Dave Horner's Website - Yet another perspective on things...
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which seems more true?

Mamma Matrix Most Mysterious
"the authentic experience of the body and the mind."

James Joyce / Terence Mckenna
Welcome to Dave Horner's Website!

penrose tribar, the impossible infinite triangle

Sunday, 24 June 2018 07:56

celebrated as a paradox or a unique contradiction, a mystery that can’t be solved...
a triangle that looks like a real, solid three-dimensional object, but isn't.
The impossible triangle, infinite triangle, penrose tribar, impossible tribar, is a triangular impossible object.
a continuous loop, an ambiguous figure, a visual paradox;
a strange loop with tangled hierarchies.
impossibility in its purest form

looks like a simple object. 2d depiction of a 3d triangle built from square beams. The eyes travel from face to face of the object, everything looks great, no problem. As the viewer traverses the continuous impossible object their perspective flips back and forth between equally possible perspectives in an unconscious and automatic way.

implicit in this strange loop is the concept of infinity. a loop representing an endless process in a finite way. -a conflict between the finite and the infinite.

helps give a sense that perceptions are limited and subjective from those of another person viewing the same thing.

A "penrose" polygon refers to the 2-dimensional depiction of the impossible object itself.
Penrose triangle - Wikipedia
Roger Penrose was the inventor of the tribar.
it's also an interesting look at Escher.
video with the Roger Penrose talking about the discovery of the tribar (spanish).
Escher's works like ascending decending, waterfall, and other tilings are influenced by the Penrose father and son's work.
non-isohedral tilings, tiles only one shape but they have different roles to play in different parts of the pattern. Roger sent Escher a wooden non-isohedral block puzzle to Escher; and Escher's solution was in Escher's final print "Ghosts" which he made just before he died. Roger says in the video "Unfortunately, Escher died before the non-periodic tilings that came somewhat later."

Tessellations - M.C. Escher Ghosts - Escher's last tessellation "Ghosts" was a solution to a puzzle sent to him by Roger Penrose, the mathematician. Escher solved it and, true to form, changed the angular wood blocks into rounded 'ghosts'.

if a line is traced around the Penrose triangle, a 4-loop Möbius strip is formed....

and ya, that's my leg and first tattoo. and ya, I'm white and nerdy. Thank you Samuel Hyndman

60 Penrose Triangle Tattoo Designs For Men - Impossible Tribar Ideas -
Triangle Tattoo Meaning | herinterest.com/
Impossibility on Behance
Making a Penrose Triangle on Behance - make a penrose perspective paper and tape model.
If you're interested in optical illusions, you might also checkout Optical tricks and illusions - Dave Horner's Website.

should maybe be on another penrose page but...

Penrose tiling - Wikipedia
Aperiodic tiling - Wikipedia
Penrose Tiles -- from Wolfram MathWorld
Impossible Cookware and Other Triumphs of the Penrose Tile - Issue 13: Symmetry - Nautilus
Anisohedral tiling - Wikipedia - In geometry, a shape is said to be anisohedral if it admits a tiling, but no such tiling is isohedral (tile-transitive); that is, in any tiling by that shape there are two tiles that are not equivalent under any symmetry of the tiling. A tiling by an anisohedral tile is referred to as an anisohedral tiling.
Isohedral figure - Wikipedia -isohedral or face-transitive when all its faces are the same. More specifically, all faces must be not merely congruent but must be transitive, i.e. must lie within the same symmetry orbit. In other words, for any faces A and B, there must be a symmetry of the entire solid by rotations and reflections that maps A onto B. For this reason, convex isohedral polyhedra are the shapes that will make fair dice.
Penrose diagram - Wikipedia - is a two-dimensional diagram capturing the causal relations between different points in spacetime. It is an extension of a Minkowski diagram where the vertical dimension represents time, and the horizontal dimension represents space, and slanted lines at an angle of 45° correspond to light rays.
Orchestrated objective reduction (Penrose–Lucas argument) - Wikipedia - The Penrose–Lucas argument states that, because humans are capable of knowing the truth of Gödel-unprovable statements, human thought is necessarily non-computable.

