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Andrew,
I might have got the terminology slightly wrong then, do i mean a field? or
should i just have said a group under an operation? I was only trying to
put it into a mathematical construct but I don't have any actual experience
of doing this for a rubik's cube and I only did a half year of maths at uni
(doing comp sci now). You guys sound like you know what you're on about so
I'll let you take the wheel on this one. Thanks for recognising they are
not the same. It may be worth noting that if you convert an instance of my
definition into Joe'ls one and then back again you may or may not have what
you originally started with, as in Joel's every cube configuration is
unique and in mine there are an infinite amount of representations for any
given cube configuration.
Regards,
Sid
On 27 June 2016 at 21:07, apturner@mit.edu [4D_Cubing] <
4D_Cubing@yahoogroups.com> wrote:
>
>
> Dear Sid,
>
> The notation for the operation doesn't really matter. The issue is that
> without another binary operation, the object you're talking about cannot =
be
> a ring. A ring is a set together with two binary operations, one of which
> forms an abelian group with the set, and the other of which is associativ=
e
> and distributes over the group operation, but may or may not be commutati=
ve
> (and may or may not have an identity element, depending on how you define=
a
> ring). As far as I am aware, there is no way to turn the Rubik's Cube gro=
up
> into a ring in any way that relates to the physical reality of the puzzle=
.
>
> As for whether the groups are the same or not, my point was simply that
> the group Joel refers to and the group that you are actually defining in
> your post are isomorphic, which means that they are really just different
> ways of talking about the same mathematical structure. But it's true that
> sometimes it's good to be careful and actually acknowledge that two group=
s
> are not truly the exact same group, but rather isomorphic, so I will
> concede that point.
>
> Cheers,
> Andrew
>
>=20
>
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Dear Sid,
--------------A3ABF60C154E97558AA65FB6
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Well, welcome to both of you and to all of the recent solvers here due=20
to the Mathologer's video
=20
It's fine to lurk all you like but please do introduce yourself if you=20
can muster the courage. I know that it can be intimidating in a group of=20
such obviously smart people, but you wouldn't be here if you did not=20
belong. You're in the HOF and you also have the Mathologer's Seal of=20
Approval so don't sell yourselves short!
I do need to correct you slightly. We've actually been averaging about=20
15 first solutions a year for a while, not 6. But you're right that=20
we've had a big jump recently thanks to Burkard. Maybe 20 new entries in=20
a little over a week, and I'm guessing that we'll see at least that many=20
more in the weeks to come, if not several times that many. The funny=20
thing is that a lot of the people say the same things in their=20
submission emails. One common thing is a confession that they had=20
already looked at the puzzle years prior but came across it again and=20
decided to give it a try. I think what was missing was a good way to get=20
out the message or the proof that if you can solve the 3D puzzle, then=20
it really should not be very difficult to solve this one. It certainly=20
takes work--no question about that--but it's usually not nearly as hard=20
as people assume. So I hope that everyone will share the link with their=20
friends and social networks so that even more potential hyper-puzzlers=20
will face their fears and succeed.
-Melinda
On 6/27/2016 9:09 PM, Ashton Santee ashtonsantee@gmail.com [4D_Cubing]=20
wrote:
>
>
> Just as Chandler introduced himself I figured we could use this email=20
> thread for further introductions.
>
> My name is Ashton I hail from California USA. My education includes=20
> Computer Science and Engineering from the University of Nevada Reno,=20
> and a Masters in Business Administration from the University of=20
> Colorado, Denver. I love using the problem solving of computer science=20
> to solve business questions. I had seen the 3^4 online a few years=20
> ago, but had thought it would be beyond my level of solving. That was=20
> until I saw Mathologer's videos breaking down how to solve any twisty=20
> puzzle.
>
> I am glad to see that there are about 3 people finishing the 4D cube=20
> puzzle every day now, compared to the previous average of 6 per year.=20
> I want to encourage those who have just finished and are sitting=20
> quietly in this group to use this email thread to introduce=20
> themselves. Groups like this can be great for networking. You can find=20
> me on LinkedIn. If anyone has questions about business math I am=20
> always looking for a question to research and help others when I can.
>
> https://www.linkedin.com/in/ashtonsantee
> On Sat, Jun 25, 2016, 10:22 PM Chandler Meyers chandlerm2016@yahoo.com=20
>
> <4D_Cubing@yahoogroups.com
>
> I recently finished the 3x3x3x3 and was invited to introduce
> myself here. I live in Michigan in the USA and I am 18 years old.
