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While explaining things like triangles, light years and the ever
expanding universe, an 11 year old student of mine asked:
1. If the universe can be proven to be moving out from a single
center, then everything in our universe must be finite, with a
finite time/distance of everything from the
center.
2. But if the universe is finite and is all expanding, that means
there is something beyond everything in the universe,
something that defines "the beyond". So the universe cannot be
finite. It must be infinite.
3. But if the universe is infinite, it cannot have a single center
(or any finite number of centers, for that) from which
everything is expanding.
Interesting thoughts.
Why start with a "Big Bang", why not just believe something like the Casimir force exists if you've got a math space to put it in; the thing that mostly piles up everywhere is photons. Enough time you get matter then a gravitational singularity?
https://www.quora.c...u-get-matter-then-a
[beanangel, Dec 18 2020]
What are some great math memes for people 11-13?
https://www.quora.c...es-for-people-11-13
[beanangel, Dec 18 2020]
[link]
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Your student's thoughts are indeed interesting. The important
facts missing from her* thinking include the following: |
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A. The word "finite" and its cognates have come adrift from their
original metaphor. Originally, "finite" meant "having a boundary"
(implying something else beyond the boundary). Nowadays, it
doesn't. |
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B. The curvature of space-time. |
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But she's definitely asking the right sort of questions, and should
be encouraged. |
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The universe is not moving out from a single point, though. It's expanding from everywhere. It's like the surface of an inflating balloon. Imagine you're an ant on the surface of a balloon - it starts out tiny, and then gets bigger, but not from any single point. |
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Nice, probing the possibilities is definitely a sign of an opened mind and adds to the expansion of our universe.
Contrarily,
//The universe is not// |
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So my expanding stomach can be explained by the
expansion of the universe? |
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The twists and turns of a mandelbrot diagram are
encapsulated in a finite space, yet are infinitely windy
and,
from the perspective of someone zooming in at ever
greater
precision, ever-expanding. That expansion happens
irrespective of which point you zoom in on - so this
example
fits all the starting assumptions, and yet manages to skirt
the third conclusion. It is a fairly well studied pocket-
example of an object that is both finite and infinite at
the
same time. |
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Plus, you can express it, and all the complexity contained
within as: |
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(along with some contextual stuff about complex numbers
and counting how quickly the equation at each point z
zooms off to infinity) |
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[pertinax] is right - go back to your student and
ask them to tell you the difference between
'unbounded' and 'infinite'. Try and move the
conversation to a 2D rather than a 3D universe, as
it's easier to think about. For example, the
surface of the Earth is basically flat and 2D. It
is unbounded (i.e. doesn't have an edge) but is not
infinite. Likewise, if 3D space was wrapped around
on itself in 4D (like the 2D surface of the Earth
is wrapped around in 3D) what would that be like?
If you carried on in a straight line through space
in your spaceship would you return to where you
started? |
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// probing the possibilities is definitely a sign of an opened mind // |
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It's important that talent, curiosity and intellect like that are identified as early a possible, so that they can be nurtured and encouraged. |
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And also carefully noted for future reference as potential troublemakers.... |
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I think this illustrates why that way of looking at the
expansion of space is mistaken. I keep saying this, so I
may have done so on here, and if so I apologise: |
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Space is not a thing, containing locations. It's a
relationship between items which combines distance and
direction which seems on a small scale merely to involve
a limitless increase in distance and constancy of direction
between two items, which are locations. However, what
it in fact involves is an increase of distance to a maximum
in any given direction, beyond which the directions in
which the locations concerned reverse and the distance
between them reduces. Also, the maximum potential
distance between two locations is increasing. |
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The idea of an inflating universe expanding from a point
into pre-existing unoccupied hyperspace is metaphorical
(unless brane theory turns out to be true I suppose). |
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Give them a few more years of schooling and will
make them stop asking such interesting questions |
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Where do you end up if you go north from the North Pole? |
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You should beat your impudent student with a stick, pashute. Then send them to work down a mine. That's what the education system is for. |
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No, it's for teaching them to beat one another, without knowing why - just blindly obeying orders. |
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// Where do you end up if you go north from the North Pole? // |
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This student is clearly in need of behavior
modification
drugs such as
Ritalin or Adderall.(tm) This will calm the
inquisitive soul
and quash the troublesome spirit. Asking
questions,
playing, smiling, laughing or straying at any
time from
being blissfully, foaming at the mouth happy every
waking hour of the day may be signs of "Inquisitive
Spirit Disorder", "Independent Thought Syndrome"
or
"Subjugation Rejection Disease".* |
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Signed: Your fellow Halfbaker friend and not a
major drug
company at all. |
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*Side effects include zombieitus, glazed eyes,
voting
Democrat, caring about what happens in this
weeks
episode of any major network TV drama and
pretending
to like modern
music. Ask your doctor of mind numbing life
squashing
drugs are right for you. Doctorremulac3 and " Your
fellow
Halfbaker friend and not a major drug company at
all."
