I am back!

After 9 months of silence, I am back again to my weblog. It is hard to explain why I was not around in one post, since past few months were full of ups and downs at least for me. To be short, after many years being in academia, either as a student or researcher, I started a position as a R&D in one of my favorite topics on the intersection of mathematics and computation while working with real world examples, i.e., as a machine learning data scientist. That by itself is a good reason to be away for a few months. However, in my case this was not the only thing.

The other thing that I have realized is the fact that, after being away for a few months, it is hard to come back, as there are many things to say and you basically don’t know where to start. To choose one particular out of many, I just quickly write about why I partially left academia, at least for the moment.

First of all, it is almost clear to everyone who is already engaged in academic activities that the whole subject of “academic interest” does no longer exist. By academic interest, I do not mean a useless scenario that people came up these days to publish a few more papers. No, I really mean to spend time and energy on something for the sake of curiosity. I can’t say that there is no one doing that, but I can certainly say that the new generation of scientists, are either businessmen or engineers. (Nothing wrong is with being businessman/engineer, just they should practically be different from scientists, and now they merged somehow. )

Second, again those who have been involved in academic setting are realizing that, for many reasons, creativity is kind of discouraged. Most of the times finding a more creative solution is not desired. During these many years, I came across many important subjects worth studying, which were dismissed because they considered HARD to do in a few months or seemed irrelevant.

Thirdly, computer science in north america has cast a shadow on many professions, and academia is not excluded. Hence, everybody tries to codify some mathematical problems and in the best case scenario bring it close to experiments. I should say that, I do not discourage this activity, the point is theoretical studies should be different from computational studies, but theory almost cease to exist these days. Finally, not to mention the fact that, academic fields are tightly narrowed these days that even in one particular fields, it is very hard to move around. Part of it is due to the fast growth of science, but it is mostly due to the crowdedness of the environment!  Indeed, this list goes on, but I guess these are the main reasons.

Putting altogether, I realized for people like me who are interested in wide breadth of research on different aspects of life, data science seems a way to go. I reserve the right for me to change the above statement as time goes on!

coursera is the beginning of new era!

In case you have not come across the Coursera website, I strongly suggest you to take a look at this wonderful initiative. You can simply explore the courses menu to locate possible courses you might be interested in. I have personally followed some of the courses, such as the Machine Learning course by Andrew Ng, and it was amazing. At first, it might seem similar to other online lectures! However, there are some subtle but essential differences. The main difference is that, each course is divided into several small lectures, where each lecture is very well designed with some follow-up questions (or quiz). It is very accessible and practical, and more importantly, it is not designed as A PART OF curriculum, but each course is a stand alone subject.

Since the beginning of blogging, I tend to believe the future hiring would change from the current passive process to something more interactive. For example, I thought employers can initiate a blog to post essential materials for applicants who want to undertake a particular position. Then, interact with those members who continuously contributes to the blog and in the end, hire one or some of them, instead of just trusting applicants resumes. Not to mention, not everybody is good in demonstrating their abilities in hypothetical situations introduced in the interviews.

Now that I know more about Coursera, I believe it is even better than blogging. Basically, an employer can post a course (or series of courses) to freely teach applicants about the subject and evaluate the ones have taken the course, at the end, the best possible candidates can be called up for an interview. This way, employers can make sure that the applicants are at least familiar with the subject and have been evaluated once. Additionally, applicants have this opportunity to learn something new throughout the hiring process. So, each job application can be a new experience and new lesson instead of a disappointing process.

I also believe that the future of graduate studies would change similarly. For example, one can design their own curricula through Coursera. After taking enough courses, the corresponding certificate can be added to their resume. For getting the certificate, applicants are asked to do a project. Then for pursuing higher degrees, they can apply for those professors who either posted a project or a course or both on Coursera. This way, both sides are certain about the common interest and background. At the same time, professors are encouraged to broadcast their knowledge, freely. University expenses for graduate courses would also drop down.

After Wikipedia this is the next internet product which I am really excited about. The cool thing about Coursera is that, with a little money one can earn certificates of the courses they have taken. Or they can choose to watch the course and learn something (without getting a certificate) for free.

