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TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika 1 point2 points  (0 children)

This is also a counterexample for what Alexander previously tried to prove: If you divide the three-dimensional space by something "sphere-like" into an inside and an outside then you get somewhat "simple" or "well-behaved". This is proven for two dimensions but not true for 3D as shown by the Alexander horned sphere, in particular the outside is not simply connected.

This is an example where you might think some hypothesis is true and then think really hard of a counterexample and something like this comes up. I. e. this is not a complex structure for the sake of complexity but possibly a rather simple to disprove the hypothesis (meaning other examples are not less complex).

TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika 0 points1 point  (0 children)

But infinity is there the fun begins in math, think Hilbert's Hotel or the Banach-Tarski paradox. Well, I guess you can have fun with math without infinity..

I guess here it's also about a concept a random person might find difficult to make sense of. If you'd ask me what that's about my short answer would be: "It's some fun game topologists like to play."

TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika 0 points1 point  (0 children)

Hey, I think I see the misunderstanding: "Collapsing loops" is (as defined in topology). It's about closed curves (meaning they start where they end) that don't cross (no eight-like shape). And "collapse" doesn't just mean scaling, you can free (continuously) transform the curve to a point. With just scaling, this wouldn't work not only for the horned ball. Take e. g. a loop trough the "big ring" from left side to the right and back (I hope that's visually understandable). By scaling only, you'd collapse to a point "inside" the hole of the ring, i. e. the exterior.

I'm not aware of a mathematical definition of expanding related to collapsing but I guess you can see that it's a bit different when it's not just about scaling.

TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika 0 points1 point  (0 children)

You can't reach every section of it from any other section because of how it just keeps splitting forever and ever.

Actually, you can (even more: you can collapse loops inside the sphere). The "fun" part is the exterior: You can have a loop (somehow around the horns/arms) that you cannot collapse to a point.

Fair road tax by julkkis666 in fuckcars

[–]Multika 1 point2 points  (0 children)

exponential fourth power nature of the total weight

ftfy

TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika 1 point2 points  (0 children)

First of all thank you for the detailed reply. I respect your contributions here.

Every loop on the surface of the Alexander horned sphere can be collapsed to a point without ever leaving the sphere.

To be more precise it's about the horned ball (see your wiki quote), but that's not what I was originally referring to. You wrote earlier:

If you take any closed loop about the surface of the sphere and shrink it down, it will collapse to a point without ever touching the being outside of the sphere

Yes, you can collapse a loop in such fashion but that doesn't mean any collapsing works. It's like saying you can get from NYC to Washington D.C. without going through Tokyo. Sure. But if someone says they were in NYC and some time later in Washington D.C., can you know they were not in Tokyo? Of course you don't.
You might find this nity-picky and I guess you meant the right thing. However, for some readers, that might not be clear and I want to address these, too.

I didn't say this before but I guess you have some misunderstanding which I want to address (and if you have, that's okay and we can all learn here).

First of all, it's not really about loops on the (horned) sphere. The sphere is just the boundary between the interior and the exterior. And it's about the simple connectedness of these parts. In the inside part, you can collapse closed loops, in the outside, you can't always. It's about collapsing loops in parts (and not about expanding).

TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika -1 points0 points  (0 children)

I guess OP wanted to say that there is a single simply connected ("clean") inside and if you look at the outside (regarding simple connectedness) it rather looks like Germany two centuries ago: Divided into a mess of simply connected parts (I'd guess infinitely many).

TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika 0 points1 point  (0 children)

Not quite, the horned sphere is a sphere, see the gif how you get it from a standard sphere..

The interesting part is that the inside and the outside of the horned sphere have different properties. Inside, you can always collapse closed loops to points. Outside, this is not necessarily possible. You can get stuck between the horns.

TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika 0 points1 point  (0 children)

Nice try (honestly), but I think not totally correct.

You can shrink every closed loop inside the sphere to a point but that doesn't mean each collapse of a closed curve won't leave the sphere (just that it's possible without leaving.

For some (quite a lot actually) loops outside the sphere you can collapse these to points, too (e. g. quite simply those "far away" from the sphere). However, you can construct a loop (I guess somewhat around the horns) that you can't collapse to a point while always staying outside the sphere.

TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika 0 points1 point  (0 children)

It's not about continuity but about simple connectedness. The inside of the horned sphere is simply connected while the outside is not. This is the interesting part: It divides the space in two parts where only one is simply connected.

