### Thomas Egense

Shared publicly -**Size of the Universe - beautiful animation**

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Thomas Egense

Works at Statsbiblioteket

Attended Århus Universitet

Lives in Aarhus

17,125 followers|580,996 views

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4

1

I've watched this. It's kind of freaky.

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A loose explanation of the Hilbert Curve is that it is a 1-dimensional curve that 'fills' the 2-dimensional plane.

It has several practical applications as well. One of them is to quickly come up with a very good solution to the traveling salesman problem that has not generally solved (and probably never will). You visit the points in the same order as dense enough (for your purpose) Hilbert Curve would visit them when you overlay the Hilbert curve on the plane with the points.

The Hilbert curve begins at generation zero as a single point in the middle of the square. Subsequent generations are formed by a recursive process of replication and linking. Four shrunken copies of the curve are distributed to the four quadrants of the square, then reoriented so that the end ...

5

2 comments

Impressive performance, drawing 6. iteration by hand:

https://www.youtube.com/watch?v=qRuHzitPEKs

https://www.youtube.com/watch?v=qRuHzitPEKs

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The following number is apparently prime (can you spot the odd digit out, without ctrl-F?) #idle (via Michael Murray pointing me to a reddit page on maths)

99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999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+David Roberts

Thank goodness. Some people consider me extremely eccentric because I happen to have a natural knack for mechanically performing sequences of actions in the manner of a computer program. In fact, one programmer once commented to me, "You think remarkably like a computer program." However, this skill turns out to be extremely useful when proofreading (I am a professional translator/proofreader/editor).

Thank goodness. Some people consider me extremely eccentric because I happen to have a natural knack for mechanically performing sequences of actions in the manner of a computer program. In fact, one programmer once commented to me, "You think remarkably like a computer program." However, this skill turns out to be extremely useful when proofreading (I am a professional translator/proofreader/editor).

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Elon Musk just revealed the first week sales number. He admitted that they need to ramp up production somehow to meet that high a demand... More than twice what anyone within Tesla had expected.

#teslamotors

#teslamodel3

A week ago, we started taking reservations for Model 3, and the excitement has been incredible. We’ve now received more than 325,000 reservations, which corresponds to about $14 billion in implied future sales, making this the single biggest one-week launch of any product ever. This interest has spread completely organically. Unlike other major product launches, we haven’t advertised or paid for any endorsements.

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Another mystery of the universe solved.

Ten days ago, Maryna Viazovska showed how to pack spheres in 8 dimensions as tightly as possible. In this arrangement the spheres occupy about 25.367% of the space. That looks like a strange number - but it's actually a wonderful number, as shown here.

People had guessed the answer to this problem for a long time. If you try to get as many equal-sized spheres to touch a sphere in 8 dimensions, there's exactly one way to do it - unlike in 3 dimensions, where there's a lot of wiggle room! And if you keep doing this, on and on, you're forced into a unique arrangement, called the

In 2001, Henry Cohn and Noam Elkies showed that no sphere packing in 8 dimensions could be more than 1.000001 times as dense than E8. Close... but no cigar.

Now Maryna Viazovska has used the same technique, but pushed it further. Now we know:

Viazovska is an expert on the math of "modular forms", and that's what she used to crack this problem. But when she's not working on modular forms, she writes papers on physics! Serious stuff, like "Symmetry and disorder of the vitreous vortex lattice in an overdoped BaFe_{2-x}Co_x As_2 superconductor."

After coming up with her new ideas, Viaskovska teamed up with other experts including Henry Cohn and proved that another lattice, the

Different dimensions have very different personalities. Dimensions 8 and 24 are special. You may have heard that string theory works best in 10 and 26 dimensions - two more than 8 and 24. That's not a coincidence.

The densest sphere packings of spheres are only known in dimensions 0, 1, 2, 3, and now 8 and 24. Good candidates are known in many other low dimensions: the problem is

For example, in 3 dimensions there are uncountably many non-periodic packings of spheres that are just as dense as the densest lattice packing!

In fact, the sphere packing problem is harder in 3 dimensions than 8. It was only solved earlier because it was more famous, and one man - Thomas Hales - had the nearly insane persistence required to crack it.

His original proof was 250 pages long, together with 3 gigabytes of computer programs, data and results. He subsequently verified it using a computerized proof assistant, in a project that required 12 years and many people.

By contrast, Viazovska's proof is extremely elegant. It boils down to finding a function whose Fourier transform has a simple and surprising property! For details on that, try my blog article:

https://golem.ph.utexas.edu/category/2016/03/e8_is_the_best.html

#geometry

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""for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory.""

