${x^4}$ as “tesseracting” a number $x$ [closed]
$begingroup$
So, this strange thought popped up into my head. You know how we call ${x^2}$ squaring due to the fact that what you're essentially doing is finding the area of a square with side length $x$? The same goes for cubing. Saying ${x^3}$ is really going to give you the volume of a cube with side length $x$. Now, what if I tried to coin a term that would take this -ing pattern to another level with ${x^4}$? This would technically give me the 4D volume, per se, of a tesseract(a 4D cube). So, couldn't this really be thought of as "tesseracting" a number?
In fact, I may have a deduction/thought. Saying ${x^n}$ could just be thought of as n-cubing a number. A square can be thought of as a cube in 2D. As in, a cube with only length and height, no depth. So, saying ${x^2}$ can be seen as 2-cubing, or squaring a number. The same goes for ${x^3}$. You are 3-cubing, or just cubing, a number. So it seems this n-cubing pattern holds. So, why not extend it to the tesseract? Why isn't ${x^4}$ just thought of as 4-cubing or "tesseracting"? The pattern I thought of would still hold.
Also, do you mind going easy with the criticisms? I'm not trying to sound like a you-know-what, but just keep in mind I'm extremely amateur and only in 11th grade. And since it seems like this is original to my thoughts, I'm a bit overexcited about this thought.
exponentiation
asked Dec 7 '18 at 3:17
Xavier StantonXavier Stanton
311211
$endgroup$
closed as unclear what you're asking by Lord Shark the Unknown, Xander Henderson, Cesareo, amWhy, KReiser Dec 8 '18 at 0:15
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
So, this strange thought popped up into my head. You know how we call ${x^2}$ squaring due to the fact that what you're essentially doing is finding the area of a square with side length $x$? The same goes for cubing. Saying ${x^3}$ is really going to give you the volume of a cube with side length $x$. Now, what if I tried to coin a term that would take this -ing pattern to another level with ${x^4}$? This would technically give me the 4D volume, per se, of a tesseract(a 4D cube). So, couldn't this really be thought of as "tesseracting" a number?
In fact, I may have a deduction/thought. Saying ${x^n}$ could just be thought of as n-cubing a number. A square can be thought of as a cube in 2D. As in, a cube with only length and height, no depth. So, saying ${x^2}$ can be seen as 2-cubing, or squaring a number. The same goes for ${x^3}$. You are 3-cubing, or just cubing, a number. So it seems this n-cubing pattern holds. So, why not extend it to the tesseract? Why isn't ${x^4}$ just thought of as 4-cubing or "tesseracting"? The pattern I thought of would still hold.
Also, do you mind going easy with the criticisms? I'm not trying to sound like a you-know-what, but just keep in mind I'm extremely amateur and only in 11th grade. And since it seems like this is original to my thoughts, I'm a bit overexcited about this thought.
exponentiation
asked Dec 7 '18 at 3:17
Xavier StantonXavier Stanton
311211
$endgroup$
closed as unclear what you're asking by Lord Shark the Unknown, Xander Henderson, Cesareo, amWhy, KReiser Dec 8 '18 at 0:15
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
So, this strange thought popped up into my head. You know how we call ${x^2}$ squaring due to the fact that what you're essentially doing is finding the area of a square with side length $x$? The same goes for cubing. Saying ${x^3}$ is really going to give you the volume of a cube with side length $x$. Now, what if I tried to coin a term that would take this -ing pattern to another level with ${x^4}$? This would technically give me the 4D volume, per se, of a tesseract(a 4D cube). So, couldn't this really be thought of as "tesseracting" a number?
In fact, I may have a deduction/thought. Saying ${x^n}$ could just be thought of as n-cubing a number. A square can be thought of as a cube in 2D. As in, a cube with only length and height, no depth. So, saying ${x^2}$ can be seen as 2-cubing, or squaring a number. The same goes for ${x^3}$. You are 3-cubing, or just cubing, a number. So it seems this n-cubing pattern holds. So, why not extend it to the tesseract? Why isn't ${x^4}$ just thought of as 4-cubing or "tesseracting"? The pattern I thought of would still hold.