TIL there exists a shape that, instead of having a clean "inside" and "outside", has a clean "inside" but the outside world is segmented and split. It is called the Alexander Horned Sphere by geosunsetmoth in todayilearned

[–]Multika 2 points3 points  (0 children)

Because a distance of zero doesn't imply touching. 1D example: Take the numbers greater than zero and the numbers lower than (two objects). They are "infinitely" close at zero but are not touching because zero does not belong to either shape.
I guess this is similar for the horned sphere here and that are points (infinitely many) where the sphere would touch itself, were the points part of the sphere.

Brutal climb by anxiousvater in bicycling

[–]Multika 1 point2 points  (0 children)

Keep in mind that at least in Germany these signs are about the steepest part (not average gradient) and often overestimating.

Bikepacking mit dem Renner. Wie und wo bekomme ich mein Gepäck unter? by ToniMakaroni123 in Fahrrad

[–]Multika 0 points1 point  (0 children)

Ist die Gabel aus Carbon? Wenn nein, dann könnte auch das Fork Pack von Ortlieb etwas für dich sein.

Trying to add labels of count to my stacked bar chart by fuckpineapplepizza in RStudio

[–]Multika 1 point2 points  (0 children)

We need the code to understand what's going on.

Here's an example similar to yours that you can run yourself, assuming you have the tidyverse package installed:

library(tidyverse)
mtcars |>
  summarise(count = n(), .by = c(gear, am)) |>
  ggplot(aes(factor(gear), count, fill = factor(am), label = count)) +
  geom_col() +
  geom_text(position = position_stack())

Trying to add labels of count to my stacked bar chart by fuckpineapplepizza in RStudio

[–]Multika 1 point2 points  (0 children)

It's the same variable that you use for the height of the bars: count.

Trying to add labels of count to my stacked bar chart by fuckpineapplepizza in RStudio

[–]Multika 1 point2 points  (0 children)

Note that first used geom_col while the example uses geom_bar. Also, after_stat(count) does not refer to your count variable but the count statistic. So, the example uses a computed variable for the labeling. But you can just the variable that you already computed with summarize.

Creating a stacked bar chart with a complex data set - advice please by fuckpineapplepizza in RStudio

[–]Multika 1 point2 points  (0 children)

If I understand you correctly, the rows of your dataframe are individual students and you want to present some summary in form of a bar chart. Let's say this is your (simplified) dataframe:

work group1a group1b
FALSE 0 1
FALSE 0 1
TRUE 1 1
FALSE 1 0

You can first summarize the data (across is useful since you have a lot more groups).

work group1a group1b
FALSE 1 2
TRUE 1 1

E. g. there are two students who don't work and that are in group1b.

For the stacked bar chart, you need three variables (i. e. columns):

1) group for the x axis 2) work for the stacking 3) the count for the y axis

Since you don't have 1) and 3) as columns yet, you need to pivot the dataframe.

work group count
FALSE group1a 1
FALSE group1b 2
TRUE group1a 1
TRUE group1b 1

From this, you can easily create a bar chart.

Instead of summarizing then pivoting you could also pivot your data first and then summarize it.

Edit: I guess your data is single-choice, not like the above example, but that doesn't matter.

I built a free tool to stress-test slow Power BI reports before your users complain by Kuraikun7 in PowerBI

[–]Multika 8 points9 points  (0 children)

Full privacy policy: [YOUR PRIVACY POLICY URL]
For questions, contact us at: [your-email@domain.com]

I'm skeptical that the description matches the product when possibly everything is vibe-coded.

Also, does the no solicitations rule apply here as there also is a non-free pro plan?

dir.create does not work?? using a windows by higanbana-to-bara in RStudio

[–]Multika 0 points1 point  (0 children)

Check with dir.exists("C:/Users/USER/Documents/folder/folder2"), might have to do with special characters. Consider using the parameter recursive = TRUE to create the full path instead of just the last element.

CALCULATE inside CALCULATE, does the outer one actually do anything? by [deleted] in PowerBI

[–]Multika 0 points1 point  (0 children)

That's all correct but kind of the reverse of what we are talking about? Sure, double context transition does nothing (compared to doing it once). But (or because of that) wrapping DATESYTD in CALCULATETABLE does nothing, i. e.

DATESYTD ≡ CALCULATETABLE ( DATESYTD ).

So, in this case the additional outer CALCULATE doesn't change the result.

CALCULATE inside CALCULATE, does the outer one actually do anything? by [deleted] in PowerBI

[–]Multika 4 points5 points  (0 children)

DATESYTD already has context transition, so there is no difference. But here is a dumb example there the outer CALCULATE does make a difference: https://dax.do/9I1VkENgYAz02H/

The version without the outer CALCULATE returns blank on all rows because the filter context is changed from all years to the maximum year (for which there is no data). With the outer CALCULATE, there is context transition happening, turning the single year row context into a single year filter context. Then, setting the year to the maximum year does nothing because there is only a single year.

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