What a fun course this was. The lecturer of Introduction to Number Theory, Ed Burger, a math PhD, looks like what one would expect a mathematician to look like: thin, tall, geeky looking, wearing a rather bland costume, but with a colorful tie, curly hair and large glasses, with a sincere smile that seems a bit sad. The thing is, he is also a lot of fun and his enthusiasm regarding mathematics is not only obvious, but catchy as well.

The course itself requires very little if any mathematical education to understand, being mostly about ideas, rather than formulas. It is a Teaching Company course, and each lecture builds upon the understanding from the previous ones, making surprising and really fun connections.

I was very sad when the course ended, I wanted more! Happily, I've got "The Joy of Thinking" and "Zero to Infinity - a History of Numbers" that are also lectured by Ed Burger and I can't wait to watch them all. I highly recommend the course, even if one is not interested in math. It opens the mind on a way of thinking, useful in any situation, rather than anything specific.

My world view is limited by the data that comes to me. I have my tiny slice of reality, a few friends, my work, then there are movies, news, documentaries, the Internet and so on. You will notice that I placed them in a certain order, it is the order that to me seems to go from more bullshit and less information to more information. I never believed the expression "Truth is stranger than fiction", so lets set the slice of reality aside. And, being first on my list... full of bullshit :)

Movies teach me a lot, but there is just as much untruth and deceit in them as there is stuff worth knowing. News are focused on a part of life that normally doesn't interest me, but they still have a higher percent of useful information. Then there are the documentaries, stuff from Discovery Channel and the likes. Well, I have mixed feelings about those. There are things that they teach me and they do it in a pleasant manner, yet, by the time they end, I feel like there is so much more that I wanted to know and that it all just stopped when it got interesting. On further analysis, it seems the quantum of information in an hour of film was something I could blog in two or three paragraphs.

And then there is the Internet. It is bursting with information, if only I knew where to look and only if I had the discipline of researching, summarising and storing that information. I am working on that, even this blog is used to store what I find, but I am still only an amateur. There is something that attracted me a while ago, something called Open Courseware. There were courses from the largest universities, freely available on the net. However, they left me feeling disappointed as they were mostly text, the few that were in media format were mostly audio and, in the end, they were only poor recordings of classroom courses, sounds of scribling on the blackboard included.

Enter The Teaching Company, a company that produces recordings of lectures by nationally top-ranked university professors as well as high-school teachers. The lectures are well done, they feature some guy or gal that present the information without having to write stuff on blackboards. If anything is to be shown, it will be a computer slide or animation, while the details on spoken information are added to the screen (for example the names of people). Wonderful stuff, only it is not free.

If you go to the official site you will find courses on just about anything, priced at around 35$ per download and 70$ per DVD if they are "on sale" and the rest of them going to about 250$, with a range of 20-40 lectures per course. Of course, there is the option of looking for "TTC torrent" on Google and see what you find there. For the people in Africa that just got an Internet cable installed, I mean.

I had the luck to start with linguistics (Understanding Linguistics: The Science of Language by John McWhorter), lucky not because linguistics is so interesting, but because John McWhorter was really charismatic and had a very well constructed set of lectures. And because linguistics is an interesting topic, at least at the introductory level of this course. It was funny, too, the guy is what I imagine a typical New Yorker to be. He is black with a Scottish name, he talks a lot of Broadway plays and old movies, he is socially astute; very cosmopolitan.

Then I went for astronomy (New Frontiers: Modern Perspectives on Our Solar System by Frank Summers). If you like those National Geographic documentaries about the solar system, you will love this. Towards the end it got detailed in a bad way, but only compared with the beginning of the course, which was really well done. The lectures are about the Solar System, from the standpoint of a modern astronomer, in light of all the recent discoveries. Also, a very well made point about why the structure of the solar system was revised and Pluto got demoted. At the end it talks of other star systems and what are the methods to detect and study them.