Also, do you mind going easy with the criticisms? I'm not trying to sound like a you-know-what, but just keep in mind I'm extremely amateur and only in 11th grade. And since it seems like this is original to my thoughts, I'm a bit overexcited about this thought.
exponentiation
asked Dec 7 '18 at 3:17
Xavier StantonXavier Stanton
311211
$endgroup$
So, this strange thought popped up into my head. You know how we call ${x^2}$ squaring due to the fact that what you're essentially doing is finding the area of a square with side length $x$? The same goes for cubing. Saying ${x^3}$ is really going to give you the volume of a cube with side length $x$. Now, what if I tried to coin a term that would take this -ing pattern to another level with ${x^4}$? This would technically give me the 4D volume, per se, of a tesseract(a 4D cube). So, couldn't this really be thought of as "tesseracting" a number?
In fact, I may have a deduction/thought. Saying ${x^n}$ could just be thought of as n-cubing a number. A square can be thought of as a cube in 2D. As in, a cube with only length and height, no depth. So, saying ${x^2}$ can be seen as 2-cubing, or squaring a number. The same goes for ${x^3}$. You are 3-cubing, or just cubing, a number. So it seems this n-cubing pattern holds. So, why not extend it to the tesseract? Why isn't ${x^4}$ just thought of as 4-cubing or "tesseracting"? The pattern I thought of would still hold.
Also, do you mind going easy with the criticisms? I'm not trying to sound like a you-know-what, but just keep in mind I'm extremely amateur and only in 11th grade. And since it seems like this is original to my thoughts, I'm a bit overexcited about this thought.
exponentiation
exponentiation
asked Dec 7 '18 at 3:17
Xavier StantonXavier Stanton
311211
asked Dec 7 '18 at 3:17
Xavier StantonXavier Stanton
311211
asked Dec 7 '18 at 3:17
Xavier StantonXavier Stanton
311211
asked Dec 7 '18 at 3:17
Xavier StantonXavier Stanton
311211
asked Dec 7 '18 at 3:17
Xavier StantonXavier Stanton
311211
311211
closed as unclear what you're asking by Lord Shark the Unknown, Xander Henderson, Cesareo, amWhy, KReiser Dec 8 '18 at 0:15
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Lord Shark the Unknown, Xander Henderson, Cesareo, amWhy, KReiser Dec 8 '18 at 0:15
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Mostly this naming convention breaks down for two reasons:
1) We don't have easy to remember fancy names for every dimension of products of the unit interval.
2) Saying "$n$-cubing" is potentially ambiguous and sounds very awkward when $n=3$. The typical "to the $n$" rolls off of the tongue and leaves no room for doubt.
answered Dec 7 '18 at 3:20
RandomMathGuyRandomMathGuy
1192
$endgroup$
$begingroup$
I see, but then why even give special names to the 2nd and 3rd power? Also, it was just a pattern I was thinking about, sort of connecting exponentiation to dimensional geometry.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:21
1
$begingroup$
@XavierStanton Historical reasons mostly. The Greeks did a lot of geometry in two and three dimensions, so we usually have special names there. Also, life has three dimensions, and paper has two. As to why the tesseract has a name, I am unsure, but it is probably something very esoteric and not at all meaningful to the math community.
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:23
$begingroup$
I personally prefer the term "hypercube" to tesseract myself but that's a matter of personal taste.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
1
$begingroup$
Oh, and quickly Googling, the origin of the term per Wikipedia - "According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες (téssereis aktines, "four rays"), referring to the four lines from each vertex to other vertices.[4] In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract"."
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
$begingroup$
@EeveeTrainer For sure, but only because of Cube 2: Hypercube
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:26
add a comment |
$begingroup$
I mean, it's legitimate, but people find thinking in higher dimensions - some even in just three - really difficult. So in a sense I believe it has a nice geometric intuition to it, but people just don't like thinking in these higher dimensions unless necessary. It might also be a remnant from a time when thinking about higher dimensions just was brushed off as being nonsensical or irrelevant or unimportant.
It also just doesn't roll that nicely off the tongue, personally. I'd sooner just say "to the fourth power" than "tessaracted" or "4-cubed". Of course, that's anecdotal and moreso a matter of personal taste.
answered Dec 7 '18 at 3:21
Eevee TrainerEevee Trainer
5,7961936
$endgroup$
$begingroup$
I said the same thing to the other comment, why have the terms squaring and cubing then?