AMS :: Feature Column :: The Topology of Impossible Spaces
The Penrose Tribar(pdf)
Drawing A Tribar Figure by Hand(pdf)
AMS :: Feature Column :: The Topology of Impossible Spaces - this page includes amazing pictures and walks you through the math behind perspective and how to know if an object is impossible in mathematical terms. 1-dimensional cohomology
Impossible Triangle - this page right here has wonderful english to walk you through what's going on in a tribar, i highly recommend it. "The beams of the triangle simultaneously appear to recede and come toward you. Yet, somehow, they meet in an impossible configuration!" "it is possible to construct a physical model of the impossible triangle that looks impossible from only one angle" "It would lead to biological disaster if you were blind to the unusual, inconsistent, or paradoxical." "When you examine a drawing of an impossible triangle, you first build up a global image by examing the local parts." "When you examine a drawing of an impossible triangle, you first build up a global image by examing the local parts."
Impossible Triangle - The Illusions Index - another good page with wonderful english description of impossible triangle. It also includes a four sided impossible figure.

Last Updated on Tuesday, 11 December 2018 13:31


Euler's number e as sum of infinite series

Monday, 31 March 2014 08:28

$$e = \sum_{n=0}^\infty \frac{1}{n!}$$ satis dictum.

Last Updated on Monday, 21 December 2020 22:13


random vs random

Thursday, 27 March 2014 19:58

to infinity without comprehension.

moves in current game:0
black:0 white:0 draws:0
[stop] [slower] [faster]
last game:
min moves: max moves:0
total games:0 total moves:0

left side represents the beginning of mathematics; the right side represents the mysteries of infinity

Saturday, 01 February 2014 04:37


Last Updated on Monday, 21 December 2020 22:14



Friday, 06 December 2013 23:08

x days to Christmas.
x days to a new year.
Happy Holidays!

Last Updated on Monday, 21 December 2020 14:59


2013 three, that is a magic number.

Wednesday, 11 September 2013 08:01

2013 Horner Family Picture 3, that's a magic number.
A man and a woman had a little baby.
Yes, they did.

That's a magic number.

No more, no less.

2008 a year in review.

Thursday, 13 November 2008 08:26

Horner Family 2008My last update was Friday, 30 November 2007 12:43. The lack of update results from the front page of the site being neglected. I do update this website daily, but it is typically not to sit and reflect on what was. There are a lot of things that happen in a year and it is hard to summarize in a few paragraphs, but I will try.

Ella turned 1 year old and Noah is now 4 (such a big boy!). Noah and Ella play together constantly and are great friends. Ella's favorite word is Daddy...which makes me very happy. Noah and Ella were Mr. Bones and Daddy's little angel for Halloween this year. The kids are growing up so fast it is pretty unbelievable. We are extremely blessed.

Dayna and I went to Vegas together and saw the musical Spamalot, experienced Madame Tussauds Wax Museum, watched the Bellagio Fountains, walked the strip, ate some good food, and enjoyed a bit of the blackjack. Good stuff.

Work has been going well for me as I've been doing software consulting out of my own company TecDev since 2006. As always, please contact me if you've got a software need.

Development wise, I've been taking in all of the new features of .NET > (2.0). This includes WCF, WF, and WPF which are big improvements to software development in windows. I'm very excited to see IronPython and the DLR. Silverlight finally provides a supported cross-platform (mac,phone,windows) .NET solution to help us move past HTML. Exciting stuff.

I've been continuing research on visualizing my MRI data in the Visible Dave Project. I'm hoping to get something together soon for visualization. I am currently learning CMake, VTK, ITK, and FLTK to segment my brain structures in 3d. Such amazing open source code!

I've become even more geeky and connected with passing time....and I didn't think it was possible! But I'm now doing quite a few social networks and web 2.0 thangys...
facebook twitter linkedin youtube

Well, that about does it for this one. That wraps er all up. Thanks for stopping by.

Christmas and a new YEAR coming.

Friday, 30 November 2007 12:43

Merry Christmas 2007Here we are, 2007 coming to a close. I can't believe how fast time flies. You look down for one second and a whole year passes you by... It only gets worse as you get older....at least it seems that way anyway.

There are a lot of things that happened in the past year. Dayna and I are very excited about Ella and Noah. Ella is now 5 months and Noah is 3 years. Things have gotten much more interesting around the home, two kids is definitely more work than one. But it is also a lot more fun too.

Noah was very excited for Santa's visit and was very fortunate to have opened many presents on Christmas. Ella just starting to eat cereal and enjoys watching Noah jump around the room while he plays.

Thanks for visiting my site and have a happy new year!


Welcome home Ella Marie Horner!

Tuesday, 31 July 2007 20:12

Ella Marie Horner - Welcome! Welcome to the world baby Ella Marie Horner!