are registered trademarks of Merck and their
subsidiary
companies. All rights reserved. |
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Diseases do not have side-effects, by definition. |
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Voting Democrat has some VERY nasty side effects ... |
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//Diseases do not have side-effects, by
definition.// |
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Putting the asterisk was at the end of the
paragraph was
my attempt to loosely follow the format of a drug
commercial where statements about the product
and
imagery of its users are followed by a warning
about the
drug. Those warnings are not about being a happy
elderly
couple walking on the beach, being a grey haired
person
petting at a dog, or being a now cured middle aged
man
laughing at his salad. |
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So if you see such a commercial, know that you
may
suffer a potentially fatal brain aneurysm because
you
took the drug, not because you were playing
checkers
with your grandson while smiling. |
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On the other hand, I've always just made that
assumption. Maybe they're showing all the
activities you
should avoid while taking that drug. "I'm sorry,
were you
holding hands while walking on the beach while
taking
clidoprhophilozill? Didn't you see the commercial?
I'm
afraid we're going to have to deny your claim."
:) |
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Ask your doctor if becoming part of a mindless
hegemonic swarm is right for you... |
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LL. I won’t lie, if a commercial offered me that I wouldn’t
discount it without hearing them out. This “rebel till the
day I die” shit gets tiring. |
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Yes, but not necessarily cookies. Or milk. Milk and cookies can keep you awake. |
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// mindless hegemonic swarm // |
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Evil, relentless and overbearing, yes. Mindless, definitely not. |
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Firstly, I add my vote to those saying "encourage", "nurture", and other such words. The world needs more people who think deep thoughts like these.
Second, the idea of multiple dimensions should be introduced to the conversation (as others have mentioned). If (some of) the expansion is in a direction you can't really perceive, it's hard to grasp.
Third, (as per [zen_tom]), the Mandelbrot set is my (as yet un-used) argument against the usual creationist "you can't get complexity from simplicity" anti-evolution schtick.
More calculations (ie. more time) = more complexity and detail. |
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The only thing I have against creationists is that they are all
absolute cunting morons. |
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Not even considering signing up 'til the implants come in brass, leather and canvas. Just sayin'. |
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At the risk of being one of those, what exactly is
"cunting"? I hope it's not what I think it is because
if so, I've been very guilty of it. |
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"Eh, me and the guys are going out cunting." |
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"Oh, well, good luck! Have fun." |
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I think whenever I hear an Englishman use crude
slang I take it as a challenge. "Hmm, can I take this
any lower?" |
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I'd like to say I get shocked and my monocle drops
in my gin and tonic splashing my tunic but, well,
never been accused of being highbrow. |
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As for creationists, not sure I've ever met one. At
least not that I know of. If I do, I'll ask them if
they've ever been cunting. |
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You can't swing a dead cat around here and miss a
creationist. And for the record, they all vote
Republican. They're what's "special" about Indiana
and the rest of the Midwest. |
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Well, my additude is, somebody can believe in
Santa Claus, the Tooth Fairy and the Easter
Bunny, all combined into one bizarre
monster with multiple heads as long as it doesn't
affect me. |
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My main problem is with people who have so much
knowledge about the way thing are supposed to be
that I have to submit to their version of reality.