Not all the courses are so good, though. I had the misfortune of trying out Superstring Theory: The DNA of Reality by Sylvester James Gates, Jr. The guy is a black man in his late fifties who tries to explain Superstring theory without using any mathematics. He starts by repeating a lot of what he said in previous lectures and, indeed, in the same one earlier on, then goes asking these stupid questions that repeat what he said again. Something like "As I said in a previous lecture this and this and this happened. But why did this and this and this happen?". Ugh. If it was only about that, I would have finished watching the course, but it was something completely unstructured, boring and dragging. After 12 lectures out of 24 I knew nothing about string theory, except vague things like "if I imagine a ball that goes towards another ball and they shout at each other and the waves make other balls while the previous balls disappear but wait they appear again...". What I knew is that I had to stop watching. Sorry, Mr. Gates, lecturing... just not your thing. Stick to short appearances on Nova PBS shows.

Right now I am on Building Great Sentences: Exploring the Writer's Craft by Brooks Landon. It talks about constructing good sentences in order to improve one's writing. I have the feeling that the guy uses more detail than necessary. Like when he explains a concept he has to give at least 5 examples, when 2 or 3 would have been enough. But then again, maybe I am wrong. I will have to finish the course to give you a definite opinion.

Next on my list:
Quantum Mechanics: The Physics of the Microscopic World by Benjamin Schumacher
Understanding Genetics: DNA, Genes, and Their Real-World Applications by David Sadava
Introduction to Number Theory by Edward B. Burger
Understanding the Brain by Jeanette Norden

Does all this make me a very smart person? Not really. Remember that most of these are introductory courses. They do not contain exercises or books that you need to read, nor do they require a very high level of previous knowledge in order to understand them. They are, pure and simple, like those Discovery Channel shows, only they don't end when they get interesting and they are not so full of bullshit. After watching one of these courses (or, indeed, listening to them as podcasts while you are going to work) you will have an idea on where to go digging deeper for the topics that interest you.

Good learning!

First time I've ever heard of cymatics and I am intrigued. basically you use some (physical) devices to visualize soundwaves. Here is a small TED presentation about it:



My question is simple: can this be used to "understand" sounds for deaf people or are the pattern transitions too complex? googling for cymatics I've found a lot of videos about water and cornstarch moved by sound and links to "sound healing" and even some technical papers that never seem to have left academia. I think this could be interesting enough to emulate on a computer, yet I have not found code for it yet.

I don't pretend to know much about mathematics, but that should make it really easy to follow this article, because if I understood it, then so should you. I was watching this four episode show called Story of Maths. Its first episode was pretty nice and I started watching the second. The guy presented what he called the Chinese Remainder Theorem, something that was created and solved centuries before Europeans even knew what math was. It's a modular arithmetic problem. Anyway, here is the problem:

A woman selling eggs at the market has a number of eggs, but doesn't know exactly how many. All she knows is that if she arranges the eggs in rows of 3 eggs, she is left with one egg on the last row, if she uses rows of 5, she is left with 2 eggs, while if she uses rows of 7, 3 eggs are left on the last row. What is the (minimum) number of eggs that she can have?
You might want to try to solve it yourself before readind the following.

Here is how you solve it:

Let's call the number of eggs X. We know that X ≡ 1(mod 3) ≡ 2(mod 5) ≡ 3(mod 7). That means that there are three integer numbers a, b and c so that X = 3a+1 = 5b+2 = 7c+3.

3a = 5b+1 from the first two equalitites.
We switch to modular notation again: 3a ≡ 1(mod 5). Now we need to know what a is modulo 5 and we do this by looking at a division table or by finding the lowest number that satisfies the equation 3a = 5b+1 and that is 2. 3*2 = 5*1+1.

So 3a ≡ 1(mod 5) => a ≡ 2(mod 5).

Therefore there is an integer number m so that a = 5m+2 and 3a+1 = 7c+3. We do a substitution and we get 15m+7 = 7c+3.

In modular that means 15m+7 ≡ 3(mod 7) or (7*2)m+7+m ≡ 3(mod 7). So m ≡ 3(mod 7) so there is an integer n that satisfies this equation: m = 7n+3. Therefore X = 15m+7 = 15(7n+3)+7 = 105n+52

And that gives us the solution: X ≡ 52(mod 105). The smallest number of eggs the woman had was 52. I have to wonder how the Chinese actually performed this calculation.

