Summary: White noise is not the same as other noise — and even a quiet environment does not have the same effect as white noise. With a background of continuous white noise, hearing pure sounds becomes even more precise, as researchers have shown. Their findings could be applied to the further development of cochlear implants. — Good noise, bad noise, *ScienceDaily* reporting research from the University of Basel, 12xi2019.

*As a rotating animated gif (optimized at ezGIF).

**Performativizing Paronomasticity**

The title of this incendiary intervention, which is perhaps my most contrived title yet, is a paronomasia on Shakespeare’s “Alas, poor Yorick!” (*Hamlet*, Act 5, scene 1). “Allus” is a northern form of “always”, “pour” has its standard meaning, and “Horic” is from the Greek ὡρῐκός, *hōrikos*, which strictly speaking means “in one’s prime, blooming”. However, it could also be interpreted as meaning “hourly”. So the paronomasia means “Always pour, O Hourly One!” (i.e. hourglass).

Winnie-the-Pooh and Piglet set out to visit one another. They leave their houses at the same time and walk along the same road. But Piglet is absorbed in counting the birds overhead, and Winnie-the-Pooh is composing a new “hum,” so they pass one another without noticing. One minute after the meeting, Winnie-the-Pooh is at Piglet’s house, and 4 minutes after the meeting Piglet is at Winnie-the-Pooh’s. How long has each of them walked? — “A puzzle by S. Sefibekov”

viâFutility Closet

If you’re good at maths, you should see the answer in an intuitive instant. I’m not good at maths, so it took me much longer, because I didn’t understand what was going on. But I can explain the answer like this. Pooh is obviously walking faster than Piglet. Therefore, Pooh and Piglet can’t have met after one minute, because that would mean Pooh takes one minute to walk the distance walked by Piglet in one minute.

So let’s suppose Pooh and Piglet met after two minutes. If Pooh takes one minute to walk the distance walked by Piglet in two minutes, then Pooh is walking twice as fast as Piglet. Does that work? Yes, because Piglet walks Pooh’s distance in four minutes, which is twice as long as Pooh took. Therefore Piglet is walking twice as slowly as Pooh. It’s symmetrical and we can conclude that they did indeed meet after two minutes. Pooh then walks another minute, for three minutes in total, and Piglet walks another four minutes, for six minutes in total.

But guessing is not a good way to find the answer to the puzzle. Let’s try to reason it through properly. Suppose that Pooh and Piglet meet after one unit of time, during which Piglet has walked one unit of distance and Pooh has walked *x* units of distance, where *x* > 1. In other words, Pooh is walking *x* times faster than Piglet. The distances they walk before meeting are therefore in the ratio:

1 : *x*

Next, note that Pooh will cover the distance Piglet has already walked in 1 unit / *x* = 1 minute, while Piglet covers the distance Pooh has already walked in *x* / 1 = 4 minutes. The times they take are therefore in the ratio:

1 / x : *x* → 1 : *x*^2 → 1 : 4

And if 1 : *x*^2 is 1 : 4 (the ratio of the minutes they walk after meeting), then 1 : *x* (the ratio of the distances they walk before meeting) = 1 : √(*x*^2) = 1 : √4 = 1 : 2. Pooh is therefore walking 2x faster than Piglet and Piglet is walking 2x slower than Pooh. If Pooh covers Piglet’s distance in 1 minute, Piglet must have taken 2 minutes to walk that distance. And if Piglet covers Pooh’s distance in 4 minutes, Pooh must have taken 2 minutes to walk that distance.

Therefore, when they meet, each of them has been walking for 2 minutes. Pooh therefore walks 2 + 1 = 3 minutes in total and Piglet walks 2 + 4 = 6 minutes in total.

The result can be generalized for all relative speeds. Suppose that Pooh and Piglet meet after *m*_{1} minutes and that Pooh then takes *m*_{2} minutes to walk the distance Piglet walked in *m*_{1} minutes, while Piglet takes *m*_{3} minutes to walk the distance Pooh walked in *m*_{1} minutes. The time they walk before they meet, *m*_{1} minutes, is therefore supplied by this simple equation:

*m*_{1} = √(*m*_{3} / *m*_{2})

And you can call √(*m*_{3} / *m*_{2}), the square root of *m*_{3} / *m*_{2}, the squooh function:

*m*_{1} = √(*m*_{3} / *m*_{2}) = squooh(*m*_{2},*m*_{3})

Now suppose the distance between Pooh’s and Piglet’s houses houses is 12 units of distance and that Piglet always walks at 1 unit a minute. If Pooh walks at the same speed as Piglet, i.e. 1 unit a minute, then:

After they meet, Pooh walks 6 more min = *m*_{2}, Piglet walks 6 more min = *m*_{3}.