Ella was born on July 27th, 2007 @ 8:52am. She weighed a healthy 9 lbs 8.5 oz and measured 22 inches long. The labor was about 12 hours long, with only 20 minutes of hard pushing at the end. (not that it was easy)

We're so happy to have such a wonderful and cute baby girl!

--Dave, Dayna, Noah, and now... Ella.


Graduation 2007

Wednesday, 09 May 2007 21:30

Graduation Day 2007

It is official...we are both done with our Purdue undergrad degrees! Dayna received her BA in psychology with a sociology minor. I received a BS in computer science with a math minor.


Flickr photo boothing.

Monday, 07 May 2007 09:20

Noah and Daddy I was playing with mac OSX's photo booth app the other day. I found a plugin for photo booth which allows you to upload your photos to flickr automatically. I loaded the plugin on both my macbook and my imac. Pretty neat that you can setup a stereo rig like this! I was able to fire off quite a few pictures, many of them in sync. Check out the pics. [Slideshow] [Explore]

Hello daughter...

Thursday, 19 April 2007 06:14

baby unknown's fingers Have a look. Here is the hand of my new baby! Nice to see five fingers.

Noahs first science project!

Monday, 12 February 2007 01:12

laser speedHey guys,

Noah was bored one day so he and I built a machine which measures the speed of light and other physical constants. Noah thought it was pretty remedial but we are really kicking ass in his daycare science fair.

But seriously....I'm building one of these kits cause thats freaking cool. First kid I can convince...I'm building one. :)

Also if I haven't told you already....
Dayna and I are pregnant again!
Just heard the heartbeat.
More info on the baby soon!

Dave, Dayna, and Noah + 1/3

Happy 2007!

Tuesday, 02 January 2007 19:14

Wow, time moves fast. 2006 turned out to be a real nice year. Christmas 06 was really nice, Noah figured out what a present was and how to unwrap them. So it was a lot more fun to watch :).

Have a Happy New Year!

--Dave, Dayna, and Noah

Ideas on VR with my limited knowledge of what is ahead.

Tuesday, 03 October 2006 11:24

Ideas and concepts on VR with focus on augmented reality

Last Updated on Tuesday, 22 December 2020 13:12


Summer update 06

Saturday, 05 August 2006 09:39

webcam pic Summer has been crazy. We've been very busy, Noah is saying his first words.... daddy and mama. This picture is from a webcam we had while I was away on a work trip. --Dave

Welcome to 2006.

Monday, 16 January 2006 20:53

2005 was a good year Noah turned one, he started walking and is learning new things everyday.  He loves our new puppy Hurley that we bought him for Chirstmas.  Hurley is a puggle, which is a pug mixed with a beagle (look for photos in the gallery).

The house is coming along, we finally got our furniture and we really like it.  We've almost painted every room in the house and replaced every major appliance.

Dayna and I are both really busy finishing up school.  We are both in our last year.

--Dave, Dayna, and Noah

Last Updated on Monday, 19 November 2018 22:09


So its been a while, but we are still here!

Tuesday, 26 April 2005 19:25

Hey everyone!  It has been six months since our last update.  We are really doing great.  Noah is getting BIG!  He's started to eat baby food in addition to his normal bottles.  Dayna and I couldn't be happier.  The house is coming along, we've now painted four rooms.  Our next improvement is all new furiture which we ordered a month ago!  So we are patiently (all, I guess I have to be patient) waiting.  We had photos of Noah taken professionally, as well as a family picture of us all.  Check em out in our gallery.

--Dave & Dayna

Last Updated on Monday, 19 November 2018 19:41


Noah is HERE!

Tuesday, 02 November 2004 21:06

After nine months of waiting, Noah David Horner is finally here!  He was born on Oct. 16th 2004 @ 10:59pm.  Noah weighed  9 lbs 5 oz and was 21 inches long.  The labor itself was about 14 hours long.

He's been home now for 2 and a half weeks.  Healthy and happy. :)

I've uploaded some new pictures.  Try the slideshow or browse the photos.

Dayna and I couldn't be more happy.

--Dave, Dayna, and now... Noah.

Last Updated on Monday, 19 November 2018 19:40


Back from Summer Trip of 04

Sunday, 05 September 2004 22:27

We went to North Carolina for Chris and Leslie's wedding on Aug. 14th.  Pictures are here.  On the way there we decided to go to Fl. to visit family.  It was a fun time.  Dayna and I swam in the ocean.  We still haven't picked up our professional wedding photos.  We'll post em when we get em.

Last Updated on Monday, 19 November 2018 22:10