### Thomas Egense

Shared publicly -**Game of thrones Season five to be premiered TODAY**

And if you want a small recap of what happened in the previous four seasons these gorillas have a very short version of the plot :)

via +Søren Sprogø

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Thomas Egense

Works at Statsbiblioteket

Attended Århus Universitet

Lives in Aarhus

16,659 followers|516,012 views

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And if you want a small recap of what happened in the previous four seasons these gorillas have a very short version of the plot :)

via +Søren Sprogø

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* Five Podcasts from BBC about the most important programming languages*

The 15 minutes duration of each podcast is perfect timed with the driving time to my workplace...

The 15 minutes duration of each podcast is perfect timed with the driving time to my workplace...

As part of the BBC's Make it Digital Season, Aleks Krotoski presents a brief history of some of the most famous high-level programming languages. Each of these easily digested programmes is only fifteen minutes long and is available online as a stream and as a podcast or MP3 file.

These programmes should be available worldwide without restriction. They are easiest to play on a computer (Flash) although they will work on iOS with a few extra clicks and on Android after the BBC media player http://goo.gl/oHuhfM is installed.

BBC Make it Digital: http://goo.gl/3am6qs

Image: http://goo.gl/AvQf1O

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use to program in fortran 77

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The counterintuitive Borwein Integral

For an explanation see: http://schmid-werren.ch/hanspeter/publications/2014elemath.pdf

(Found on Quora)

#mathematics

For an explanation see: http://schmid-werren.ch/hanspeter/publications/2014elemath.pdf

(Found on Quora)

#mathematics

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Funny 😂

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Article in The New Yorker about Yitang Zhang, this time with more personal information about himself and his life, and not only about his mathematical breakthrough.

Excellent piece in The New Yorker about Yitang Zhang and his groundbreaking work establishing that there is a bound on the gap between two consequent primes no matter how far along we are on the road to infinity.

Zhang's example shows that it's possible to do top level mathematical research outside of the academia. Good new for all of us, and... shame on you, academia!

Zhang's example shows that it's possible to do top level mathematical research outside of the academia. Good new for all of us, and... shame on you, academia!

Unable to get an academic position, Zhang kept the books for a Subway franchise. Credit Photograph by Peter Bohler

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I've always thought along these lines. Science is for everyone

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Quanta Magazine printed this article a few days ago about Ciprian Manolescu and is worth a read. The mathematical concepts are explained very well for the casual math reader.

Sometimes, triangles just don't cut it.

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It is now over 2 years since he published a still unconfirmed proof of the ABC-conjecture which was thought impenetrable hard to crack. The proof was base on years of work in a branch of mathematics called 'inter-universal Teichmüller theory' that noone know or seems to understand. Following his steps and understand the proof is really difficult and would take years of dedicated work in a field that may lead nowhere if the proof is wrong.

Up to now he has not been speaking to the press, but he has created a workshop where he will answer questions and help other mathematicians to understand it.

It is not that easy to explain what the ABC conjecture in a few lines, but more information can be found here:

https://plus.google.com/u/0/117663015413546257905/posts/Npu7xDniXMS

or

https://www.youtube.com/watch?v=RkBl7WKzzRw#t=346

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Richard Elwes

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I don't think he's spoken to the press - my understanding is that this news is based on his December 2014 progress report (in which some frustration is evident): http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTeich%20Verification%20Report%202014-12.pdf

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1,868 people

After 200+ years of collecting all danish newspapers and stacking them in warehouses or copying them to microfilms, they can now be accessed online for free! At The State And University Library Aarhus we have been working on this project for years and are very happy to open it to the public today.

We have build a powerful search engine on top of all data so it is easy to find text matches down to a specific page with highlighting and you can download the newspaper as a PDF. For historians this is a gold mine and the general public will be able to search for family members or old articles they want to read again.

Limitations:

So far we have only 1 million news paper pages in the index, but this will increase to over 32 million pages over the next year.

You can only search in newspapers that are older than 100 years, unless you search from the computers within the State and University Library where there is no limitations.

The OCR (Optical character recognition) is not perfect and this is most evident in oldest newspapers, but we have several ideas how to improve this over time.

Since we just went live today there is a heavy load on the site - so be gentle :)

+Peter Mouritsen

+Toke Eskildsen

+Mads Villadsen

+Per Møldrup-Dalum

Din e-mail-adresse (hvis du vil have svar fra os): OK Mediestream bruger cookies til at lave statistik over trafikken på siden og til at forbedre brugeroplevelsen. Ved at klikke videre accepterer du brugen af cookies, som du i øvrigt til enhver tid kan slette. Læs mere om vores cookiepolitik.

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The 'Langlands program' can be compared to the similar hunt for a "Unified Theory" in physics. The program is trying to connect previous believed totally unrelated branches of mathematics and some of the found connections is still a mystery.

If you want a much deeper understanding about this project I can recommend reading "Love and Math" by Edward Frenkel. But the book require

Canadian Robert Langlands is 'like a modern-day Einstein,' who has devoted his life to the limits of pure mathematics

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Rhg

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The one to the right in wrap (Seaweed 120cm*120cm) is sold to +Jacques Riget and is copy #3 and final print of this fractal.