Even that wouldn't be a big deal but I always get to
pay for it. Our benevolent government sucks more
money from me every year than I made my entire
working career as a teenager, and I started working
at 13, making good money at the time. |
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That being said, seems like the country has more
than its fair share of creationists and communists.
Not a fan of either. They both do far too much
cunting. |
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And stop trying to change "cunting" into "cutting"
spell check. Don't get me started. |
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But what you're missing is that it does affect you.
Being in a nation surrounded by idiots most
definitely affects whether or not you move forwards
or backwards or sideways as a whole, and brain
cells devoted to theological nonsense could be
doing more useful tasks like inventing a cure to the
common cold or something. |
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<high fives [Rayfo]>
<wonders if high fiving is still hip>
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Not sure. My hips are pretty old. |
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//could be doing more useful tasks like inventing a
cure to the common cold or something// |
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These people obviously don't have high IQs so
there's not much brainpower to be freed by
convincing them the universe didn't spring out of
some superbeings boredom on a Saturday night. |
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My point is, these simple superstitious people don't
seem to want my money, the intellectual supermen
do. |
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But if you want to cure stupidity, good luck. Stupid
people have more kids than smart people and
that's just going to get worse. Doesn't matter what
tag you give one side or the other. The big stupid
just rolls on getting bigger and bigger while we
quibble about which part of the snowball is the
stupidest. |
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Stupid is a relative term that implies intelligence
existing somewhere. |
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In countries that are less preoccupied with stupidity,
the rising tide raises all boats. My guess is that
there are few libertarians, communists, and
creationists in countries with high satisfaction of
living. |
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Is there such a thing as a "I-don't-want-to-be-part-of-
any-group-itarian"? |
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Poor Pachute. What was the original idea again? |
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Some-one (I forget who...) once said (paraphrasing...): "I will only join a club that refuses to have me as a member".
Umm, sorry [pashute], I sort-of derailed the conversation there. Back to universes! |
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Yo Pash, are you at least enjoying your hijacked idea
chain? Want to join in? I just suggested stupid people
shouldn't have so many kids so we're probably coming
up on Godwin's law pretty soon, that's always fun. |
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Being a rebel against everything because it exists is
a pretty foolish position as well. |
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Wanna get a creationist all flummoxed? Quote
some of C. S. Lewis's more socialistic statements to
them sometime. |
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Who's a rebel against everything? |
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Sometimes people make self deprecating jokes to
lighten
things up. Gotta watch that I guess. |
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But religion and communism aren't "everything". In
my opinion they're two simplistic life manuals for
foolish people who can't think for themselves. |
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But that illustrates my problem with this whole
left/right paradigm. Believers in both sides think
that's the entire world, it's everything, there are
no other ways of looking at the world outside of
the Republican or Democrat view. |
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Thinking for youself and evaluating the
complexities of life on a case by case basis is
looked at by some as "foolish". |
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Precisely my point. My other point is that some
tasks take groups, and groups involve compromise. |
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That's fine, I just don't see the Republicans OR the
Democrats as doing much that I like. When either
side points to the other and says "They're horrible!"
