From Intelligent Design to Geometry

Just some thoughts...

When I express my doubts about the success of the Apollo project people smile behind my back but that's about it. Friendships aren't broken and neither are ( employment ) contracts. ( See: AULIS on Apollofor more info ). In the last century science turned into a multi billion dollar industry and that certainly has changed the world of academics. Questioning a general accepted theory can ( and will ) ruin careers. Examples are questioning the cause of Aids, and questioning Darwin's Evolution Theory.

Evolution Theory basically says that we evolved over time by a process called mutation and natural selection. Those who question the Evolution Theory in fact question that very, very complex machines evolved from 'mud'. Darwin didn't answer that question because when Darwin published 'On the Origin of Species on 24 November 1859' he wasn't even remotely aware of the complexity of the cells making up life. DNA wasn't discovered until ten years later in 1869 by Friederich Miescher and it took until 1953 when James Watson and Francis Crick discovered the double helix structure of DNA. Intelligent Design Theory accept Evolution Theory but only up to a certain point. They argue that somewhere in the beginning some information or 'design' had to be injected into the system. Who put it there? I would ask.

To the point.

Anyway, these thoughts entered my mind because I am thinking of building a 'DNA-type-of' geometry building block for a computer program. With the help of a computer these geometries should be able to construct ( divide ) themselves in a scene graph and evolve, multiply and so on. At the moment it's just an idea. I started to look for a way to understand more about DNA by finding popular science books on the subject. I haven't learned much about biology and chemistry and what I have learned seems forgotten. But I am only interested in DNA as a computer, or data structure. Then I found this website 'DNA seen through the eyes of a coder'. Since I am a coder ( computer, Android, programmer ) by profession that was exactly what I was looking for. Take this for example, DNA is not binary, DNA is quaternary. Computer letters normally consist of 8 bits called a byte, so using that system there are 256 possible letters. The equivalent of a byte in DNA is the codon and has three places. So in DNA language there are 64 possible letters. Read more on the site.

More to follow on this geometry project soon, I expect.

Conceptual knowledge maps for mathematics

About working and studying, the main topic of this blog: well, it is no longer an option. It is mandatory, society needs people who are committed to their jobs and invest in their lifetime education. Everything changes at an ever faster pace and it is thus our responsibility to stay of value in all of our dynamics.  It is an issue we must align regularly.

Studying in a particular field will gradually align your life to your new interests. For example, I have recently, more or less -landed- in a job where some of my colleagues are mathematicians. In fact, a lot of the work I do involves mathematics. More about that in posts to come.

Everything changes. So do study skills. And a vast amount of tools for computer aided learning is now available. From MIT lectures via YouTube to software for flash cards to sophisticated knowledge databases for personal use. I would like to mention two items I have found recently.

InfoRapid Knowledge Builder is a graphical tool to document conceptual knowledge maps, free for personal use at http://www.buildyourmap.com/. ( Before this I used Mindjet and TheBrain. ) I am working on a map with topics in Analytical Number Theory.

Another item I found is a book. It is called On Course, Strategies for success in College and Life. ( And if you work and study read the title as Strategies for successful combining work and study.) The book is packed with information. It is not a book you should read once but it is a companion you can use, consult, for years. I have the Study Skills Plus edition.

Chris Finlay's Blog

Chris Finlay has more degrees than blogs but here is his blog: http://chrisfmathsphysicsmusic.blogspot.com/

P.S.
I owe Chris a Thank You. He knows why.

Fixing study problems(2) - "I skip the proofs."

#openuniversity#

( Continued from yesterday. )

Lack of mass.

Take trigonometry for example. I remember myself saying things like "Why do I have to study this? Is this really important? Will I ever be able to apply this?" Readers of this blog know that trig is very important in mathematics. And in the physical sciences, engineering, game development and even in financial engineering, trig skills are essential. Still, at this very moment, millions of children are struggling with trig because trig is =difficult= (*). As a result however they start asking questions like I used to ask 'why do I have to learn this?'.

Do you ever speak about the topic you have to study at the moment ( besides that you don't get it )? If you do, then it has mass for you, and lack of mass is not the problem. So if you have a study issues at all, they occur further down the line. But if you think your issues are related to the topic itself then the following things may be of interest.