Let me summarize:
X ≡ 1(mod 3) ≡ 2(mod 5) ≡ 3(mod 7) =>
X = 3a+1 = 5b+2 = 7c+3 =>
3a ≡ 1(mod 5) =>
a ≡ 2(mod 5)=>
a = 5m+2 =>
X = 15m+7 = 7c+3 =>
15m+7 ≡ 3(mod 7) =>
m ≡ 3(mod 7) =>
m = 7n+3 =>
X = 15(7n+3)+7 = 105n+52 =>
X ≡ 52(mod 105).

For me, what seemed the most hard to understand issue was how does 3a ≡ 1(mod 5) turn into a ≡ 2(mod 5). But we are in modulo 5 country here, so if 3a equals 1(mod 5), then it also equals 6(mod 5) and 11 and 16 and 21 and so on. And if 3a equals 6(mod 5), then a is 2(mod 5). If 3a equals 21(mod 5), then a equals 7(mod 5) which is 2(mod 5) all over again.

First of all I want to say that I know I haven't been writing many tech articles lately and I've disappointed quite a few of the people reading this blog. I intend to rectify that, even if I am suferring from one of those dry tech spells at the moment :)

Anyway, about the oil. What if one could replicate the process that creates oil naturally, speed it up, and use it to not only for creating oil, but also for getting rid of a lot of organic waste? The technology is called Thermal Depolymerization and is pattented by the Changing World Technologies company. So, if one is to believe the Wikipedia article, while the test factory and the company itself have had problems ranging from technological hickups, to having to pay for the waste they use as fuel up to neverending complains from neighbours about the smell of bio waste, the technique was shown to work!

So, while the process does allow the production of slightly cheaper oil than the one extracted, it will certainly gain a big boost from the increase of prices in underground oil.

Here is a link to a 2003 interview with the CEO of Changing World Technologies, but utterly demolished by Paul Palmer, a chemistry PhD here. Also, this process is nothing very new or unique! there are other methods that are said to transform organic waste to Ethanol, as described in this link. So, oil may not dead yet.

The concept of Open Courses is not so new. You've probably stumbled across some course package that is both free and online, but that is just not doing anything for you. A good example is the Microsoft courses, which need that annoying passport registration, you need to take the html based courses in a specific amount of time and they spam you with all the email reminders. What you actually wanted was information, quickly summarized, indexed maybe, and a video/audio stream that would demonstrate what the theory is all about. You don't want to register, have restrictions or even do it online. You want to download stuff and run it locally whenever you feel like it.

I am glad to say I found exactly what I wanted in the MIT Open Course Ware site. They have a huge list of classes, most have only PDF materials, but some have video recordings of the actuall class! With PDF notes! Even MP3 materials for your mp3 player! No registration required and everything you have there you can also find on YouTube! And the videos are profesionally shot, not some web cam in the back thing.

Interested yet? Access the site and browse about. You might want to use this link to get to the audio/video only courses or use Google to find only the courses that have video. You won't get MIT to say you studied with them, but you will learn what they teach if you make the effort!

One thing you need to be able to run the .RM files is Real Alternative, a package that allows you to play Real Media without installing the annoying and not free Real Player.

And MIT is not the only one doing that. You can access the links of:
Open Courseware Consortium
OpenContentOnline
Open Courseware finder

I've found this while randomly browsing the net, a substance that is supposed to be increasing memory and brain plasticity called ampakine. An article called it steroids for the brain and I borrowed that in the title, since I found it is appropriate enough.

Like all mind enhancing drugs it was discovered by accident, while working on a cure for Alzheimer. Why would anyone try to enhance one's brain on purpose, anyway? :-|

I am not much of a biochemist (even if I recently made some acquaintances that are :) and I could ask them to enlighten me) so I will just post a list of links that I found on the subject. It seems that there are no publicly available pills yet, as the drug is still in trials, but who knows... maybe we can become smarter rather than dumber for a change.

Here are the links:

ampakines
A profile of the behavioral changes produced by
facilitation of AMPA-type glutamate receptors
ampakine
Ampakines
'Memory pill' for the forgetful

How to Sleep Better is a BBC programme that tries to solve some of the issues related to sleep. It does NOT show you how to sleep better in a shorter time, it is about fixing the problems that make you sleep badly or less than you want.