there's a reason that they're usually right. |
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All the good stuff in the world comes from
motivated, smart people who come up with better
ideas, new approaches and processes or works of
art, not from the leadership class. |
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They just turn us against each other for fun and
profit. Me and you for agree on a lot of stuff, but
you've got the D on your uniform and I don't have
any insignia at all so that comes to the forefront
more often than not. |
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The only thing that's good about two horrible
political parties fighting for power is that one
keeps the other in check. It's when they agree on
something that I get nervous. |
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Luckily that doesn't happen very often. |
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There's something I've always wondered. What - in the
American context - is a libertarian? Wikipedia defines
libertarianism as "a collection of political philosophies and
movements that uphold liberty as a core principle", which
sounds basically good to me. But I am guessing that the
term has some other connotation in the US? |
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In my opinion, it's a political doctrine of minimal
government and free markets. |
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They get a bad rap as being anarchists but they believe in
laws and regulations, just laws and regulations that do
more good than harm. |
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The left thinks of them as wanting to let industry sell
poor people's body parts for profit before they're done
with them and the right thinks they're a bunch of godless
heathens. |
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I'm not very good at representing them or any other group
especially since there are a wide spectrum of views in
this group, like in any other political party. |
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Sometimes it's helpful to keep in mind that in both or our
countries we have libertarian, socialist, theocratic and all
sorts of political forces running things in various measure
at all times. It's not just who's in power now having total
say on the way we do things. |
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For me, I might favor a libertarian approach to
allowing a kid's lemonade stand to make money without a
license and a socialist approach to housing for those who
can't work due to physical or mental limitation. |
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But this case by case approach gets boring. We want to
line up on either side with our swords and shields and
charge at the other side. |
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Hey, I want to do that too, I just have yet to pick a side.
Maybe I'll just stand in the middle with a sword in either
hand and see what happens. It might work out. |
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// Who's a rebel against everything? // |
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I think it's good to be a rebel sometimes. |
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In the US, libertarians generally embrace private
market solutions to all problems be they feasible or
infeasible, distrust any sort of national solution, and
tend to see government as an evil to be destroyed or
minimized. They tend to exchange religious devotion
to theology for a religious devotion to theory and
ideology involving distrust of all authority, for which
the obvious irony tends to be lost, although there are
religious libertarians as well who would want the
church and/or God to obtain or show more power.
They are typically for deregulation in all directions,
but for some reason trust private enterprise to
always do the right thing, despite all evidence to the
contrary. |
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Like anarchists, they underappreciate the value of
community, except for some sacred devotion to the
Constitution as a near religious document. |
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Because of the undercurrent of distrust for authority,
they tend to be a nexus point accumulating anti-
vaxers, conspiracy theorists, drug freedom
proponents, Christian triumphialists, and anti-
scientific community types of all stripes. Any sort of
authority vexes them as an evil to be eliminated.
Social safety nets of any type be damned as a
perpetuating disease with a flawed premise. |
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The D on my uniform is not a permanent ink-job. It
was placed there as a reaction to the uncivility that I
saw growing in the R side. You don't mess with the
credit rating of the US as a political bargaining chip
and start leaning against the scientific community
and not endure my wrath. |
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Well, now that we've established that the southern
striped Libertarian has scales while the northern
Libertarian warbler has horns, let's look at an actual
Libertarian vs Democrat scenario. |
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The way we get around in the modern world is by taking
Uber or Lyft, two private companies that allow citizens to
act as taxi drivers using modern technology to hook up
with customers. It's revolutionized the way we get
around. Before this, one time I went on a day hike with
my family along the ocean in San Francisco. We waited at
the beach for hours for a taxi to pick us up and take us
back to our hotel. The cab company that had a monopoly
on transportation in this Democrat controlled city kept
saying "Tha nu ter yut?" (They're not there yet?) Finally,
tired and hungry, we were forced to hike miles back to
our hotel as the sun began to set and it started getting
cold. We luckily came across a museum that sold
little sandwiches so we didn't starve, but the system was
clearly broken. |
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Enter Uber and Lyft. The first big battle was getting past
the Democrat cronies of the cab industry. The cab
industry keeps competition out by very high license fees.
