I am trying to create a rounded triangular cylinder bound by height, width and depth parameters.
I am trying to do it like so:
minkowski () {
linear_extrude (height=5, center=true){
polygon (points=[[-9/2, -9/2], [9/2, -9/2], [-9/2, 9/2]]);
}
cylinder ($fn=1000, h=5, r=1/2, center=true);
}
This creates a triangular polygon centered at the origin of hight and width of 10 - 2r.
Next it extrudes it to be depth 10
Next it creates a cylinder of radius 1/2 with a depth matching that of the triangular object centered at the origin.
Finally it runs minkowski on the triangluar object and the cylinder.
I am curious, can I say that the resultant object is bound by a 10x10x10 cube centered at the origin? Or is my math off.
In Andy Buckley's answer on a Quora question about spacial dimensions, he mentions "As far as SR is concerned, time is just a dimension with a -1 entry in the diagonal Minkowski metric tensor."
As someone who once in the blue moon actively reads articles and material on physics, I don't understand that statement in the vaguest sense, and I suspect I'd have to acquire a ton of prerequisite knowledge to be able to understand it well enough.
Of course I will dissect and look up individual parts of the statement myself, before attempting to connect the dots, but I find that posting on reddit garners some interesting perspectives or points out flaws in my own realized or researched understanding.
So, can "As far as SR is concerned, time is just a dimension with a -1 entry in the diagonal Minkowski metric tensor" be explained in a more expanded, but simple manner to students not in the physics field (or even formal science I'd say)?
3D printing a hybrid structure that combines the nacreous abalone shield structure and the Bouligand structure of mantis shrimp dactyl hammers. Super interesting!
During the proof demonstrating that the length of the 4 velocity vector in a Minkowski metric is c, there is a point during a derivation where there was;
[(u^x)^2 + (u^y)^2 + (u^z)^2].
there is some way it transformed into u^2 from the guy who was explaining it.(eigenchris on Youtube)
I already know that u= u^t + u^x + u^y + u^z
but how does u^2=(u^x)^2 + (u^y)^2 + (u^z)^2?
Is it that the component velocities are different, and thus if their dot product is worked out like (u^x).(u^y), it becomes zero, but if the dot product of the same component velocities is worked out like (u^x).(u^x), it equals to one?
Edit: Where it is u^x, I mean u to the superscript of x not to the power of x.
I have problems in understanding the space-time diagram of Minkowski. I, somehow, get the point of having an absolute future above the present point p and of having an absolute past below the present point p. But there are points which are "spacelike seperated from p"; it may be to abstract for me. What does it mean to be spacelike seperated? My main issues tend to be the overall understanding, idk, but it would be great if anyone would have an answer in mind. Thanks in advance!
If we draw a ct vs. x diagram, it just makes sense to think of the metric as the same as for a regular Cartesian plane instead of the minus for the time term. Is there a better way of thinking about it so that the metric makes more sense conceptually or is it just defined as such?
I get what the Minkowski sum does mathematically but how do I know what shape to expect when I perform a Minkowski operation on a bunch of shapes?
Link: https://www.operaonvideo.com/semele-paris-2004-minkowski-massis-croft-connolly/
Although it is technically an oratorio and part of Handel's English oratorio period, Handel's Semele is often staged and performed as an opera, and it works very well in that context. Here is a truly excellent staged performance with Sarah Conelly.
Hi folks, I've been creating something (actually, one half of the baseplate for the mopping function of an iLife V5 Pro robo-vacuum, in case you're interested) and I've been trying to do some rounding of parts using minkowskiRound (I don't kind if it takes a while to process). However, I got an error when I did this preview and it appears to be a bug, and I've done minkowski rounding earlier without having this problem, so it isn't fundamentally broken as such. I don't get the error without minkowski rounding, but even finer rounding (ie, $fn=20) has worked just fine when the model was a bit simpler. Does anyone have an idea what provoked this or what fix might be done? Obviously, I'm just whinging about a completely free, brilliant product but I might still ask for my money back.
Any help appreciated.