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:22
$begingroup$
Because it's easier to think in the lower dimensions, resulting in much easier to understand geometric analogues. "Square" and "cube" are also relatively easy to say, as well as very familiar terms, whereas most people aren't familiar with a tessaract (unless you want to talk about the Marvel Comic Universe), just as one example - and at higher dimensions even that reference goes away.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:24
$begingroup$
LOL at the Marvel reference
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:25
$begingroup$
Also, I will admit, after the tesseract, there's no special names for the 5-hypercube, 6-hypercube, etc.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:27
add a comment |
$begingroup$
I think this is a really good way to bring geometric intuition into exponentiation. I'm not sure "tesseract" is universally the term for the "4-cube," but "4-cubing" seems great.
answered Dec 7 '18 at 3:22
Y. FormanY. Forman
11.5k523
$endgroup$
$begingroup$
It's the technical term. I looked it up.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:23
$begingroup$
@XavierStanton Okay then. "Tesseracting" it is.
$endgroup$
– Y. Forman
Dec 7 '18 at 3:24
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Mostly this naming convention breaks down for two reasons:
1) We don't have easy to remember fancy names for every dimension of products of the unit interval.
2) Saying "$n$-cubing" is potentially ambiguous and sounds very awkward when $n=3$. The typical "to the $n$" rolls off of the tongue and leaves no room for doubt.
answered Dec 7 '18 at 3:20
RandomMathGuyRandomMathGuy
1192
$endgroup$
$begingroup$
I see, but then why even give special names to the 2nd and 3rd power? Also, it was just a pattern I was thinking about, sort of connecting exponentiation to dimensional geometry.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:21
1
$begingroup$
@XavierStanton Historical reasons mostly. The Greeks did a lot of geometry in two and three dimensions, so we usually have special names there. Also, life has three dimensions, and paper has two. As to why the tesseract has a name, I am unsure, but it is probably something very esoteric and not at all meaningful to the math community.
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:23
$begingroup$
I personally prefer the term "hypercube" to tesseract myself but that's a matter of personal taste.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
1
$begingroup$
Oh, and quickly Googling, the origin of the term per Wikipedia - "According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες (téssereis aktines, "four rays"), referring to the four lines from each vertex to other vertices.[4] In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract"."
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
$begingroup$
@EeveeTrainer For sure, but only because of Cube 2: Hypercube
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:26
add a comment |
$begingroup$
Mostly this naming convention breaks down for two reasons:
1) We don't have easy to remember fancy names for every dimension of products of the unit interval.
2) Saying "$n$-cubing" is potentially ambiguous and sounds very awkward when $n=3$. The typical "to the $n$" rolls off of the tongue and leaves no room for doubt.
answered Dec 7 '18 at 3:20
RandomMathGuyRandomMathGuy
1192
$endgroup$
$begingroup$
I see, but then why even give special names to the 2nd and 3rd power? Also, it was just a pattern I was thinking about, sort of connecting exponentiation to dimensional geometry.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:21
1
$begingroup$
@XavierStanton Historical reasons mostly. The Greeks did a lot of geometry in two and three dimensions, so we usually have special names there. Also, life has three dimensions, and paper has two. As to why the tesseract has a name, I am unsure, but it is probably something very esoteric and not at all meaningful to the math community.
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:23
$begingroup$
I personally prefer the term "hypercube" to tesseract myself but that's a matter of personal taste.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
1
$begingroup$
Oh, and quickly Googling, the origin of the term per Wikipedia - "According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες (téssereis aktines, "four rays"), referring to the four lines from each vertex to other vertices.[4] In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract"."
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
$begingroup$
@EeveeTrainer For sure, but only because of Cube 2: Hypercube
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:26
add a comment |
$begingroup$
Mostly this naming convention breaks down for two reasons:
1) We don't have easy to remember fancy names for every dimension of products of the unit interval.
2) Saying "$n$-cubing" is potentially ambiguous and sounds very awkward when $n=3$. The typical "to the $n$" rolls off of the tongue and leaves no room for doubt.
answered Dec 7 '18 at 3:20
RandomMathGuyRandomMathGuy
1192
$endgroup$
Mostly this naming convention breaks down for two reasons:
1) We don't have easy to remember fancy names for every dimension of products of the unit interval.
2) Saying "$n$-cubing" is potentially ambiguous and sounds very awkward when $n=3$. The typical "to the $n$" rolls off of the tongue and leaves no room for doubt.
answered Dec 7 '18 at 3:20
RandomMathGuyRandomMathGuy
1192
answered Dec 7 '18 at 3:20
RandomMathGuyRandomMathGuy
1192
answered Dec 7 '18 at 3:20
RandomMathGuyRandomMathGuy
1192
answered Dec 7 '18 at 3:20
RandomMathGuyRandomMathGuy
1192
1192
$begingroup$
I see, but then why even give special names to the 2nd and 3rd power? Also, it was just a pattern I was thinking about, sort of connecting exponentiation to dimensional geometry.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:21
1
$begingroup$
@XavierStanton Historical reasons mostly. The Greeks did a lot of geometry in two and three dimensions, so we usually have special names there. Also, life has three dimensions, and paper has two. As to why the tesseract has a name, I am unsure, but it is probably something very esoteric and not at all meaningful to the math community.