(مرور کوتاهی بر مشکلات و مزایای زندگی‌ در کانادا (۲

در نوشته گذشته (اینجا)، یک مرور کوتاهی بر واقعیّت‌های اجتماعی زندگی‌ در کانادا داشتم. در این نوشته می‌خوام به واقعیّت تفاوتهای اجتماعی در زمینه شغلی‌ بپردازم. چند روز پیش وقتی‌ داشتم با یکی‌ از دوستان صحبت می‌کردم، یک خاطره رو گفت که شنیدنش خالی‌ از لطف نیست. دوستم میگفت که درسفری با یک مسول مهاجرت کانادا هم مسیر بوده، و اون فرد از ایشون پرسیده که نمیدونم چرا وقتی‌ ایرانیا به کانادا میان، از همه بیشتر تو دانشگاه برای گرفتن دکترا مشغول تحصیل میشن، بجای اینکه در بازار کار مشغول بشن.

در این نوشته دوست دارم جوانب این نکته رو باز کنم. در ابتدا اجازه بدید که به طور خیلی‌ خلاصه به منشأٔ داخلی این تفکر بپردازم. در ایران، یه تفکر کاذبی شایع شده که تحصیلات بیشتر به پول بیشتر منجر می‌شه. البته دلیل این امر به دولت زدگی و مدرک گرایی در ایران مربوطه. در ایران، خیلی‌ از پدران و مادران ما در مشاغل دولتی مشغول هستند و در این مشاغل، هرچه مدرک بالاتر باشه، در مدارج بالاتری مشغول میشن و به طبع از امکانات مالی‌ و حقوقی بیشتری برخوردار خواهند بودند. در واقع تفکر در ایران اینجوریه که “یک سال بخور نون و تره، یک عمر بخور نون و کره”. یعنی‌ اگه یه چند سالی‌ به خودت سختی‌ بدی، یک عمر میتونی‌ پات رو بندازی رو پات، و ریاست کنی‌ و پول خوب در بیاری. در ضمن، جایگاه اجتماعی خوبی هم داره. بررسی‌ جایگاه دانش و دانشگاه در ایران موضوعی است که شاید در پستی دیگر بر اون پرداختم. البته جا داره، که همینجا به تفاوت علم و دانش هم، به عقیده من البته، که در یکی‌ از نوشته‌های گذشته به اون پرداختم اشاره کنم. لازم به ذکره که قوانین سختگیرانه ویزا برای ایرانیا، به این نکته بیشتر دامن می‌زنه که موجب این می‌شه که فقط تحصیل کرده هامون بتونن به طور قانونی از کشور خارج بشن.

 فهم این نکته که هر کشوری یک سری امکانات محدودی داره که باید طبق یک سیاست گذاری این امکانات رو در زمینه تولید دانش و زمینه ی شغلی‌ سرمایه گذاری کنه. فهم دقیق این سیاستها به تعیین مسیر شغلی‌ افراد خیلی‌ کمک می‌کنه. اگه به لیست ۱۹ شغلی‌ که برای اونها دولت کانادا تمایل به جذب مهاجر داره، رجوع کنید شاید این تفاوت سیاست گذاری براتون واضح‌تر بشه. در کشور کانادا، سیاستگذاری طوریه که حد وسط جامعه بتونن دخل و خرجشون رو بدن. یا اینکه اگه یک زوج به تحصیلات متوسط مثلا لیسانس، یا دبیرستان، در یک شغل ساده که تخصصی نمیخواد مشغول باشن بتونن حدوداً ۵۰ هزار دلار  در سال در بیارن که با این پول می‌شه یک ماشین و بعد از حدود ۵-۶ سال کار یک خونه به طور ۳۰ سال قسط خریداری کرد. البته شرطش اینه که این زوج به طور پیوسته به مدت ۸ ساعت در روز، در طول این مدت کار کنن. البته اگه بجای رفتن به دانشگاه، به مؤسسات فنی‌ و حرفه ی رجوع کنن، حقوقشون بالاتر میره. مثلا یک مکانیک حدود ۲۲ دلار به ازای هر ساعت میگیره، که با احتساب ۸ ساعت در روز کار، حقوقی معدل ۴۵ هزار دلار سر سال می‌شه. در حالیکه که یه متخصص ژئوفیزیک حدود ۶۸ هزار دلار میگیره.