Costs about $100,000 if you want to drive a cab I've
heard. This keeps the competition away. In New York,
there was a big battle with the New York politicians
backing the cab companies as they fought to keep their
monopoly safe from competition and new, more effective
approaches. |
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But like the steam engine eventually wins over the horse
drawn carriage, the better way won out, but the battle's
not over. Democrats having failed to shut down the
competition of their cronies and payola dumpsters have
filed hundreds of regulation lawsuits in various cities
saying they need to get their cut. |
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Now I'm sure the spin is "We just want to make sure we
don't have axe murderers driving people around." but I
was watching during the early battles. The Democrats
fought tooth and nail to shut this thriving, vibrant and
important industry down because the existing cab
industry paid them to do so. |
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So I think in the overall battle of who has the stinkiest
butts, I'll concede that I don't have that information on
hand so if the Democrats say it's the Libertarians, ok, I'll
give them that one. But if after establishing the ranking
on the stinky butt scale we're to talk about specific
instances and issues, THAT I can do. |
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Need to say again though, while the Democrats are now
fighting to get their cut of these businesses, only
THREATENING to shut them down, but having followed
this battle
from it's beginning, I can tell you that the Democrat party
did everything in
its power to destroy these companies at the behest of the
democrat donor cab companies, not regulate them, shut
them down. |
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As far as Libertarians wanting to repeal drug laws, THAT
is true. Drug laws are stupid. They should be replaced by
civil liability laws as I've suggested. If you sell somebody
heroin and they die, you get to pay their family in a ten
million dollar lawsuit. Or we could just keep drugs off the
streets by regulation as we have so effectively all these
years. By the way, I'm very against recreational drug use.
I'm also against over use of alcohol, tobacco and sugar but
I think education is the way to fight these health
scourges, not laws that people won't follow anyway. |
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But what if you're a big drug company that wants to get
their share of all that sweet drug addict money out there?
Want
to know how to have the Democrat regulators
give the ok to whatever poison you're selling the public?
Nothing says "I'm a good Democrat who wants to work
within the system." like a suitcase full of cash. |
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We’ve all got a million stories about how this political
ideology failed or that one failed and look at what this lead
to. Trust me, I live in the original UAW union state. |
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You want to see a Republican cloud up and rain all over
you? Say something against whatever industry they’re
protecting. Try the coal industry, or saying that tobacco
causes cancer, or the sugar industry, or the farm corn
subsidy, or going after oil subsidies sometime.
You’re going to need more than a suitcase for the cash that
trades hands there. |
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And the Democrats DON'T take their orders from big
business? |
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I think they target the occasional industry like coal as a
warning to other industries to make sure that cash arrives
on time and without question, but the Democrats get
their money from big business and they deliver what
those businesses tell them to. |
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I'd love to see a study of who's more corrupt. In fact, I'd
love to see a little more scientific method applied to all
the issues we face but that gets complicated. Much easier
to just point out that the enemy has an orange face as
further proof that anybody who agrees with him on any
one issue is inferior. Battle over. |
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But if I absolutely have to defend someone, I'm a
registered Libertarian, not a Republican so I'll answer for
some of their sins, but the Republicans are on their own. |
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So, what's the standing of egalité and fraternité in the US? |
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A pox on all their houses. |
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While [Ray] is right that Libertarians attract their own brand
of fringe (as of course do the left and the right), the credo of
"first, leave people alone" is ultimately key to letting more
people live the way they want to live. |
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Community is great. Commune? Not so much. |
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//and the Democrats don’t...// |
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“Living the way you want to live” is one of those conflicting
goals that requires a few common but easily-disrupted
things, namely, air, water, food, safety, and some type of
shelter. |
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Too much of “leaving people alone” can result in the
disruption of any of the above at times. |
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What are those strange single quote things above the e’s?