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:23
$begingroup$
I personally prefer the term "hypercube" to tesseract myself but that's a matter of personal taste.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
1
$begingroup$
Oh, and quickly Googling, the origin of the term per Wikipedia - "According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες (téssereis aktines, "four rays"), referring to the four lines from each vertex to other vertices.[4] In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract"."
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
$begingroup$
@EeveeTrainer For sure, but only because of Cube 2: Hypercube
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:26
add a comment |
$begingroup$
I see, but then why even give special names to the 2nd and 3rd power? Also, it was just a pattern I was thinking about, sort of connecting exponentiation to dimensional geometry.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:21
1
$begingroup$
@XavierStanton Historical reasons mostly. The Greeks did a lot of geometry in two and three dimensions, so we usually have special names there. Also, life has three dimensions, and paper has two. As to why the tesseract has a name, I am unsure, but it is probably something very esoteric and not at all meaningful to the math community.
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:23
$begingroup$
I personally prefer the term "hypercube" to tesseract myself but that's a matter of personal taste.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
1
$begingroup$
Oh, and quickly Googling, the origin of the term per Wikipedia - "According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες (téssereis aktines, "four rays"), referring to the four lines from each vertex to other vertices.[4] In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract"."
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
$begingroup$
@EeveeTrainer For sure, but only because of Cube 2: Hypercube
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:26
$begingroup$
I see, but then why even give special names to the 2nd and 3rd power? Also, it was just a pattern I was thinking about, sort of connecting exponentiation to dimensional geometry.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:21
$begingroup$
I see, but then why even give special names to the 2nd and 3rd power? Also, it was just a pattern I was thinking about, sort of connecting exponentiation to dimensional geometry.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:21
1
1
$begingroup$
@XavierStanton Historical reasons mostly. The Greeks did a lot of geometry in two and three dimensions, so we usually have special names there. Also, life has three dimensions, and paper has two. As to why the tesseract has a name, I am unsure, but it is probably something very esoteric and not at all meaningful to the math community.
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:23
$begingroup$
@XavierStanton Historical reasons mostly. The Greeks did a lot of geometry in two and three dimensions, so we usually have special names there. Also, life has three dimensions, and paper has two. As to why the tesseract has a name, I am unsure, but it is probably something very esoteric and not at all meaningful to the math community.
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:23
$begingroup$
I personally prefer the term "hypercube" to tesseract myself but that's a matter of personal taste.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
$begingroup$
I personally prefer the term "hypercube" to tesseract myself but that's a matter of personal taste.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
1
1
$begingroup$
Oh, and quickly Googling, the origin of the term per Wikipedia - "According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες (téssereis aktines, "four rays"), referring to the four lines from each vertex to other vertices.[4] In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract"."
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
$begingroup$
Oh, and quickly Googling, the origin of the term per Wikipedia - "According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες (téssereis aktines, "four rays"), referring to the four lines from each vertex to other vertices.[4] In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract"."
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:25
$begingroup$
@EeveeTrainer For sure, but only because of Cube 2: Hypercube
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:26
$begingroup$
@EeveeTrainer For sure, but only because of Cube 2: Hypercube
$endgroup$
– RandomMathGuy
Dec 7 '18 at 3:26
add a comment |
$begingroup$
I mean, it's legitimate, but people find thinking in higher dimensions - some even in just three - really difficult. So in a sense I believe it has a nice geometric intuition to it, but people just don't like thinking in these higher dimensions unless necessary. It might also be a remnant from a time when thinking about higher dimensions just was brushed off as being nonsensical or irrelevant or unimportant.
It also just doesn't roll that nicely off the tongue, personally. I'd sooner just say "to the fourth power" than "tessaracted" or "4-cubed". Of course, that's anecdotal and moreso a matter of personal taste.
answered Dec 7 '18 at 3:21
Eevee TrainerEevee Trainer
5,7961936
$endgroup$
$begingroup$
I said the same thing to the other comment, why have the terms squaring and cubing then?
