This blog post is about 3 documents I found recently, which are both interesting and correlating.
The first is the 1998 article by Francis Crick and Christof Koch with the title : Consciousness and Neuroscience.
The second is a brochure by SIAM (Society for Industrial and Applied Mathematics) about the possibility of a carrier as a mathematician.
And finally, Wolfgang Klimesch’s article on EEG oscillations in alpha and theta band.
End of the first week here at DTU and the 66th ESGI and we already work for 2 days on the Industrial Problems.
We had to give some assignments on the end of the first part of the DCAMM Ph.D. course, so I gave one in modeling a company and another one about the use of Charpit’s Equations to solve a Geometrical Optics problem.
I’m on the problem proposed by Novo Nordisc, regarding the Protein Structure Modeling and we try to understand how we can predict the 3d structure of a protein based only on it’s amino acids sequence.
I also found an interesting game, called FoldIt, where people try to solve protein folding puzzles, which is difficult, funny and helps the science.
I’m also happy for buying a card game called SET, which I played last year in Vancouver and couldn’t find it in Greece. The day I bought it, I met some great Danish guys in Copenhagen and we played SET while drinking beers on a garbage container, in one of the most touristic places of Copenhagen. 
We also went to a thing called Kro, which means “inn”, and is a popular kind of danish pubs.
There we played a danish game with dices, which is something between Kranen and Liar’s dice (I’m not really sure).
Sunday was dedicated to sightseeing. I went to some touristic locations in Copenhagen, saw the famous Little Mermaid, tried to find the Google offices in downtown Copenhagen (no luck with that), spent some time studying at the beautiful garden of the Museum of Decoration (or something ) and then I spent the afternoon in Christiania, where I followed the music and ended up at a punk concert (no live bands at that moment) where a strange and original bike-war was taking place. The teams had modified bicycles turning them into some sort of war trucks and they were trying to destroy the opponent’s truck. It was funny and had a lot of people there.
Apart from that I walked to the beautiful deer park near DTU, found the Dyrehavsbakken, the world’s oldest amusement park (1583) and ended up to the beach, where I was able to wet my hands with the waters of Øresund. There I found a party organized by the local Gymnasium’s students which was taking place at a beautiful location. Tonight I did the same thing but with a borrowed bike, which allowed me to cover many more kilometers in a fraction of the time.
In my next post I’m going to discuss some facts about Denmark.
Here is a list of the summer schools organized in Greece this summer and a few interesting seminars in the next months. As you can see, this is a (scientifically) hot summer in Greece! 
Summer Schools
Economics & Econometrics Advanced Summer School (Rethymno, Crete)
EKEFE Demokritos Summer School (Athens)
Mathematical Modeling (Athens)
Non Linear Science & Complexity (Athens)
5th Mathematics Summer School (Heraklion, Creta)
20th Advanced Physics School (Heraklion, Creta)
9th Astronomy Summer School (Volos)
Onassis Foundation Science Lectures (Heraklion, Creta)
Looks in Modern Physics — for high school students
Seminars and Congresses
Stoa tou Bibliou - Free University
12th Panhellenic Conference in Mathematical Analysis (University of Athens)
8th Panhellenic Conference in Algebra, Number Theory and Application (NTUA)
4th International Summer School on Emerging Technologies in Biomedicine (Patra)
8th International Conference on Bioinformatics and Bioengineering (Athens)
Now that the snows have gone and the seismology project is over, I can concentrate on my exams…
However, the other night I tried to sleep (after drinking a late coffee). I couldn’t, so while thinking about some numbers, i realized that i can’t think of a numbers without “spelling” it in my mind. For example, it is impossible to think the shape or the idea of 3 without saying “three”. Some times, i can even feel my tongue trying to move when thinking of numbers. Of course, the same thing happens while writing this post, but i guess this could be expected.
From my point of view, this means that (at least for my brain) there is a “connection” between the cognitive processes of speaking and thinking about numbers and words. I’m not sure whether this is a form of synaesthesia or an inability to process numbers in a more abstract level.
I tried to find papers and references on this, but i didn’t have much luck. An interesting paper (on a slightly different subject) i found is : S.Dehaene, L.Cohen Cultural recycling of cortical maps, Neuron. 2007 Oct 25;56 (2):384-98
Any feedback on this would be highly appreciated.
Please write about any similar experiences you had and even try this mental experiment and share your results!
P.S. Two photos I shot yesterday… Our university in white.
Like the Hawking-Thorne bet, we have been talking with my good friend and fellow mathematician Primelude about the Clay Millennium Problems and if and how they are going to be solved. For a few of them we agree and for others not. So we decided to bet on that. We will post our predictions, and wait if and how some of these are going to be solved. The bet is a one year subscription to a (scientific? ) magazine of the winners choice.
So here are my predictions…
It will be proved to be True, using tools from the Etale cohomology.
Probably False. Counterexample will be found.
Probably will be proved to be False. But even if it turns out to be True,
computationally (–> practically), P will still be not equal to NP.
************************
Grigori Perelman
************************
Smooth solutions always exist for both Navier-Stokes Equations and Euler Equations.
True. I can even predict who is going to prove it, if it happens in the next 30 years.
No! I’m not telling you!
My guess, it is going to happen by finding attributes of the distribution of the primes.
Com’ on! I almost said who!
Btw, i think that if one of the 7 problems is unsolvable,then this is the one.
There exists a theory and it can explain the mass gap… True, true true! 
And now we sit and wait! Or try to win the bet (together with the 1.000.000$)
P.S.