We don’t
have to deal with those foreign-looking things in this
country. I’ll bet some immigrant brought snuck them in. |
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//So, what's the standing of egalité and fraternité in the
US?// |
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We're engaged in a sort of "cold civil war" right now so
there's none of that. Speaking of the French revolution
though, we've revived the popular guillotine show. We
don't actually cut off heads, we just say "J'accuse!!" and
hoist the transgressor up on the public stage. I'm talking
about all the dirt being dug up on sexual harassers from
years, sometimes decades old transgressions. Granted,
many of these guys deserve it, and I don't necessarily
think the prosecutions should stop. Yet. But I'm a little
concerned about how excited our society is about ruining
people. I don't know how much is prompted for the
concern for victims and how much is just a blood lust to
see heads roll. The peasants want blood, and we're
seeing a sort of purge that needs victims from all sides.
The left, interestingly enough, has lost the most leaders
in this. |
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After Trump won the election the left promised blood and
revolution but being un-able to perform it seems that the
masses are being given a sacrifice show completely un-
related to the election results that caused this war. |
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Anyway, I believe there's a link. The promise of revolution
wasn't realized so an easier target gets chosen. Can't get
the Republicans so let's get the Harvey Weinsteins. |
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To be clear, let's let the guillotine do its job, but let's
keep an eye on who we're lining up for this thing. Letting
the accused defend themselves in a court of law is still a
good thing. If they're found to have done something
wrong, let the heads roll, but if there are false
accusations, those need to be addressed as well. |
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The reaction of each side to the sexual scandals has been
rather telling. From my perspective I’ve seen the R’s do
anything in their power to discredit the stories and women
while the D’s with some exceptions largely own up and
offer up. |
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Such as time marching backwardsdrawkcab
gnihcram emit sa hcuS |
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// “Living the way you want to live” is one of those
conflicting goals that requires a few common but easily-
disrupted things, namely, air, water, food, safety, and some
type of shelter. // |
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Why is it so hard to understand that "we'll give you law an
order", or "we'll get rid of immigrants" is a scare tactic, but
"without us, you won't have roads" is also a scare tactic? |
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Because we’ve been through periods in history
where the
scary has happened primarily as a result of a lack of
more
thorough investigation into the downstream
effects, and
because as the world gets more crowded, it
becomes more
fragile to abuse. |
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Because ecological disasters like Delhi, Beijing,
and
Centralia Pennsylvania exist. |
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//The reaction of each side to the sexual
scandals has been rather telling. From my
perspective I’ve seen the R’s do anything in their
power to discredit the stories and women while the
D’s with some exceptions largely own up and offer
up.// |
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With all respect Ray, I fail to see what that has to do
with the universal paradox of infinity. |
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Blame 8th. He started it... |
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Dissent, suspicion and controversy... our work here is done. |
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//as the world becomes more crowded// |
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We're a pimple -- perhaps a festering one -- on a dog's ass as
far as the world is concerned. And if I remember my Cosmos,
the planet is pretty insignificant as well. |
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Worry about human happiness. Primarily your own. |
|
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//as the world becomes more crowded// |
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We're a pimple -- perhaps a festering one -- on a dog's ass as
far as the world is concerned. And if I remember my Cosmos,
the planet is pretty insignificant as well. |
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Worry about human happiness. Primarily your own. |
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Sorry that's just me. I cannot be happy simply
worrying about my own happiness while the world
goes to hell. |
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What you're suffering from, [Rayfo], is "hope". If you can
abandon that, you will find that the world is much more
tolerable. |
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No, I swam around in that swamp for awhile. Didn't
like it there. |
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at least admit Ray that it's an anthropomorphic view of the
situation, even if you're right. If the world was overrun with
rats and roaches, it would still be heaven for them. |
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But of course Pinker and others have proved this is nonsense,
the world is not going to hell, and the messaging that it is,
from the left or from the right, is primarily about making you
concerned enough to check in. |
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As a bit of a history dork, I'd say the world is coming from
hell, not going to it. |
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For one thing, if you had the opportunity to switch places
with one of the pharos of Egypt you'd be a fool to do it.
(One idiot I tried this on said he'd do it in a minute
because of all the women and slaves who would serve
him hand and foot, so I'll assume for this exercise you're
not a sociopath like this guy was.) |
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You've got central heating, air conditioning, a wide
variety of delicious, safe foods, drinking water that won't
kill you, medicine and of course, telecommunications that
allow you to learn as much about the world as you want.