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:22
$begingroup$
Because it's easier to think in the lower dimensions, resulting in much easier to understand geometric analogues. "Square" and "cube" are also relatively easy to say, as well as very familiar terms, whereas most people aren't familiar with a tessaract (unless you want to talk about the Marvel Comic Universe), just as one example - and at higher dimensions even that reference goes away.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:24
$begingroup$
LOL at the Marvel reference
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:25
$begingroup$
Also, I will admit, after the tesseract, there's no special names for the 5-hypercube, 6-hypercube, etc.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:27
add a comment |
$begingroup$
I mean, it's legitimate, but people find thinking in higher dimensions - some even in just three - really difficult. So in a sense I believe it has a nice geometric intuition to it, but people just don't like thinking in these higher dimensions unless necessary. It might also be a remnant from a time when thinking about higher dimensions just was brushed off as being nonsensical or irrelevant or unimportant.
It also just doesn't roll that nicely off the tongue, personally. I'd sooner just say "to the fourth power" than "tessaracted" or "4-cubed". Of course, that's anecdotal and moreso a matter of personal taste.
answered Dec 7 '18 at 3:21
Eevee TrainerEevee Trainer
5,7961936
$endgroup$
$begingroup$
I said the same thing to the other comment, why have the terms squaring and cubing then?
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:22
$begingroup$
Because it's easier to think in the lower dimensions, resulting in much easier to understand geometric analogues. "Square" and "cube" are also relatively easy to say, as well as very familiar terms, whereas most people aren't familiar with a tessaract (unless you want to talk about the Marvel Comic Universe), just as one example - and at higher dimensions even that reference goes away.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:24
$begingroup$
LOL at the Marvel reference
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:25
$begingroup$
Also, I will admit, after the tesseract, there's no special names for the 5-hypercube, 6-hypercube, etc.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:27
add a comment |
$begingroup$
I mean, it's legitimate, but people find thinking in higher dimensions - some even in just three - really difficult. So in a sense I believe it has a nice geometric intuition to it, but people just don't like thinking in these higher dimensions unless necessary. It might also be a remnant from a time when thinking about higher dimensions just was brushed off as being nonsensical or irrelevant or unimportant.
It also just doesn't roll that nicely off the tongue, personally. I'd sooner just say "to the fourth power" than "tessaracted" or "4-cubed". Of course, that's anecdotal and moreso a matter of personal taste.
answered Dec 7 '18 at 3:21
Eevee TrainerEevee Trainer
5,7961936
$endgroup$
I mean, it's legitimate, but people find thinking in higher dimensions - some even in just three - really difficult. So in a sense I believe it has a nice geometric intuition to it, but people just don't like thinking in these higher dimensions unless necessary. It might also be a remnant from a time when thinking about higher dimensions just was brushed off as being nonsensical or irrelevant or unimportant.
It also just doesn't roll that nicely off the tongue, personally. I'd sooner just say "to the fourth power" than "tessaracted" or "4-cubed". Of course, that's anecdotal and moreso a matter of personal taste.
answered Dec 7 '18 at 3:21
Eevee TrainerEevee Trainer
5,7961936
answered Dec 7 '18 at 3:21
Eevee TrainerEevee Trainer
5,7961936
answered Dec 7 '18 at 3:21
Eevee TrainerEevee Trainer
5,7961936
answered Dec 7 '18 at 3:21
Eevee TrainerEevee Trainer
5,7961936
5,7961936
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I said the same thing to the other comment, why have the terms squaring and cubing then?
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– Xavier Stanton
Dec 7 '18 at 3:22
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Because it's easier to think in the lower dimensions, resulting in much easier to understand geometric analogues. "Square" and "cube" are also relatively easy to say, as well as very familiar terms, whereas most people aren't familiar with a tessaract (unless you want to talk about the Marvel Comic Universe), just as one example - and at higher dimensions even that reference goes away.
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– Eevee Trainer
Dec 7 '18 at 3:24
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LOL at the Marvel reference
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– Xavier Stanton
Dec 7 '18 at 3:25
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Also, I will admit, after the tesseract, there's no special names for the 5-hypercube, 6-hypercube, etc.
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– Xavier Stanton
Dec 7 '18 at 3:27
add a comment |
$begingroup$
I said the same thing to the other comment, why have the terms squaring and cubing then?