Mike Hersee
so the first part of the problem entailed proving convexity for:
(αa + βb)ᵖ ≤ (α + β)ᵖ (αaᵖ/(α + β) + βbᵖ/(α + β))
(1≤p<+∞, a, b ≥ 0, α, β > 0)
basically, i defined α/(α + β) as λ and showed it to be the convexity ineq. for f(t)=tᵖ
now i'm supposed to make use of that to prove that
ǁxǁₚ= (Σ{1≤i≤n}|xi|ᵖ)¹/ᵖ
is a norm on ℂⁿ
now the here's the hint:
To prove the triangle inequality, set α = ǁxǁₚ, β = ǁyǁₚ, aᵢ = |xᵢ|/α, bᵢ = |yᵢ|/β, use the previous item, and sum for i = 1 to n.
i tried plugging those into the convex inequality above, but i don't see how i'm getting there
I'm asking about one-dimensional objects for a 2D Minkowski graph. The whole concept confuses me incredibly. What I think is that if the object has mass, it has a slope too high to get from the point (0;0) into the quarters of the graph where x^2 is smaller than 0. So, if it starts from (0;0) it will always be in the future light cone. But what if it starts on another point in the graph? Can I draw it as a straight line with infinite slope, cutting into the future light cone? Do I also need to draw it "backwards" in time, cutting therefore both light cones once?
Episode Description:
Following the Plant Monster's reappearance, Minkowski makes it her mission to eliminate the mutant stowaway once and for all. But when her quarry proves surprisingly difficult to corner, the Commander resorts to increasingly desperate and dangerous tactics. As the deadly game of cat and mouse intensifies and the lines between roles start to blur, Minkowski must decide on the best path to take to ensure the safety of her crew. Plus, Howard Beale breakdowns, escalating hostilities, Holy Hand Grenades, friendly conversations, and Heart of Darkness lighting.
Vasselin Petkov is a member of the Philosophy of Science Association (philsci.org) and honorable member of the Canadian Society for the History and Philosophy of Science. More on Dr. Petkov can be found here.
Petkov established himself as the principle proponent of 4D spacetime (roughly the idea that all of time exists at once) in a 2005 paper titled, "Is there an alternative to the Block universe view?" His paper answers in the negative. A portion of the abstract is repeated here.
> ABSTRACT This paper pursues two aims. First, to show that the block universe view, regarding the universe as a timelessly existing four-dimensional world, is the only one that is consistent with special relativity.
Brian Greene is a master communicator of science, and an accomplished physicists himself. But in academia, Petkov's name has become synonymous with this idea. Over the years, when discussing these topics with my colleagues, we often use his name as a placeholder in quick conversations (so it is "Petkov's idea" or the "Petkov universe" and so on.)
Petkov V. "Is there an alternative to the Block universe view?" . (2006)
Philosophy and Foundations of Physics The Ontology of Spacetime. D. Dieks (Editor) 2006 Elsevier B.V. DOI 0.1016/S1871-1774(06)01011-4
Just read about Minkowski diagrams and it reminds me of this stuff. But I can't put my finger on it. Is there any connection?
Let me know if I need to broad stroke what a Minkowski diagram is.
I am self-learning the theory of relativity (both special and general).
I understand the basic principles of the Minkowski metric (and in general, the GR metric tensor) and how it is different from the Euclidean metric. However, from what I can see, the key differences (such as negative distances) only become apparent at large scales and not at our local human scale.
I was wondering is there any noticeable difference between the Minkowski metric and the Euclidean metric at scales such as our everyday human scale?
This is just FYI, because I'm new to openscad. I couldn't find anything online so I had to figure it out myself.
I'm making a tablet stand/grip and noticed this line in the manual:
https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Transformations#minkowski
>(note that the outer dimensions of the box are now 10+2+2 = 14 units by 14 units by 2 units high as the heights of the objects are summed):
It felt wrong so I added a highlighted cube with the original dimensions. Sure enough it was massive.