Unlimited entertainment, unlimited access to all the
information man has ever known, the entire world at your
fingertips. |
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Would you trade that to sit in a massive stone building
sweltering in the heat while some slaves wafted palm
leaves at you in a futile attempt to stop the perspiration
from dripping out from under your crown? Watching your
children die because "Osiris" got pissed off at you? Being
entertained by somebody plucking some one stringed
instrument for hours? Again? |
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And if you did enjoy the trade, enjoy it quick, because
you're dead at 34 years old. Yup, just about the time you
start to really figure things out it's mummy time. You're
guts are in a jar, they turn you into beef jerky and then
put you in a cave with some
golden nicknacks. |
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We've been at war with radical Islam for 17 years. In that
time American casualties are at around 9 thousand. In the
Civil War, the 12 hour battle Antietam 3,650 men were
killed. In the 4 month long battle of the Somme in WW1,
one million men were killed or wounded. Even war is
safer. (Except for our enemies, which is a good thing.) |
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Since only 1980, child mortality rates have fallen from
1,288 per hundred thousand to 588 in 2014. When you go
further back families would lose half their kids to various
diseases that aren't a problem now. |
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There are always challenges in keeping this civilization
afloat and we're all striving to make a better world for
all, but the good old days weren't. |
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I am not pining for the good old days. I'm simply
trying to keep the current days from becoming the
bad new ones. |
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Eliminate the worship of "cool" guns like the AR15 by
eliminating it altogether, and you make a dent in the
preoccupation with them. |
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Maybe I've seen too many nature shows, but I worry
about ecological disaster. I get really pissed at
willful ignorance in the face of virtually limitless
access to knowledge. I've suffered too many
personal tragedies to wave them off when they
happen to someone else. |
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If you're worried about the environment, fight the socialists
who are waging a war on nuclear power in favor of taxable,
money producing carbon fuels with a windmill stuck on top
of that pile of money for decoration. |
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I do. But I find the conservatives just as
troublesome in that regard. |
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//I do. But I find the conservatives just as
troublesome in that regard.// |
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Then fight them too. I'll join you. |
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//maybe the universe is inside a triangle...or a
pyramid...although all the heavenly bodies seem
to be spherical...but who says the ultimate
boundarie(s) are spherical?// |
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Who was the guy who spent years trying to fit
various shapes together to build a model of how
the universe was arranged or something? He'd put a
cube in a pyramid in a sphere etc looking for some
kind of pattern. I believe he got famous for doing
something else that actually worked. |
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[doctorremulac3], that would be Kelper. He positted that the 5 Platonic solids fit between the orbits of the planets (only 6 known way back then, of course) ie: the sphere that corresponded to an orbit was inscribed by one solid, and circumscribed by the next. It did'nt work, but the precise measurements he needed/made while attempting this (and other astronomical stuff) eventually led to the Kepler Laws. Look up the "Mysterium Cosmographicum" for more. |
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Oh yea, very cool. Kind of a message for the rest of
us in there. "Sometimes you find diamonds when
digging for gold." or something. |
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I'm a big fan of stuff discovered while somebody was looking
for something else. The search for refrigerant that led to
teflon, experiments with the cathode ray tube leading to x-
ray images etc. |
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Then the mind leans out over the cliff, how did it start rotating? what is it rotating in? are we just an Ad man's spin? |
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>But if you want to cure stupidity, good luck. Stupid people
have more kids than smart people and that's just going to get
worse. Doesn't matter what tag you give one side or the
other. The big stupid just rolls on getting bigger and bigger
while we quibble about which part of the snowball is the
stupidest. [Dr Emulac III] |
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I think I wrote something about that paradox. And a seriously
intriguing one it is too. |
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The earth isn't really finite is it? By the time I walked the whole globe, parts have changed, some lost, some gained, a new highrise with record floors has been constructed.The surface is no no longer the same. Isn't that infinite? I suppose It comes down to the definition of the box being looked at and whether time is included. Human centric, a newly launched aircraft carrier is an engineered part of the earths surface. |