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:22
$begingroup$
Because it's easier to think in the lower dimensions, resulting in much easier to understand geometric analogues. "Square" and "cube" are also relatively easy to say, as well as very familiar terms, whereas most people aren't familiar with a tessaract (unless you want to talk about the Marvel Comic Universe), just as one example - and at higher dimensions even that reference goes away.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:24
$begingroup$
LOL at the Marvel reference
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:25
$begingroup$
Also, I will admit, after the tesseract, there's no special names for the 5-hypercube, 6-hypercube, etc.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:27
$begingroup$
I said the same thing to the other comment, why have the terms squaring and cubing then?
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:22
$begingroup$
I said the same thing to the other comment, why have the terms squaring and cubing then?
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:22
$begingroup$
Because it's easier to think in the lower dimensions, resulting in much easier to understand geometric analogues. "Square" and "cube" are also relatively easy to say, as well as very familiar terms, whereas most people aren't familiar with a tessaract (unless you want to talk about the Marvel Comic Universe), just as one example - and at higher dimensions even that reference goes away.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:24
$begingroup$
Because it's easier to think in the lower dimensions, resulting in much easier to understand geometric analogues. "Square" and "cube" are also relatively easy to say, as well as very familiar terms, whereas most people aren't familiar with a tessaract (unless you want to talk about the Marvel Comic Universe), just as one example - and at higher dimensions even that reference goes away.
$endgroup$
– Eevee Trainer
Dec 7 '18 at 3:24
$begingroup$
LOL at the Marvel reference
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:25
$begingroup$
LOL at the Marvel reference
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:25
$begingroup$
Also, I will admit, after the tesseract, there's no special names for the 5-hypercube, 6-hypercube, etc.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:27
$begingroup$
Also, I will admit, after the tesseract, there's no special names for the 5-hypercube, 6-hypercube, etc.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:27
add a comment |
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I think this is a really good way to bring geometric intuition into exponentiation. I'm not sure "tesseract" is universally the term for the "4-cube," but "4-cubing" seems great.
answered Dec 7 '18 at 3:22
Y. FormanY. Forman
11.5k523
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It's the technical term. I looked it up.
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– Xavier Stanton
Dec 7 '18 at 3:23
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@XavierStanton Okay then. "Tesseracting" it is.
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– Y. Forman
Dec 7 '18 at 3:24
add a comment |
$begingroup$
I think this is a really good way to bring geometric intuition into exponentiation. I'm not sure "tesseract" is universally the term for the "4-cube," but "4-cubing" seems great.
answered Dec 7 '18 at 3:22
Y. FormanY. Forman
11.5k523
$endgroup$
$begingroup$
It's the technical term. I looked it up.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:23
$begingroup$
@XavierStanton Okay then. "Tesseracting" it is.
$endgroup$
– Y. Forman
Dec 7 '18 at 3:24
add a comment |
$begingroup$
I think this is a really good way to bring geometric intuition into exponentiation. I'm not sure "tesseract" is universally the term for the "4-cube," but "4-cubing" seems great.
answered Dec 7 '18 at 3:22
Y. FormanY. Forman
11.5k523
$endgroup$
I think this is a really good way to bring geometric intuition into exponentiation. I'm not sure "tesseract" is universally the term for the "4-cube," but "4-cubing" seems great.
answered Dec 7 '18 at 3:22
Y. FormanY. Forman
11.5k523
answered Dec 7 '18 at 3:22
Y. FormanY. Forman
11.5k523
answered Dec 7 '18 at 3:22
Y. FormanY. Forman
11.5k523
answered Dec 7 '18 at 3:22
Y. FormanY. Forman
11.5k523
11.5k523
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It's the technical term. I looked it up.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:23
$begingroup$
@XavierStanton Okay then. "Tesseracting" it is.
$endgroup$
– Y. Forman
Dec 7 '18 at 3:24
add a comment |
$begingroup$
It's the technical term. I looked it up.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:23
$begingroup$
@XavierStanton Okay then. "Tesseracting" it is.
$endgroup$
– Y. Forman
Dec 7 '18 at 3:24
$begingroup$
It's the technical term. I looked it up.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:23
$begingroup$
It's the technical term. I looked it up.
$endgroup$
– Xavier Stanton
Dec 7 '18 at 3:23
$begingroup$
@XavierStanton Okay then. "Tesseracting" it is.
$endgroup$
– Y. Forman
Dec 7 '18 at 3:24
$begingroup$
@XavierStanton Okay then. "Tesseracting" it is.
$endgroup$
– Y. Forman
Dec 7 '18 at 3:24
add a comment |