The program is very interesting indeed. I was kind of put off when I didn't find it on video.google.com and it is not found freely on the programme's site either, so you should seek it on BitTorrent or DC++.

Anyway, long story ridiculously short, it started from a survey of common sleep problems and then they tried to find solutions. There was a snorer, a couple with a screaming child, a woman too obsessed by work to sleep well, an old man who couldn't sleep well from his youth, a flight attendant that could not sleep well in her own home, but could do it in a hotel and some guy that worked driving night shifts.

Solutions:

The snorer should lose weight to relieve some of the fat on her neck, but she could also try tennis balls hooked on her back (with a bra) to stop her from sleeping on her back. But there was a thing that she put in her mouth that solved it. Apparently, snoring is treatable in 99% of the cases.

The couple with the screaming child should not have had so many children in the first place and they could also have aborted, killed or at least seriously beat them to make the kid shut up. But what they actually did was to first analyse the problem, which was that the child associated sleep with the presence of his parents close by, and then solve it by slowly going further away from the child each night when put to sleep. Eventually the brat learned to sleep by himself and not feel frightened when alone in bed.

The woman that was obsessive about her work and other problems solved it by scheduling her activities each day and sticking to the schedule and also writing down any problem that obsessed her. It seems, at least in her case, to ease the need for her brain to ceaselessly remember and analyse the problem if it was written down.

The old man was so worked up about not being able to sleep that he actually kept himself awake by worrying that he won't be able to sleep. They solved it by forcing him to try to stay awake :)

The flight attendant has a clogged bedroom. Her room looked more like a prison cell than a sanctuary (that's more or less their words) and when they rearranged her room (basically by drawing a line in it and separating a third of the room for storage and the other two thirds for relaxation). That helped her ease up and feel comfortable in her own apartment.

The night shift guy "cheated". He quit his job! :)

There was also interesting information about the drinks that keep us awake (like coffee, tea, fizz drinks) and foods (apparently aged foods like salamis and a bit potatoes) and about how some people are night people and some are day people. Trying to wake and go to sleep early would work wonders on some and terrible on others.

Try to find it, even if the presenter, Robert Winston, is a bit silly looking. He is a smart man even if he does look like one of the Marx Brothers :)

I've accidentally stumbled upon a very interesting video of a science conference about sleep. Called "Sleep, Waking and Arousal" it details a very interesting compendium of information about sleep in humans, mammals, other vertebrates and even fruit flies. I am posting the link here, but what is even more interesting is that it is part of something called the "The University of California Television" that has its own web site with a lot of (presumably) interesting videos.

Sleep, Waking and Arousal
The University of California Television

I've accidentally stumbled upon the concept of Text Readability while I was searching some books on Amazon. They have this feature to show you how easy it is to read by the use of some automated indexing and analysis methods. I've researched a little and I came up with this collection of links:

SMOG (Simple Measure Of Gobbledygook) estimates the years of education needed to understand a text. As input data it uses the number of polysyllables (words with 3 or more syllables) and number of sentences. Note: if your text needs a PhD to read it doesn't mean it's smart, but that it is difficult.

Flesch-Kincaid Readability Tests - the Reading Ease and Grade Level tests. They both use as input values the number of words, sentences and syllables.

Automated Readability Index - also tries to determine the years of US education needed to understand a text. It uses as input values characters/word and words/sentence.

Fry Readability Formula - it is a graphical method of determining the education level needed to understand a text. It computes the number of sentences and syllables over a hundred words and the values are plotted onto a graph.

Gunning fog index - same thing. Uses words/sentence and number of complex words and total words. A complex word is the same thing as a polysyllable, only with a higher readability index :)

Raygor Readability Estimate - looks very similar to the Fry.

Coleman-Liau Index - like the ARI and not the others, it uses characters to compute readability. Uses total number of characters, words and syllables.

Linsear Write - Uses number of simple and complex words and the number of sentences.

Zipf's law - an empirical law (based on observation rather than determined theoretically) it states that the frequency of any word in a natural language text is roughly inversely proportional to it's rank in the frequency table.