Here's the code
// tablet dimensions
tx=124.4; //tablet length
ty=210; //tablet width
tz=8; //tablet height
$fn=72; //circle facets
tcr=20; //tablet corner radius
// original tablet size
#translate([0,0,tz]) cube([tx,ty,tz]); //for reference only. remove this in final code
minkowski() { //WARNING: Increases object size
//Minkowski Adjustments for Tablet $(x) to allow for rounded corners
matx=tx-tcr*2;
maty=ty-tcr*2;
matz=tz/2;
// body without minkowski adjustments
//cube([tx,ty,tz]);
// body with minkowski adjustments
cube([matx,maty,matz]);
// corners ... could be a bit more round.
translate([tcr,tcr,0]) cylinder(h=matz, r1=tcr/2, r2=tcr);
}
LIVE BROADCAST BEGINS 8:00 EST
100% of donations at Phish.com/waterwheel will go to these philanthropic partners:
Divided Sky Foundation, Mockingbird Foundation, Headcount.org, The Mimi Fishman Foundation, Phans for Racial Equity, and the Conservation Law Foundation. Do it since you're not buying a spicy chicken sandwich tonight. Add in Colorodo Fire relief at the request of u/spirit_dimension: https://bouldercounty.wufoo.com/forms/zw48x9f1p0h53v/
Start Time: ~8:30PM EST, 7:30PM CT, 6:30PM MT, 5:30PM PT
**Set 1:** (Start: 8:31, End: 9:50)
Moma Dance (8), Tube (8), Michael Plunkett (break down the 9th wall) ^(1) (1), 46 Days (6), Time Turns Elastic^(2 /)(12), Fish Learns Betty White Died ^(3) , Free (7), Ghost^(4) (14) > Slave to the Traffic Light (9), Cavern^(5) (5)
**Set 2:** (Start: 10:03, End: 11:23)
Sigma Oasis (6)> Down with Disease (15) > Miss You (6), Happy Anniversary Brenda Havens and happy new year Iggy,^(6) You Enjoy Myself^(7) (22) ->Frankie Says (3) > Mercury^(8) (9)-> Possum (6), Life Beyond A Dream (5)
**Set 3:** (Start: 11:39 , End: 12:51 )
Blaze On (9)-> What's the Use?(7), Everything's Right (6)-> Auld Lang Syne (2)-> Everything's Right (10) > Twist (11), Baby Lemonade^(9)(3)-> Hold Your Head Up^(10) (5) Harry Hood (13)
(End of Show: 12:51)
Notes:
^(1) Debut
^(2) LTP 2010-10-24
^(3) Debut with "Masked, Vaxxed, and Pantsless" quotes
^(4) w/ Drill
^(5) Lyrics changed from "slip into the night" to "slip into your bedroom"
^(6) A drum lesson is owed. YEM is very audibly called
^(7) YEM contained a second instrumental jam out of the vocal jam
^(8) Featuring Fishman on Marimba Lumina
^(9) For Ulululu and Sulu, Syd Barrett Cover. LTP 1992-03-11
^(10) With "Baby Lemonade" quotes
---------
Pre-Show Bumps:
YAK ATTAK Nectar Lounge (Seattle) Virtual Concert Series
COSTELLO's NEW MOTOWN SPOTIFY MIX
Official Stream Preshow- Surefire Soul Ensemble
Setbreak 1 Music: Jr. Thomas and the Volcanoes
Setbreak 2
... keep reading on reddit ➡
I understand that the line element in Cartesian coordinates of the Minkowski Space is
ds^(2) = −c^(2)dt^(2) + dx^(2) + dy^(2) + dz^(2).
Why is the c^(2) term negative?
In Andy Buckley's answer on a Quora question about spacial dimensions, he mentions "As far as SR is concerned, time is just a dimension with a -1 entry in the diagonal Minkowski metric tensor."
As someone who once in the blue moon actively reads articles and material on physics, I don't understand that statement in the vaguest sense, and I suspect I'd have to acquire a ton of prerequisite knowledge to be able to understand it well enough.
Of course I will dissect and look up individual parts of the statement myself, before attempting to connect the dots, but I find that posting on reddit garners some interesting perspectives or points out flaws in my own realized or researched understanding.
So, can "As far as SR is concerned, time is just a dimension with a -1 entry in the diagonal Minkowski metric tensor" be explained in a more expanded, but simple manner to students not in the physics field (or even formal science I'd say)?
I have problems in understanding the space-time diagram from Minkowski. I do, somehow, understand the point of having an absolute future above the present point p and of having an absolute past below the present point p. I guess thats the easy part to grasp. But there are points which are "spacelike seperated from p"; it may be to abstract for me. What does it mean to be spacelike seperated or to be light-like seperated (?). My main issues tend to be the overall understanding, idk, but it would be great if anyone would has got an answer in mind. Thanks in advance!