How long do they walk before they meet?

*m*_{1} = *m*_{3} / *m*_{2} = 1, √1 * 6 = 6

They meet after 6 min.

Now suppose that after they meet, Pooh walks 2 more min, Piglet walks 8 more min.

Therefore, *m*_{3} / *m*_{2} = 4, √4 * 2 = 2 * 2 = 4 = *m*_{1}

Therefore they walk for 4 min before they meet and Pooh walks 2x faster than Piglet.

After they meet, Pooh walks 1 more min, Piglet walks 9 more min (*m*_{3} / *m*_{2} = 9, √9 * 1 = 3)

Therefore they walk for 3 min before they meet and Pooh walks 3x faster than Piglet.

After they meet, Pooh walks 0·6 more min, Piglet walks 9·6 more min (*m*_{3} / *m*_{2} = 16, √16 * 0·6 = 4 * 0·6 = 2·4)

Therefore they walk for 2·4 min before they meet and Pooh walks 4x faster than Piglet:

After they meet, Pooh walks 0·4 more min, Piglet walks 10 more min (*m*_{3} / *m*_{2} = 25, √25 * 0·4 = 5 * 0·4 = 2)

Therefore they walk for 2 min before they meet and Pooh walks 5x faster than Piglet.

And so on.

]]>Previously pre-posted:

• He Say, He Sigh, He Sow #23 — an *earlier* engagement by Genesis P. Orridge in terms of issues around “in terms of” (dot dot dot)

• Ex-term-in-ate!

To create the Koch snowflake, you replace each straight line in the initial triangle with the seed:

Now here’s another seed for another fractal:

Fractal stage #1

The seed is like a capital “I”, consisting of a line of length *l* sitting between two lines of length *l*/2 at right angles. The rule this time is: Replace the center of the longer line and the two shorter lines with ½-sized versions of the seed:

Fractal stage #2

Try and guess what the final fractal looks like when this rule is applied again and again:

Fractal stage #3

Fractal stage #4

Fractal stage #5

Fractal stage #6

Fractal stage #7

Fractal stage #8

Fractal stage #9

Fractal stage #10

I call this fractal the hourglass. And there are a lot of ways to create it. Here’s an animated version of the way shown in this post:

Hourglass fractal (animated)

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The hourglass fractal

I showed three ways to create the fractal. Next, in “Hour Re-Powered”, I showed a fourth way. Now here’s a fifth (previously shown in “Tri Again”).

This is a rep-4 isosceles right triangle:

Rep-4 isosceles right triangle

If you divide and discard one of the four sub-triangles, then adjust one of the three remaining sub-triangles, then keep on dividing-and-discarding (and adjusting), you can create a certain fractal — the hourglass fractal:

Triangle to hourglass #1

Triangle to hourglass #2

Triangle to hourglass #3

Triangle to hourglass #4

Triangle to hourglass #5

Triangle to hourglass #6

Triangle to hourglass #7

Triangle to hourglass #8

Triangle to hourglass #9

Triangle to hourglass #10

Triangle to hourglass (anim) (open in new tab to see full-sized version)

And here is a zoomed version:

Triangle to hourglass (large)

Triangle to hourglass (large) (anim)

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**mortal** *adj.* Refreshed (qv) within an inch of one’s life.

**mortal combat** *n.* Fighting between intoxicated fellows. Or occasionally, in the case of certain self-sufficient Harold Ramps (qv), between a single intoxicated fellow. — from *Roger’s Profanisaurus: Das Krapital, The Revolutionary Dictionary of Bad Language* (Viz 2010)

The hourglass fractal

A real hourglass for comparison

As I described how I discovered the hourglass fractal indirectly and by accident, then showed how to create it directly, using two isosceles triangles set apex-to-apex in the form of an hourglass:

Triangles to hourglass #1

Triangles to hourglass #2

Triangles to hourglass #3

Triangles to hourglass #4

Triangles to hourglass #5

Triangles to hourglass #6

Triangles to hourglass #10

Triangles to hourglass #11

Triangles to hourglass #12

Triangles to hourglass (animated)

Now, here’s an even simpler way to create the hourglass fractal, starting with a single vertical line:

Line to hourglass #1

Line to hourglass #2

Line to hourglass #3

Line to hourglass #4

Line to hourglass #5

Line to hourglass #6

Line to hourglass #7

Line to hourglass #8

Line to hourglass #9

Line to hourglass #10

Line to hourglass #11

Line to hourglass (animated)

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