Looking at your topic from a different perspective might help, read books written for the general public, watch documentaries. You need to find a 'click' with your subject. So that finding out things about it comes natural and not as a struggle just to collect some tma points.

Imagine a student fairly good in math but with little affection to abstract algebra. A typical reaction might be, that he/she likes 'applied math', or likes to 'calculate stuff', or the notorious:

'I skip the proofs.'.

Most scientists see that numbers are everywhere, but it takes mathematical maturity to see that numbers are merely properties of mathematical objects at a ( much ) deeper level. My point being that before the student can get over that reluctance to study abstract algebra he has to know that it is literally everywhere.

Talking to people who love your subject helps a lot. And thanks to the Internet you can always find them. You can always decide later that studying your topic is not for you anyway. It is important to recognize that you are not to blame for not 'getting it'. But it is not the subject fault's either. Studying a subject only works if you like it. Is that all there is? I am afraid so. Its like communicating with a person over Internet that you have never met before. Its easy to give up on them.

So:
#1. There is no such thing as 'not getting it'.
#2. Get to know your topic first.
#3. Studying comes natural if you ( start to ) like your topic.

More later.

(*) A more important question is if trigonometry is really difficult or just made difficult.

Fixing study problems (1)

#openuniversity#

Studying, esspecially mathematics, is a consecutive series of a-ha moments, of I-don't-get-its I do get

Studying, especially mathematics, can be hard, very hard at times. There are moments when you -don't get it-. Studying is, as I see it, continuously working your way out situations like that. When you browse through a new math book everything looks totally uncomprehensible but when you put the book away, when the TMA is done or when the exam is done, you -own- the topic. At least that's 'the plan'. Here are a few tips for if the plan doesn't work.

Red flags

The only problem a student can have is -not getting- the subject. Red flags to watch out for are:
- you are putting off study time;
- studying doesn't seem as interesting as it used to be;
- when you study your mind wanders off;l
- concentration periods decrease ( you have to check facebook, e-mail );
- doing assignments is hard or impossible;
- after you read some text you forgot what you were reading;
- the list is endless.

There are four possible causes of why you don't get it which can be handled quite easy providing you are able to determine what is blocking your study progress.
- 1. Distraction. You are NOT working in a distraction free study environment.
- 2. 'Lack of mass'. A technical term for the situation where you have no connection at all with your topic. Your brain literally stopped. It can't process any information about the topic.
- 3. You know exactly what you are trying to learn. You think that you have mastered the topic but when you try to do some of the ( harder ) exercises you are lost.
- 4. The learning went well, exercises went well but the result on the exams were below your expectations or when you confront your understanding of the topic to one of your peers your comm isn't understood or is invalidated by your peer.

Distraction.

We can't switch off internet while we are studying since it has become indispensable for students and knowledge workers so we have to control it. Even self-discipline can be mastered but you have to take the first step. We are all possessed by litle demons that need to be fed with entertainment and pleasure. If you feed them they'll ask for more next time. They are never satisfied.

( ... More later ... )

Open University Transitional Qualification

#openuniversity

I have set my transitional qualification to B31. This entitles me to a completion of my B31 degree for the rates prior to the major increase of course fees.

Mathematics and culture

#maths

Because I study mathematics at a British university I am starting to notice that the British insist on doing things their -own- way as much in mathematics as they do in general. I am not judging this, but it fits the pattern, i.e. traffic, currency, etc.

It is just that I thought mathematicians would be -wiser-. Wiser, how ignorant of me, how can I possibly understand the essence of 'being British'? I can't, of course.

Let me give two ( recent ) examples.

#1
An Open University forum moderator switching to UPPERCASE in reply to my mentioning that permutations are applied from left to right in default GAP while the only correct way is the British right-to-left. ( Going uppercase is about the rudest imaginable attitude known in internet etiquette and as you can imagine I was flabbergasted. )

#2
A note in a book published by the American Mathematical Society written by an English mathematician. I quote:

"Readers who prefer this convention should read this book upside down in a mirror."

He referred to a generally accepted style of notation in continental Europe. My jaws dropped. This wasn't meant as a joke.


P.S.
;-) !

[ Housekeeping ] Comment Moderation = ON

I have switched comment moderation back to on. Switching it off hasn't worked, it made things worse. I keep forgetting to check if there are comments to reply too and worse: very odd comments got through. Like: "What an interesting point on group theory you just made. Joe" Where Joe supposedly was a link to a profile but instead it jumped to a gambling site, or worse.