> I will be attending the University of Michigan this fall. For fun,
> I have enjoyed twisty puzzles for years, though it is now a
> secondary hobby to speedrunning video games. I remember seeing the
> MC4D program years back and never thinking I would be able to do
> it, but after watching Mathologer's video I realized that it
> wasn't so bad if I just applied the same algorithms and
> commutators that worked on a 3x3x3 puzzle. Once I got started, it
> was a fun and relatively smooth journey to solving the puzzle.
> Thanks to him for the inspiration and of course to everyone who
> has contributed to making such an awesome program :)
>
> --=20
> Ashton Santee
> 916-7766-775
>
>
>=20
--------------A3ABF60C154E97558AA65FB6
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">
Well, welcome to both of you and to all of the recent solvers here
due to the
Mathologer's video. It's fine to lurk all you like but please
do introduce yourself if you can muster the courage. I know that it
can be intimidating in a group of such obviously smart people, but
you wouldn't be here if you did not belong. You're in the HOF and
you also have the Mathologer's Seal of Approval so don't sell
yourselves short!
I do need to correct you slightly. We've actually been averaging
about 15 first solutions a year for a while, not 6. But you're right
that we've had a big jump recently thanks to Burkard. Maybe 20 new
entries in a little over a week, and I'm guessing that we'll see at
least that many more in the weeks to come, if not several times that
many. The funny thing is that a lot of the people say the same
things in their submission emails. One common thing is a confession
that they had already looked at the puzzle years prior but came
across it again and decided to give it a try. I think what was
missing was a good way to get out the message or the proof that if
you can solve the 3D puzzle, then it really should not be very
difficult to solve this one. It certainly takes work--no question
about that--but it's usually not nearly as hard as people assume. So
I hope that everyone will share the link with their friends and
social networks so that even more potential hyper-puzzlers will face
their fears and succeed.
-Melinda
ail.com"
type=3D"cite">
could use this email thread for further introductions.=C2=A0
education includes Computer Science and Engineering from the
University of Nevada Reno, and a Masters in Business
Administration from the University of Colorado, Denver. I love
using the problem solving of computer science to solve business
questions. I had seen the 3^4 online a few years ago, but had
thought it would be beyond my level of solving. That was until I
saw Mathologer's videos breaking down how to solve any twisty
puzzle.=C2=A0
finishing the 4D cube puzzle every day now, compared to the
previous average of 6 per year. I want to encourage those who
have just finished and are sitting quietly in this group to use
this email thread to introduce themselves. Groups like this can
be great for networking. You can find me on LinkedIn. If anyone
has questions about business math I am always looking for a
question to research and help others when I can.
href=3D"https://www.linkedin.com/in/ashtonsantee">https://www.linke=
din.com/in/ashtonsantee
"
target=3D"_blank">"mailto:chandlerm2016@yahoo.com">chandlerm2016@yahoo.com [4D_Cubing=
] <
href=3D"mailto:4D_Cubing@yahoogroups.com" target=3D"_blank">class=3D"moz-txt-link-abbreviated" href=3D"mailto:4D_Cubing@yahoogroups.com=
">4D_Cubing@yahoogroups.com>
wrote:
.8ex;border-left:1px #ccc solid;padding-left:1ex"
id=3D"gmail_block_quote0">
=C2=A0
ca
Neue,Helvetica,Arial,Lucida
Grande,sans-serif;font-size:16px">
was invited to introduce myself here. I live in
Michigan in the USA and I am 18 years old. I will
be attending the University of Michigan this fall.
For fun, I have enjoyed twisty puzzles for years,
though it is now a secondary hobby to speedrunning
video games. I remember seeing the MC4D program
years back and never thinking I would be able to
do it, but after watching Mathologer's video I
realized that it wasn't so bad if I just applied
the same algorithms and commutators that worked on
a 3x3x3 puzzle. Once I got started, it was a fun
and relatively smooth journey to solving the
puzzle. Thanks to him for the inspiration and of
course to everyone who has contributed to making
such an awesome program :)
=20=20=20=20=20=20
--------------A3ABF60C154E97558AA65FB6--
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I also play the flute. I had tried a lot of different instruments=20
(piano, marimba, trombone, clarinet) but none of them really grabbed me=20
until I found the flute. Piano was great for giving me a grounding for=20
music theory, but it's one of the more difficult instruments so it's=20
difficult to recommend. Recorders and penny whistles are great ways to=20
see if someone might be interested in the flute and similar instruments=20
because they produce the sound naturally. With the flute you have to=20
learn to do that yourself and it's difficult to do well but satisfying=20
when you succeed. Mainly you want to produce a round and compact stream=20
of air and direct it at the far side of the hole so that the air gets=20
cut into two streams, one that goes into the flute and the other that=20
goes across the top. This makes the stream waggle back and forth,=20
producing the tone. You need to adjust your aim slightly depending upon=20
pitch but that's the basic idea.
