to be a maximum of 12 (months) but a maximum of 31 days when appropiate and 28 worst case. a more annoying problem to compute.
if you write dates like mmddyy or ddmmyy then also the possibilities change.
also there can be symmetry with a non unique symmetry reference in any dimension.
to show this the trivial example of an infinite (yet onedimensional) string ...11111111.... or a self connected *{11111}* string of any length. Where is the point of symmetry? everywhere? anywhere?
Physicists often exploit symmetries to simplify problems. sometimes they find a solution and backtrack to the supposed symmetries that allowed for that solution. it's almost a mystical thing to them. A coincidence.
Engineers don't really believe in perfect symmetry that's why they've devised all sorts of measurements and procedures to quantify 'symmetricness' in real objects.
but to stop myself from a combinatoric rant that will put everyone to sleep i leave you with the challenge of making palindromic new year resolutions.
I want to talk about a reflective symmetry.
Our right hand is the mirror image of our left hand. d is the mirror image of b (more or less graphically). Generally in order for mirror images to be constructed there must be a frame of reference or frame of symmetry.
- in the case of 1 dimensional objects there is a point of symmetry in the 1D space that denotes the two reflections.
- in the case of 2 dimensional objects there has to be an axis (line) of symmetry.
- for 3d solids there has to be a plane of symmetry (mirrors).
Now let's talk about something not always associated with geometry: words, sentences, language.
Palindromes are sentences of 1d (like all sentences not in hyperfiction or madlibs) that express reflective symmetry.
I prefer pi.
reading it backwards we can see it says the same thing. the 0dimensional symmetry point is the 'f'.
race car
is also a palindrome. right hannah?
and the day before yesterday (do you know there's a single word for this in spanish) 01-02-2010 is a palindrome if you consider the string without any kind of separators. NOT ONLY THAT but it is a palindrome that could also be read as a base 3 number since only the digits 0 1 and 2 appear. In the next 100 years this will only happen in:
01022010, 11022011, 02022020, 12022021, 10122101. (5 times)
for 012 only.
and for general palindrome dates
01022010, 11022011, 02022020, 12022021, 03022030, 04022040, 05022050, 06022060, 07022070, 08022080, 09022090, 10122101. (12)
and almost 01122110 (8 days short).
but I know what you're thinking. "I don't live in America!/I dont write dates mm/dd/yyyy!" well there is an endless number of ways to write dates if you follow ddmmyyyy then there are even more palindromes because you are not restricted by the first two numbers to be a maximum of 12 (months) but a maximum of 31 days when appropiate and 28 worst case. a more annoying problem to compute.
if you write dates like mmddyy or ddmmyy then also the possibilities change.
also there can be symmetry with a non unique symmetry reference in any dimension.
to show this the trivial example of an infinite (yet onedimensional) string ...11111111.... or a self connected *{11111}* string of any length. Where is the point of symmetry? everywhere? anywhere?
Physicists often exploit symmetries to simplify problems. sometimes they find a solution and backtrack to the supposed symmetries that allowed for that solution. it's almost a mystical thing to them. A coincidence.
Engineers don't really believe in perfect symmetry that's why they've devised all sorts of measurements and procedures to quantify 'symmetricness' in real objects.
but to stop myself from a combinatoric rant that will put everyone to sleep i leave you with the challenge of making palindromic new year resolutions.
3 comments:
haha, fun stuff...
I'm a mathematician too. Sort of: I have a math Bach of Arts even though I do statistics. I also like looking for relationships between disparate things. You wrote a nice post on palindromes and verbal symmetry. I enjoyed it.
Whenever I think of symmetry in any sense other than a very literal one, I think of a William Blake poem:
Tiger,tiger burning bright
In the forests of the night
What immortal hand or eye
Dare frame thy fearful symmetry?
First poetry I recall learning. I never understood the meaning, even now. But it runs through my head a lot, like when I read your post that mentioned symmetry. Can you tell me what it means? If not, I understand.
Thank you for writing such a nice blog.
Thank you for your comment Ellie.
I read somewhere that Blake was inspired by a caged tiger he saw to write this poem. I think in the original he says Tyger Tyger.
what the poem itself means is a subject of much debate.
To me the poem is just about a tiger and perhaps also about any other entity of insurmountable force.
I think by symmetry that Billy Blake was impressed by all those stripes on tigers and how they are parallel and not cross each other and are the same in the other side of the tiger. who knows
I had left the blog dormant maybe ill start posting again. thanks again for reading
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