#Occupy #Rotterdam 11 feb 2012 STOP ACTA

Off-topic, but on-purpose.

Inform yourself about: Stop ACTA !

Take action as we do in #Rotterdam: https://www.facebook.com/occupyrotterdam

( Action Advertisement )

Study tip: Kill procrastination with the Pomodoro Technique

If you procrastrinate a lot while studying then you need to apply the Pomodoro Technique. Read what an experienced has to say about it: Marco Giannone about studying and the Pomodoro Technique.

Maths and ballet

Dance looks beautiful when arm and leg movements are coordinated.





Did you know that counting is a very important part of ballet. Dancers must constantly be counting their steps in order to keep time with the music.

New York City Ballet Soloist Robert Fairchild talks about his role in Douglas Lee's "Lifecasting". Notice that he mentions the complex counting schemes he has to use.

( Mathematics PDF ) books formatted for e-readers...

Formatting, typesetting books specifically for e-readers. I am a bit late to notice, but J.S. Milne is probably the first who formatted a mathematics book for an e-reader. Look at his Group Theory book ( PDF e-reader format ) here.

There was a time when moving to a new flat ( house ) meant carrying boxes of books and even more boxes of vinyl records. All the vinyl the average music collector had fits nicely on one USB stick with more than enough space left to store all his books, in e-reader format.

Milne did not have to rewrite his books ( maybe he made a few cosmetic changes, I don't know ) to reformat his PDF books for e-readers. Simply because he writes his books in LaTeX. He can publish to PDF in any format, he can have them nicely printed or he can merge his content in a wiki. His mathematical source stays untouched.

One of the things computers can't do yet is scanning a mathematics book, one of Euler's publications for example to LaTeX.

It makes me a bit sad that Windows 8 will be a lot like iOS from the iPhone ( Microsoft wasn't able to leap-frog Apple after Windows 95 ), I mean Windows 8 will be fingers based instead of pen-based. In the 1980s computers were for male geeks, today computers have become social media tools which are mainly used by women. I mean which male doesn't get bored by hanging out on facebook day-in day-out.

Writing mathematics is done with a pencil after which it is typeset.

What makes me sad is that just when pen-computers started to recognize handwritten math ( in Mathematica for example ), the world is flooded with an interface that is essentially geared for Facebook. Lots of pictures and every text has the intelligence of the two thumbs it has been typed with. Writing is just like reading. Very few people ( like to ) do it well. With or without e-reader.

Happy New Year

Thank you for reading my blog in 2011.
nilo
( I'll save the 'looking back' post for next year. )

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Merry Christmas !

*★Merry★* 。 • ˚ ˚ ˛ ˚ ˛ •
•。★Christmas★ 。* 。
° 。 ° ˛˚˛ * _Π_____*。*˚
˚ ˛ •˛•˚ */______/~＼。˚ ˚ ˛
*° •˛• ☃｜ 田田 ｜門｜ ☃˚╰☆╮
...To ALL readers :) ♥♥♥

Thinking about mathematics

Mathematics is the study of quantity, structure, space and change. Mathematicians seek out patterns and formulate new conjectures. Conjectures are either proven by a formal mathematical proof or falsified by some counter-example.

Wikipedia on the definition of mathematics

Programmers developed a language which enables them to communicate effectively and at a high level about software and their profession: creating software. It is a small language but very powerful, it is the language of design. - Mathematics, as a language, enables scientists ( astronomers, biologists, chemists, ... ) to talk and think about the patterns in the universe.

Take for example symmetry. Everybody, children included, has some notion of symmetry, i.e. reflection symmetry. When we are confronted with the art of Escher we realize that there is more to symmetry.

Circle Limit II 1959 woodcut in red and black, printed from 2 blocks

Symmetry is real, it is a physical phenomenon we can observe from the structure of atoms to the spirals of galaxies. Symmetry is more than a property of space it is what defines the structure of everything around us.

But what is quantity, and how we describe it? Here we enter the realm of numbers and number theory. Although, I am seriously fascinated by ( prime ) numbers, we cannot -see- them anywhere in nature. They are not real and seem inventions by humans. If we ever pick-up a signal from outer space that somehow involves prime numbers that would mean that that signal is created by extraterrestrial life.