بطور کلی‌ قانون نانوشته اینجوریه. هرچه مدرک بالاتر بره، با یک شیب بسیار ملایمی حقوق هم بالاتر میره. مثلا یک مکانیک با تحصیلات فنی‌ حرفه‌ای که شاید ۲ سال هم وقت نذاشته باشه، حدود ۴۵-۶۰ هزار دلار در سال میگیره، و یک دکترای ژئوفیزیک که حدود ۸-۱۰ سال تو دانشگاه سپری کرده (و کلی‌ هزینه ی تحصیل داده)، حدود ۶۰-۸۰ هزار دلار در سال میگیره. البته باید به این نکته ی مهم و ظریف هم توجه داشته باشید، که تعداد مشاغل با بالا رفتن مدرک کمتر و کمتر میشن. مثلا اگه تو هر شهری واسه یک مکانیک یا یک منشی‌ شغل هست، واسه یک دکترای عمران شغل نیست. این نکته‌ای که خیلی‌ از مهاجرین ایرانی‌ از اون غافل هستند، واسه همین در دور و بر خودم کلی‌ ایرانی‌ با مدارک بالا میبینم که جویای کار هستند، در حالیکه اگه همونا به ایران برگردن به راحتی‌ شغل میگیرند. باید این نکته رو هم یاد آور بشم که چندین رشته از این قانون مستثنی هستند. رشته ی کامپیوتر، حسابداری، امور مالی، و مشاغل مرتبط به سلامت در کانادا و آمریکا بازار خوبی دارد. البته واسه شغل گرفتن تو شرکتهای بزرگ نیازی به دکترا نیست، و با گرفتن یک فوق لیسانس، یا حتا یک دوره کوتاه حرفه‌ای کفایت می‌کنه.

در نهایت اینطور جمع بندی می‌کنم که بطور کلی‌ با بالا رفتن مدرک حقوق با یک شیب ملایم بالا میره، ولی‌ موقعیت شغلی‌ با یک شیب تند پائین میاد. در ضمن کلی‌ از عمرتون رو باید در راه دریافت مدرک سپری کنید. پس اگه به صورت مهاجرت و یا حتا به صورت دانشجویی (حتا اگه با پذیرش و دریافت کمک هزینه تحصیل) به کانادا آمدید ، بجای ادامه تحصیل،  یک دوره کوتاه در یکی‌ از مشاغل مورد علاقتون بگذرونید و بلافاصله وارد بازار کار بشید. اینجوری مهاجرت دل‌پذیرتری در کانادا تجربه خواهید کرد. در نهایت هم توصیه می‌کنم که به این لیست بهترین مشاغل در کانادا خوب نگاه کنید که راحت تر بتونید واسه آیندتون انتخاب کنید

(http://www.canadianbusiness.com/lists-and-rankings/best-jobs/۲۰۱۴-full-ranking-canada-۱۰۰-best-jobs/).

Why Do Many Reasonable People Doubt Science?

Some days ago, I read an article in the national geographic website, with the same title (here). This article first starts by stating that people, even scientists, ignore science since in accepting scientific facts we “cling” to our “naive beliefs”.  There are several examples, in the article which the author argues they are just scientific facts, but people have the hard time believing in them, simply because human nature is naive!

Recently, I came across several articles with the same type of logic, and discussions about the “naive beliefs”. I find the reasoning used in this article and similar ones ridiculous. In another post, I explained what is wrong with “scientific facts”. However, please let me explain in some more details why people doubt science. First of all, it happened to all of us when we started our day by looking at the weather forecast. However, once we looked outside, we saw something completely different! So you could obviously see there are many unexpected things that can happen which was not included in our scientific models. Everybody sees this shortage and understands that, particularly, when we are dealing with large multivariable systems.

Somewhere in the article says that “We’re asked to accept, for example, that it’s safe to eat GMO (genetically modified organisms)…because, the experts point out, there’s no evidence that it isn’t and no reason to believe that altering genes precisely in a lab is more dangerous than altering them wholesale through traditional breeding.” This statement is wrong at so many levels.  First of all, when we are talking about our health we tend to stay close to our tradition simply because we know that it has been working fine for many many years. Second, I have seen no clear data to rule out the correlation between these many new diseases and GMOs. For example, we don’t know at what time scale we should expect to see the correlation. It may take more than 10 or 50 years for something to affect us.  Or even worse, it is not clear for what type of disease we should look for. Finally, we don’t know what could be the effect of GMO on environment, the time scale for the environment could be much longer than 50 or 100 years. Just as an example, look at the history of DDT. 