Interest and skill in music and math tend to go together though I don't=20
think anyone yet knows why. I believe that our general interest in music=20
is a byproduct of our evolution of language. I think that music=20
stimulates the same brain regions as language listening and speaking.=20
Language appears to be based around associative stories, and musical=20
pieces seem to follow similar patterns of story arcs and include=20
patterns such as call-and-response, etc. I don't know what music's=20
connection is with math but it's clearly there. Maybe something to do=20
with finding, following and producing rules and patterns? I'm betting=20
someone will figure it out soon.
Just for fun I created a group poll to find out what instruments are=20
popular in our group. Please everyone go there=20
select your instrument if you have one. This is not to ask your favorite=20
instrument to listen to, It should be the one that feels like it was=20
made for you to play. I only listed a few popular instruments. Please=20
add yours if you don't find it listed.
-Melinda
On 7/13/2016 2:54 PM, Ray Zhao thermostatico@gmail.com [4D_Cubing] wrote:
>
>
> Hi Edward,
>
> First of all, I love listing things!...I just don't do it often.
>
> Anyway, congrats on the solve. 1200+ moves doesn't sound like that=20
> much considering how it's your first solve; I bet if you solve it once=20
> or twice the number will go down to around 1000 (or even less). Layer=20
> by layer is a good idea; you can even use CFOP on it. However, I'm not=20
> sure about solving the 5^4 one layer at a time.
>
> Number theory is cool sometimes, and I mean sometimes since modular=20
> arithmetic didn't click for me last term (especially non-linear=20
> congruences) and since I often add up two-digit numbers wrong in my=20
> head. Maybe once I get those sorted out, I'll continue reading about=20
> numbers. The research + simulations part seems real fun though.
>
> Also, you play flute? I've always wanted to learn how to play the=20
> flute...except when I have more energy. A tenor sax would probably w=20
> ork better in that case. Anyway, how to make a note come out on the=20
> flute is still a great mystery to me. Actually, music and math is=20
> still a great mystery to me in general. Is number theory involved there?
>
>
> 10/10 suggest you go solve the 5^4 or at least the 4^4,
>
> Ray
>
>
>
>=20
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">
I also play the flute. I had tried a lot of different instruments
(piano, marimba, trombone, clarinet) but none of them really grabbed
me until I found the flute. Piano was great for giving me a
grounding for music theory, but it's one of the more difficult
instruments so it's difficult to recommend. Recorders and penny
whistles are great ways to see if someone might be interested in the
flute and similar instruments because they produce the sound
naturally. With the flute you have to learn to do that yourself and
it's difficult to do well but satisfying when you succeed. Mainly
you want to produce a round and compact stream of air and direct it
at the far side of the hole so that the air gets cut into two
streams, one that goes into the flute and the other that goes across
the top. This makes the stream waggle back and forth, producing the
tone. You need to adjust your aim slightly depending upon pitch but
that's the basic idea.
Interest and skill in music and math tend to go together though I
don't think anyone yet knows why. I believe that our general
interest in music is a byproduct of our evolution of language. I
think that music stimulates the same brain regions as language
listening and speaking. Language appears to be based around
associative stories, and musical pieces seem to follow similar
patterns of story arcs and include patterns such as
call-and-response, etc. I don't know what music's connection is with
math but it's clearly there. Maybe something to do with finding,
following and producing rules and patterns? I'm betting someone will
figure it out soon.
Just for fun I created a group poll to find out what instruments are
popular in our group. Please everyone go
7602">there
and select your instrument if you have one. This is not to ask your
favorite instrument to listen to, It should be the one that feels
like it was made for you to play. I only listed a few popular
instruments. Please add yours if you don't find it listed.
-Melinda
com"
type=3D"cite">
First of all, I love listing things!...I just don't do
it often.