When you study group theory you will find that there is a deep connection between groups ( i.e. symmetries ) and... prime numbers! Prime numbers are thus part of the signature of the Creator no matter what image you have of that concept.

Reading ( conflicts time management )

When I was in high school I ( and others of my generation ) considered reading a waste of time. Teachers took every effort to convince us of the opposite.

There is only one way you can effectively change yourself and that is through reading.

Some of the best memories I have are somehow related to reading. Good times! I have read quite a few time management books. These books are primarily written for people who want to do better in life, i.e. change themselves into more productive people. In none of these books I have found the advice: "Read more". Strange. Anyway, I managed to undo the habit of reading. And that is bad.

In "The New Student Hat" Hubbard explains why people don't read, he talks about the strange sensations people experience when they sit down and attempt to read a book.

Amazing reactions occur when conscious effort is made to do this. Dullness, perception trouble, fogginess, sleep and even pains, emotions and convulsions can occur when one knowingly sets out to BE THERE AND COMFORTABLY PERCEIVE with the various parts of a subject.
These reactions discharge and vanish as one perseveres ( continues ) and at last, sometimes soon, sometimes after a long while, once can be there and perceive the component.

When I sit down with a book ( or device ) I get these sensations which only go away when I CAN OCCUPY MY MIND ON A (MATH-)PROBLEM. I know exactly what Hubbard means, I have to -simply sit there and read-, confront it.

Many years ago Goedel, Escher, Bach helped me to through a reading-barrier. This time I chose "Fearless Symmetry, Exposing the Hidden Patterns of Numbers, by Avner Ash and Robert Gross published by Princeton 2006.

I'll keep you posted about my struggle to become a reader again.

100.000th blog view expected on 11/11/11

This blog has had close to 100,000 page views since August 2008 and it looks like that the 100,000th page will be viewed on 11/11/11. This is a coincidence, of course. But with all the hype surrounding 11/11/11 I thought I should mention it. - Another example of the NumerologyIsNotMathematics principle. ;-)

EDIT:
( Although not 11/11-'11 yet on all parts of the world. )

Social Media for mathematicians

The places 'to be' for mathematicians are -not- Twitter and facebook, although they are both great places to socialize, chit-chat you know what I mean, they basically steal your valuable time.

Mathematicians hang out at:
- http://math.stackexchange.com/
- http://www.reddit.com/r/math
- http://www.stumbleupon.com/to/stumble/topic:247
- http://mathoverflow.net/
- http://mathblogging.org/
- http://arxiv.org/

Thanks to Gaurav Tiwari, read his review at his own site My Digital Notebook

Off-topic: 15 October 2011 - World-wide protest day

Was it Cairo or New York, - Occupy Wall Street - where it started? It sure is spreading. I want to express my solidarity with the people out on the streets today in almost 1600 cities world-wide: Occupy Together.


Since the revolution started in Egypt I watched and compared the news from BBC, CNN, Infowars, Al Jazeera, RT ( Russia ), and Press TV ( Iran ). Now Press TV has been taken off-air in the UK. Draw your own conclusions. Here is what Infowars ( US Libertarian ) had to say about it: Press TV taken off air in UK – war for freedom of speech now on.


Now that the alternative media are flourishing, it turns out that we haven't had a free press for decades, Press TV made that painfully clear.
 

During the last world war, scientists created the atom bomb, period. 'Because they were afraid the Germans would be first.' We have to assure that they don't have an easy excuse like that next time, a free Internet ensures that.

Fibonacci Sequence - Revisited

Some thoughts about my progress in maths. - I browsed through some old blog posts to get a feeling for how much I progressed with my maths. That was the original purpose anyway. Six years ago I wrote about the Fibonacci sequence as I am nowadays. It often feels if I make no real progress. I see mountains ahead of me, when I look back I see a tiny road. I don't believe in working hard, working smart should do the trick. On the plus side I can say that today I can prove Binet's formula and give at least three alternative formulas for the series. I don't know I even knew the formula in 2006. If progress is thinking about the Fibonacci series as something trivial then that is not what I expected. When I was in secondary school the mathematics teachers seemed to have acquired infinite knowledge about mathematics. I am sure that I know at least as much about math as the average high school teacher. That should give me a sense of satisfaction, achievement. It does not. Link: - Max Cohen draws the golden spiral