People doubt science due to the failures of science throughout the years, not because they cling to their naive beliefs. They doubt science because of many things that can go wrong in one scientific research. As I emphasized in previous posts (e.g., here),  science is not for believing, but it is a process to falsify our understandings. I should say, although I agree that scientific process is the only trustworthy method to investigate each and every question, we have all the reasons to doubt “scientific facts”, particularly those sciences which rely heavily on statistical inferences.

Why there are many stories, metaphors, and proverbs in religious texts?

It doesn’t matter which religion, in all of them you see storytelling, and extensive usage of metaphors and expressions in communicating a message.  When I was learning writing in English, I was told that I should write concise short sentence with a clear message, and try to avoid any complication in delivering my message. Compared to what I learned, the religious texts are way off!  The question is why? Why in communicating spiritual messages we urge to use stories, instead of directly cutting into the chase. As a Persian, I can name several well known books by religious authors which are filled with delicate religious stories. Ancient Persian poetry is also famous for that. There are thousands of pages written with high caliber of ingenuity just to deliver simple spiritual messages!

I have been puzzled by this question for a while. Now, I believe that I understood why that’s the case, and I try to express my understanding with minimum complications. To answer this question, let me start by answering a similar mathematical question. How can one explain a three-dimensional object with the two-dimensional mathematics? The best way is to slice it up to many two-dimensional surfaces and then introduce each and every surface, one by one. For example, introducing a simple tree to a 2D universe, needs many (infinite to be exact) layers of 2D images. So, as you see whenever we aim to explain even a simple object, but from a higher dimension, we would face a challenge.

In another example, how one can explain the taste of an apple (say McIntosh) to a society who have never had an apple in their life! The first step is to find out what type of taste that particular people are being exposed to. Then the idea is to mix different tastes to get closer and closer to the taste of apple. So, this is exactly the process of delivering something which does not belong to our ordinary common senses.

In the spiritual world, I believe that is the same. Once a person observe something which does not well fit in our current realm of understanding, one needs to slice it up to many different little stories where the role of each of this stories is to lighten up one side of the observation. For the sake of this conversation, I don’t mind if the origin of this observation is due to the ecstasy of meditation, or due to some chemical compound.  What I do care, in this post, is that sometimes a simple observation requires a lot of explanations, simply because it doesn’t belong to our everyday life experiences, and yet you can not make the point exactly.

Most scientific papers are probably wrong!

I remember talking to a friend of mine mentioning the fact that I am really skeptic about the results of the studies in the multi-variable fields with no underlying theories, such as life sciences, social sciences, and earth sciences. My argument is as following, there are many parameters to change, and since we have no theory to compare the experimental predictions with, we could easily get misled by the results. In fact, in most of these fields we can’t even answer the basic questions, such as how many parameters are there to estimate the right sample size!

Recently, I came across this article in newscientists which basically proves that many scientific results are probably wrong! What I like about physics, in general, is that we have theoretical guidelines which help us to better understand the experiments. Of course, our theories are based on many approximations and assumptions, however, it is still unreasonably accurate. In fact, the main difference between theoretical physics and applied mathematics is how to lay down different approximations. This is one of the main reasons that, I believe, we have a steady progress in physics, and sorts of a random walk in other fields. By the random walk, I do not mean that we are not making progress, of course, we are. However, there is no sense of direction in what we are doing, at least by an outsider like me!

آیا سنت با مدرنیته در تقابل است؟

توی این سالها متوجه تفکری شدم که در بین مردم و مسئولین کشورهای در حال پیشرفت، مثل ایران خودمون، رواج داره، و اون اینه که، سنت‌های رایج در کشور یکی‌ از دلیل اصلی‌ عقب موندگی اوناست. و به طبع برای پیشرفت نیاز به دور شدن و فاصله گرفتن از اون سنن است. خوب بحثهای زیادی در موافقت و مخالفت این موضوع بیان شده، اینجا من تلاش می‌کنم که نظر خودم رو بیان کنم.