The two to the left (Turtle and Octopus) are replacements of the two sold to +Marselisborg Gymnasium.

The two middle smaller fractals are on printed on glass and due to reflections very hard to catch sharp on camera.

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moderator

For an explanation see: http://schmid-werren.ch/hanspeter/publications/2014elemath.pdf

(Found on Quora)

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Well .499999999999 can be written as .5 which is 1/2

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During lunch discussion at my workplace we started wondering if there existed a fixpoint for the md5 cryptographic hash function.

That is a point such that md5('x')='x' where x is the 32-digit hexadecimal string representation.

To be completely truthful the md5 algorithm works on 512 bit values. A 32-digit hexidecimal string is 128 bit and is first padded(with zeroes) to 512 bits before the md5 function is taken and

returns a 128 bit value which then is converted to a 32 digit hexidecimal string thus explaining my md5('x')='x' expression.

Some googling showed this is known as the "Kember Identity" and is an unsolved problem. Also a few programmers had tried to brute force it over the years with no luck (not surprisingly as you will see below). Even though I would never succeed I decided to look into the problem anyway.

Interestingly there is a simple mathematical argument that there is ~63.21% probability for at least one fixpoint. This does not mean there is one of course! But it also reveals there is probably only a few, if any! The argument is based on the same principly that when you shuffle a deck of card, what is the probability that at least one card will end up in the same position in the deck. The probability actually converges to 1-1/e very fast as the number of the elements shufled increases. There is no guarantee that the md5 function is a shuffling though, there could exist different 32-digit hexidecimal strings x,y such that md5(x)=md5(y). But such collisions are extremtly rare and would not change the overall probability by much.

Examples of different x,y with same hashing value does exist , see http://en.wikipedia.org/wiki/MD5 etc. But this example is 512 bit and not 128 bit (32 hexidecimal). The md5 hash function is not considered safe anymore due to collision vulnerabilities , but this is completly irrelevant to my mission of finding a fix point.

Lets see how futile a brute force attempt will be:

There are 2^128= 32^16 ~ 3.4*10E38 different values.

My brute force program can do 3.5M hash/sec (For each CPU used)

This gives 3*10E24 years to try all combinations (Using 1 CPU).

Not a very uplifting result and now you know why I used the word futile.

So without a cryptographic breakthrough, humanity will never know if such a point indeed does exist.

And now back to my brute force attempt:

I made a small Java program that can be found on Github on the link below.

Thanks to +Toke Eskildsen for doubling the performance using tricky bit manipulation instead of the standard Java methods as substring, equals etc.

The code is much harder to read now though, nothing comes for free...

The program starts with a random 32 digit hexadecimal string (for each CPU) and then iterative computes md5(x) and check if it matches x. Using this endless chaining of md5 values there is no performance overhead from generating a a lot of random strings. Of course there is a (tiny!) probability that this would result in an endless loop as it eventually is bound to do! But cycle detection would slow

the program down and detecting a cycle having 1E10 elements would take way too many resources anyway. Also I restarted the program

regulary over the 2 weeks I had it running on 24 CPUs and this would have reset any loops.

Since I would not find a fix-point but still would like to program to output somthing, I logged the maximum prefix and suffix match for md('x')='x'

The maximum match I found was a 12 character suffix and a 12 character prefix match shown below:

54db1011d76dc70a0a9df3ff3e0b390f -> 54db1011d76d137956603122ad86d762

df12c1434cec7850a7900ce027af4b78 -> b2f6053087022898fe920ce027af4b78

Remember this used 24*2weeks = 0.9 year CPU time. If you run it and find a 13 character match or more, I would like to hear for you of course.

MD5FixPointSearch - A simple java program that attempts to find a fix point for the MD5 function. It will try find a maximum prefix/suffix match.

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David Jao

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The bitcoin network currently produces 2^58 hashes per second (SHA2 hashes instead of MD5, but the idea is the same). At this rate it would only take 3.8E13 years.

On the other hand it would surely improve on the prefix and suffix matches.

On the other hand it would surely improve on the prefix and suffix matches.

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Combine the golden ratio with a fractal recursion algorithm and you get the newly invented **Hariss Sprial**.

Here's me in the Guardian on some fascinating work by +Edmund Harriss, in which I take the liberty of naming this curve after him. He was, after all, the first to draw it....

Inspired by the golden ratio, mathematician Edmund Harriss discovered a delightful fractal curve that no one had ever drawn before. But it’s not just a pretty picture, it contains some lovely theory – and brings the golden ratio into a family of perfect proportions.

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Sehr schön

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In his circles

1,868 people

Communities

5 communities

Education

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

Basic Information

Gender

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Other names

Zoozie

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- My Fractal Art (current)

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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

Places

Currently

Aarhus

Previously

Århus

Contact Information

Home

Phone | 24409997 |

- thomas.egense@gmail.com
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