Anyway, congrats on the solve. 1200+ moves doesn't sound
like that much considering how it's your first solve; I
bet if you solve it once or twice the number will go down
to around 1000 (or even less). Layer by layer is a good
idea; you can even use CFOP on it. However, I'm not sure
about solving the 5^4 one layer at a time.
Number theory is cool sometimes, and I mean sometimes since
modular arithmetic didn't click for me last term (especially
non-linear congruences) and since I often add up two-digit
numbers wrong in my head. Maybe once I get those sorted out,
I'll continue reading about numbers. The research +
simulations part seems real fun though.
Also, you play flute? I've always wanted to learn how to play
the flute...except when I have more energy. A tenor sax would
probably w ork better in that case. Anyway, how to make a note
come out on the flute is still a great mystery to me.
Actually, music and math is still a great mystery to me in
general. Is number theory involved there?
=20=20=20=20=20=20
--------------69A57CF669C05DBB343DFE63--
--94eb2c1243d639c51405378e2c9b
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Huh, I actually got a few things going on the music side -- I play violin
(and some piano) and enjoy teaching music theory, except no one wants to
learn it for fun so I don't end up teaching music theory.
"so that the air gets cut into two streams"
I guess that's the secret. I always assumed it was redirecting the air
completely over or completely into.
"Recorders and penny whistles are great ways to see if someone might be
interested in the flute and similar instruments because they produce the
sound naturally."
Recorder has a bad rep though -- most people play three distinct notes,
squeak four times during, and then stop playing it. Middle school strings
or band class is an ok motivator, though there, most people play just for
easy marks, based on my experiences.
"I don't know what music's connection is with math but it's clearly there."
Tonewise, I think it has to do with harmonics on a string and the overtone
scale. The Xenharmonic wiki really explores this, but it goes really far.
For example, I found this on the bottom of a page: "For the mathematically
inclined, this kind of diagram is closely related to the Riemann zeta
function
Actually, zeta function? I guess that's number theory. Welp, time to start
reading on number theory. @Edward maybe you can understand more of the wiki
in general; someone's gotta dumb it down for the casual reader eventually.
xP
Ray
--94eb2c1243d639c51405378e2c9b
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ide -- I play violin (and some piano) and enjoy teaching music theory, exce=
pt no one wants to learn it for fun so I don't end up teaching music th=
eory.
"so that the air gets cut into two
streams"
it was redirecting the air completely over or completely into.
whistles are great ways to see if someone might be interested in the
flute and similar instruments because they produce the sound
naturally."
ople play three distinct notes, squeak four times during, and then stop pla=
ying it. Middle school strings or band class is an ok motivator, though the=
re, most people play just for easy marks, based on my experiences.
&=
quot;I don't know what music's connection is with
math but it's clearly there."
it has to do with harmonics on a string and the overtone scale. The Xenharm=
onic wiki really explores this, but it goes really far. For example, I foun=
d this on the bottom of a page: "For the mathematically inclined, this=
kind of diagram is closely related to onic.wikispaces.com/The+Riemann+Zeta+Function+and+Tuning">the Riemann zeta =
function."
;s number theory. Welp, time to start reading on number theory. @Edward may=
be you can understand more of the wiki in general; someone's gotta dumb=
it down for the casual reader eventually. xP
v>
--94eb2c1243d639c51405378e2c9b--
From: "Eduard Baumann" <ed.baumann@bluewin.ch>
Date: Thu, 14 Jul 2016 11:53:52 +0200
Subject: Re: [MC4D] Re: Introductions!
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Concerning overtones.
Do you know that everybody can immediatly succeed in overtone singing (not =
a whole melody but one tone).
Make slowly the passage from german "u" to "german "=FC" or invers.
You are forming a filter for overtones which produces a gap in frequences a=
nd the impression of two distinct tones.
There is a lot information on internet (youtubes, tutorials)
Do english people know the german voyel "=FC" ?
The french stupide (st=FCpide) becomes stiupide.
=FC is between i end u (ou) : i ----- =FC ----- u
and overtone singing happens between =FC and u: =FC ----- x ----- u
Best regards
Ed
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>
succeed=20
in overtone singing (not a whole melody but one tone).
"german=20
"=FC" or invers.
ch=20
produces a gap in frequences and the impression of two distinct=20
tones.
utubes,=20
tutorials)
=FC"=20
?
stiupide.
nbsp; =20
i ----- =FC ----- u
nd=20
u: =FC ----- x ----- u
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