+Alex Bellos made an easy to comprehend write-up about the work of Andrew Wiles.

http://www.abelprize.no/c67107/binfil/download.php?tid=67038

3

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moderator

Yellow blob fractal morph
Stop-motion video of 8000 fractal images put together to a 5 minutes video. It took 12 days to calculate the 8000 fractal… - Thomas Egense – Google+

3

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My latest project is using Natural language processing (NLP) read **Lord of the Rings** and plotting characters by 'similarity' in 2D.

The algorithm (using word2vec) knows nothing about the English language but just see how words are 'grouped' together and done statistics/neural network training. I then define a distance measure between the words and fits them in a 2D plot.

I also feed the algorithm 35000 english books from the Gutenberg project and made a plot of different animals.

It is very hard to decide how much the 2D plot captures of the similarity between the words. But I believe they are much better than a random plot.

The algorithm (using word2vec) knows nothing about the English language but just see how words are 'grouped' together and done statistics/neural network training. I then define a distance measure between the words and fits them in a 2D plot.

I also feed the algorithm 35000 english books from the Gutenberg project and made a plot of different animals.

It is very hard to decide how much the 2D plot captures of the similarity between the words. But I believe they are much better than a random plot.

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I thought the Lord of the Rings was very well represented. I haven't read the second book, so I should not comment. The animals also seem to be clustering well. Fish is far from all. Mammals tend to cluster together, reptiles, too, with the more aquatic one closer to the fish.

Pretty good!

Pretty good!

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New mathematical lower limit on the maximum size of a set without a match for the generalized case of the well known card game "Set". The "Set" game has 4 different features to match. For the "Set" game the maximum set size is 20 cards without a match etc. But for the generalized case with n features the exact maximum is too hard to calculate, but a much better lower bound has just been proven.

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There does not exist a two-coloring of the integers without a

pythagorean(a^2+b^2=c^2) triple in the same color.

Brute force attack(with many optimizations) showed for n>7824 there will always be a triple in the same color.

Before this brute force attack it was unclear if a 2-coloring existed for all integers! But we did know there existed a O(log n) coloring for integers 1 to n without a monocromatic pythagorean triple.

The problem is somewhat similar to Schur's theorem where the equation is a+b=c instead (not squared). Schur's theorem states that no finite coloring exists on all integers without a monochromatic a+b=c solution.

Programming book reviews, programming tutorials,programming news, C#, Ruby, Python,C, C++, PHP, Visual Basic, Computer book reviews, computer history, programming history, joomla, theory, spreadsheets and more.

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http://arxiv.org/abs/1605.00723 for the paper

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Toke Eskildsen

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Kinda envious here. Of course of the car, but mostly of your "Fuck it, I'll buy my dream car"-attitude. Rock on!

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Any pattern in prime numbers seems to contradict the random behaviour prime numbers have shown so far and several conjectures depending on their randomness.

The individual prime numbers might still appear random, but the claim in this article is that there is a strong pattern in subsequent primes.

arXiv PDF: ( http://arxiv.org/abs/1603.03720)

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There is going to be a 3d fractal or other geometry discovered that successfully predict primes.. I am convinced for this.

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Thomas's Collections

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- Århus UniversitetCand. Scient, Mathematics/Physics, 1991 - 2000

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Zoozie

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Tagline

I have a math blog and I am generally interested in all kinds of scientific matters. I use mathematics to create art – you can check out my album. I try to find unique content for my posts,which are mostly of scientific nature.

Introduction

Keywords that describe me as a person: scientist, mathematician, sceptic, atheist, blogger, and digital artist.

I blog about my mathematical adventures, where I, among other things, solve various puzzles, which often involves brute force CPU attack on the problems.

In my spare time I use mathematics to create art.

For the last 12 years I have worked as a Java programmer.

I like retro-gaming, and I never become tired of talking about old-school games or computer

music (C64/Amiga).

I love animals - especially cats - and I have two cats of my own.

I blog about my mathematical adventures, where I, among other things, solve various puzzles, which often involves brute force CPU attack on the problems.

In my spare time I use mathematics to create art.

For the last 12 years I have worked as a Java programmer.

I like retro-gaming, and I never become tired of talking about old-school games or computer

music (C64/Amiga).

I love animals - especially cats - and I have two cats of my own.

Bragging rights

Cream of the Crop 15/4-2012: http://www.circlecount.com/daily/?date=04%2F15%2F12

Work

Occupation

IT Specialist(J2EE)

Employment

- StatsbiblioteketIT Consultant, 2011 - present
- IBMAdvisory IT Specialist, 2006 - 2011
- AcureSoftware developer, 2005 - 2006
- Mærsk DataConsultant, 2003 - 2005
- LECConsultant, 2000 - 2003

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Aarhus

Previously

Århus

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Home

Phone | 24409997 |

- thomas.egense@gmail.com
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Thomas Egense's +1's are the things they like, agree with, or want to recommend.

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