But how does that help me?!

Well, there are online tools that do the work for you:
Tests Document Readability And Improve It
Lingua::EN::Fathom Perl CGI
EULA Analyser
Style and Diction
Reproducible Fry Graphs
Readability Studio

This text for example has the following stats:
Gunning Fog index : 12.93
Coleman Liau index : 11.25
Flesh Kincaid Grade level : 11.39
ARI (Automated Readability Index) : 10.21
SMOG : 12.72
Flesch Reading Ease : 44.16

Which means that if you didn't finish high-school, you're pretty much screwed :)

An American company has developed a microwave system that decomposes hydrocarbon into something resembling the oil it came from. That means it converts plastics of almost any kind and rubber into fuel!

Just read the link: Giant microwave turns plastic back to oil or watch the video below.

Monty Halls presents this two hour special about the Earth's structure. Again, it is not featured on IMdb.

The documentary follows the steps of Jules Verne and tries to analyse the same ideas with modern knowledge. In the process, explains how our planet is made, why it has an iron-nickel core, where does the magnetism come from, how deep humans have reached into the crust, etc. Interesting documentary, although a bit too "popular" for my taste. But it does explain a few things that I didn't know.

I would really like to see documentaries that are full of non repetitive data and that focus on information more than on special effects and deep voice presenters. But hey, in the same "session" somebody sent me a clip from a TV show where a guy was asked what orbits around the Earth, the Moon or the Sun. The guy asked the public and promptly said "the Sun". So, these docs are not completely useless. I just wish there was more.

I usually comment on films on the IMdb site, but there was no mention of this program episode there. Watching it was much like reading "I am a Mathematician", immersed in a fascinating, yet inaccessible world, the one of professional mathematicians.

I often wonder where do they get the money to sit years on end at their desk to prove a theorem, without telling anyone they intend to. Anyway, the story is about this guy, Andrew Wiles, who had the dream of solving Fermat's last unsolved puzzle and one that Fermat himself wrote he had a beautiful solution to. You see, Fermat wrote some conjectures, some ideas he had, and did not write the solutions, thus failing to turn them into theorems.

A lot of mathematicians struggled to prove them and they succeeded, all but one, a problem so simple to define and yet very difficult to solve: show that there are no natural non zero values that satisfy the following equation for any N larger than 2 : x^N+y^N=z^N.

It is amazing the math that this guy has to explore to solve it. Of course, I understand nothing of it, and the show doesn't try to make anyone understand the math, but the feeling and effort are truly remarkable. A must see for anyone needing motivation to better himself.

You want to watch the film, here it is:

I've just finished watching "Free Energy - the Race to Zero Point", which is a documentary of sorts listing ideas of ways to produce free energy with open systems, or getting a lot more efficiency than present systems. The speakers are authors of controversial books and editors at magazines names as crackpotty as possible. The narrator himself looks like a Hitchcock wannabe, presenting the end of the world. Heck, the film is not even listed on Imdb, therefore this blog entry.
But, even if I am mostly convinced that this is a piece of sensationalist propaganda and not true science, I am left wondering how much (if any) of this is truly real? Did Moray have a device that lit up light bulbs without fuel or batteries? Are the numerous inventors presented there just crackpots or do they have something? I find it difficult to believe that all video proof that was presented in the movies was faked. Why would they?
Yet most of all I resonated with the idea that is, unfortunately for this movie, presented by all featured people: economic interests reign supreme and devices that don't need to be connected to power grids, use oil or that can be regulated by established industries are not only avoided, but actively attacked. It does make sense, doesn't it?

So, without further due, here are some start up links from Wikipedia to help you make your own mind:
Zero-point energy
The Casimir effect
The Hutchison effect
Thomas Henry Moray
Cold fusion
Electrostatic levitation

Well, I don't. I was first shocked to find out that the 1918 "Spanish" Flu pandemic killed 50 million people and I found out about it only in my twenties. Now I see that the pandemics are recurring events, there are lists with the virus strains and where they originated, while information from before 1900 is unreliable since medicine was not really.



Check out this link that shows a history of flu strains and the three flu pandemics from the last century.