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As for the infinitiness of the universe, we are a bit chained to the EM field, more data is needed. Parts might be a mirage and the universes shape is totally different. |
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Unless new matter with mass and volume is
constantly being created, the universe is finite, in
as much as it now contains an unchanging
measurable amount of material. |
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Stupid people can have smart kids on occasion, and
vice-versa. |
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[xenzag]; there's also matter/energy equivalence. Since the universe
is cooling down, it's possible that the energy being lost is becoming
matter. Then there's Hawking radiation creating particles too. |
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Now that she's 13 she is asking even better questions. |
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Actually, consider the Casimir effect and vacuum generation of particle pairs. Some person on Quora says they have not merely measured it, they have isolated actual spontaneously created photons out of it. |
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Quick guide to the Casimir effect:Things spontaneously appear out of nothing, in pairs, wipe each other out, and on average its a zero; sometimes one of the created things gets away. It's real and they've measured it. |
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So revisiting Pashute's student's interest in a center and also a perimeter, what if the bulk, middle, or cortex because of the proven Casimir effect actually has more matter generation capability then an "originating center event"? I have no idea of course. Sort of in appreciation of the student's questions it's an Instant Quora question[link]. |
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It's nifty how a reflexive kind of human mental construct, a perimeter, a bulk or middle, and a center could be replaced with so many other things. Math is amazing and mathematicians know so much (and increasingly know more). Here's another reflexive human mental construct: minimax curve |
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You may have seen a minimax curve (link), it's kind of like two 3D maxi pads crossing center and pointing opposite to each other [link]. The big thing about minimax curve is that the only place things are stable is at the crossover. It's very simple as reflexive human explainer-geometries go, and you can use if for a lot. I have not heard, and have no reason to believe there are things and people at the crossover of a minimax curve. |
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I have an urge to mention things being up or down on the minimax curve but with the math version there is just curve. There is acceleration though, and only at the entire groovy 3D shape's least curvy part can things stick around. Otherwise everything accelerates away. I'm not completely sure, but because it is a math function, the minimax curve has an inverse, (just tell it to graph minimax^-1 and look at the pretty shape) and if you were using a math program you could graph it. |
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Anyway, now that she is 8th grade she can use math graphing software and learn up through trigonometry pretty ably. If she likes math at all show her how to do operations on matrices. Very mind widening. |
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Pashute, if you see her again pull up a picture of the orbitals of hydrogen and mention that "people like to make reflexive analogies and metaphors like "in and out", but check out this thing (hydrogen orbitals) that is supposed to have a reason to be simple! (blobs quatrefoils, spheres, rings, maltese popcorn kernels, etc). Show her the more math she learns the more analogies she's got. |
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I missed out on quite saying what I meant, so I will try again: If she gets good at math, she'll have a grasp of say 100-1100 functions as either math things or graphs. If she likes, she can use any of those 1100 functions to enquire about the state of the universe. She may even be so good at math where can figure out which math function the universe is Not. Huge piles of functions make hypnotizing analogies. |
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Anyway [pashute] The thing I remember about 6th grade is my friends. If I were teaching 11 year olds I would be like, "text your friends memes about graphical math functions." So, um, keeping it practical I asked on Quora: "what are some great math memes for people 11-13?" [link] Others have generated similar content there. |
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So if the Universe is indeed expanding can we look forward to the
time when the furthest expanded bits hit the outside wall and start
moving back inwards? This would be very convenient as those bits
that we could never seem to see very well due to their extreme
distance and speeding away would now be coming back, reciprocal
course, such that all we'd need to do is sit tight and wait for them to hit
us. This would make planetary exploration so much more convenient
than having to peer at them as they are running away. |
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