On Goldbach conjecture :
I believe it is true, but it will take us at least 100 more years before it is being solved.
Synæsthesia is the neurological condition where the stimulation of a cognitive pathway leads to the involuntary stimulation of another cognitive pathway. In simple English, it mean that when for example you see a number, your brain reacts as if you have seen a color. This also happens for shapes, letters, sounds etc.
People under the influence of psychedelic drugs can sometimes feel it (the popular “hear the colors and see the sounds” effect) or even people after a stroke.
The most common explanations are two.
1) The cross-activation of adjacent regions of the brain which are involved in the color and numbers/letters recognition.
2) The reduction in the amount of inhibition along feedback pathways (can explain the LSD/mescaline effects).
But what do all of these have to do with Algebra?
Well, last night while studying Algebra (from the wonderful textbook A First Course in Abstract Algebra - J.Fraleigh, which i highly recommend) i stopped on a phrase saying that the Dihedral D4 symmetry group is simple and beautiful.
And this is true. D4 is beautiful. But how can you see that in this Cayley table?
| o | I | T | R | R2 | R3 | RT | R2T | R3T |
|---|---|---|---|---|---|---|---|---|
| I | I | T | R | R2 | R3 | RT | R2T | R3T |
| T | T | I | R3T | R2T | RT | R3 | R2 | R |
| R | R | RT | R2 | R3 | I | R2T | R3T | T |
| R2 | R2 | R2T | R3 | I | R | R3T | T | RT |
| R3 | R3 | R3T | I | R | R2 | T | RT | R2T |
| RT | RT | R | T | R3T | R2T | I | R3 | R2 |
| R2T | R2T | R2 | RT | T | R3T | R | I | R3 |
| R3T | R3T | R3 | R2T | RT | T | R2 | R | I |
I believe that the following representation is much better for seeing the underlying beauty and symmetry.
So, i decided to create a web application for doing exactly this. You provide the Cayley table of the group, and it returns you the color representation of it.
You can find it here : http://papaya.hep.ntua.gr/projects/algebra/
For any suggestions/problems, fell free to contact me.
The last few months, I am viewing the Physics III (Vibrations and Waves) video lectures from MIT.
So, I am writing this post, in order to express my appreciation and my support to MIT’s effort with OpenCourseWare to provide free and quality knowledge for everyone. I always believed that this effort is important and original, but know that I’m using it in a more systematic way i see that it is a really useful tool (especially for people who don’t have access to academic education).
The second reason I’m writing this, is to inform you about one of the best professors I’ve ever had the pleasure to attend their lecture.
I’m speaking of Walter Lewin, the physics professor at MIT who teaches the Physics I, II and III there.
The things he is doing are not even close to anything else I’ve ever seen in a classroom.
He jumped on a huge pendulum to present the idea that period doesn’t change with mass.
He inhaled Helium to prove that the velocity of sound in Helium is 3 times more than in air.
He broke a glass with a special device which produces high frequency sound, to display the ω–> ω0 effects.
He brought a whole orchestra of students to play in front of a microphone connected to an oscilloscope to explain the different sound quality of each instrument.
and many many more…
You can find many of his videos online, and you can also download his lectures from OCW.
A mathematician is a machine for turning coffee into theorems. - Alfréd Rényi
After pulling an allnighter last night, in order to stay awake during the day i needed huge amounts of coffee.
So i decided to write a post (the first of a series of posts on this subject) about the neurological effects of this miraculous drug called caffeine.
<WARNING - Organic Chemistry>
Caffeine is trimethylxanthine and is found in plants to protect them from various insects.
It is metabolized in the liver, to 3 dimethylxanthines (replacing CH3 with H) which have their own distinct but physiological effects :
Paraxanthine, Theobromine and Theophylline
So, how does caffeine works?
Caffeine has a similar structure to adenosine, which is used in ATP and ADP (the “energy credits” of the cells) and is also an inhibitory neurotransmitter. As neurotransmitter, the main action of adenosine is probably to promote sleep.
(HINT: A receptor is a protein in the cell. where molecules can bind and promote a cellular response)
Due to the similar structure, after crossing the blood brain barrier (or : when it is in the brain) caffeine acts as an antagonist of the A1 and A2A adenosine receptors (and Theophylline acts as an antagonist for the other two). This means, that it binds on the receptors, and prohibits the adenosine binding. This fact stimulates the release of dopamine.
Furthermore, caffeine increases the production of serotonin, epinephrine and gastric acid.
The main effects of the 3 metabolites of caffeine are :
Paraxantine : Increases lipolysis (”more energy for the muscles”)
Theobromine : Dilates the vessels, resulting in increased supplies of oxygen and nutrients to the brain and the muscles.
Theophylline : Increases heart rate and efficiency.
Dopamine is a neurotransmitter, which bind on the Dopamine receptors, who control motivation, pleasure and learning.
Dopamine in the mesolimbic pathway (a neural pathway of the brain) decreases latent inhibition and promotes arousal.
This facts, induce the creativity and idea generation. However, very high levels of dopamine in the mesolimbic pathway are connected with psychosis and schizophrenia.
</WARNING - Organic Chemistry>
The subject of Creativity, Caffeine, and Latent Inhibition which was the main reason i was prompted to write about caffeine, will be addressed in a later post.
P.S. Biochemistry is a topic where my knowledge is really limited. So most of my information for writing this post came from books and Internet. I found writing this post a good exercise of writing for something you don’t know much, while avoiding plagiarism.