به نظر من، این حرف تا حدی درسته، البته دلیلی‌ که دارم، با دلایلی که غالباً در موافقت با موضوع بالا موجود هست فرق داره. اول برداشت خودم رو از دلیل دیگران بیان کنم، بعد به دلیل خودم میپردازم. بعضی عقیده دارند که گذشته از سستی و حماقت پادشاهان، اشعار و فرهنگ ما پر شده از توصیه هایی که بیشتر باز دارنده هستند از قبیل اینکه، خوش باش و در کنار جوی آب بشین و صفا کن و معشوق رو دریاب و غیره، و کمتر به تحرک و پیشرفت اشاره شده! در نهایت, این حس فرا زمینی‌ و آسایش و قناعت باعث رکود و در جا زدن جامعه شده. پس با دور شدن از این تفکرات و با پرداختن به فرهنگ جدید، ما می‌تونیم تحرک رو در جامعه بیشتر کنیم.

در حالیکه من عقیده دارم فرهنگ ما سرعت پیشرفت ما رو کند کرده به این دلیل که به ما توصیه می‌کنه که در اجرایی کردن ایده‌های خودمون چیزهای زیادی رو در نظر بگیریم. و همینجوری هر فکری به سرمون زد عملیش نکنیم، و سعی‌ کنیم راه حلی‌ پیدا کنیم که توش به آرامش خودمون، دیگران، و پایداری طبیعت لطمه وارد نشه. به عنوان مثال، شاید سال‌های پیش ما میتوانستیم ماشین بخار رو اختراع کنیم، ولی‌ این تفکر که اجازه داریم طبیعت رو نابود کنیم برای اینکه بتونیم سازندگی کنیم در فرهنگ ما شدیدا منع شده بود. همین فرهنگ باعث شده برای انجام هر کاری جوانب بیشتری رو در نظر بگیریم. پس مثلا اگه جمعیت زیاد می‌شه، و نیاز به انرژی داریم، حق نداریم که اولین چیزی رو که دستمون رسید از بین ببریم تا مشکلمون رو حل کنیم، بلکه وظیفه ماست که در چارچوب احترام متقابل به دیگران اعم از انسان و حیوان به یک راه حل برسیم. نمونه این نوع تفکر وعملکرد, می‌شه ساختن حمامی‌ که فقط با یک شمع روشنه! فرهنگ ما نمیگه که وال استریت نداشته باشیم، بلکه میگه گرگ وال ستریت نداشته باشیم. نمیگه خرید و فروش نکنیم، بلکه میگه شرایط دیگران رو در تعیین قیمت در نظر بگیریم.

در واقع, برداشت من این نیست که فرهنگ ما مانع پیشرفته، بلکه در فرهنگ ما  توصیه شده که در حین پیشرفت چه چیزهایی رو نباید از یاد ببریم. چیزهایی از قبیل قناعت (برای جلوگیری از حرص و طمع )، حیوانات، طبیعت، و البته ‌خم ابروی یار! پس ما برای پیشرفت راه سخت‌تری  در پیش رو خواهیم داشت، ولی‌ نتیجه این سختی‌ این خواهد بود که دنیای سالم‌تری ساخته خواهد شد. این عدم پیشرفتی هست که من نه تنها تقبیح نمیکنم، بلکه تشویق هم می‌کنم. در واقع, یکی‌ از دلایلی که برخی‌ از کشورها امروزه پیشتاز هستند اینه که ملاحضاتی از این قسم جلوی خودشون نمیبنینند! ولی‌ خوب میبینیم که چه اثرات منفی‌ روی خودشون و روی جهان گذاشته اند.همین رویکرد باعث شده که هرروز شاهد این هستیم که جوامع بشری، به نام پیشرفت، در از بین بردن آرامش و زیستگاه خودشون و دیگر موجودات از هم پیشی‌ میگیرند در واقع, پیشرفت خوبه ولی‌ به چه قیمتی؟

machine to human or human to machine?

While ago, I read an article about simulating a 13 years old boy by computer which pass the Turing test. You can read about this here, if you have not yet read. Since then, I aimed to write something about this news which has been postponed until now. The argument by Alan Turing, the father of artificial intelligence, is as following; if a machine was indistinguishable from a human, then it was “thinking”. Ever since, there has been many failed efforts to make one of such machines.

Upon reading this news many people surprised that we became such technologically advanced to simulate a human. But there is also other side to this story, we could say we became such unintelligent that a machine can do whatever we do. However, I believe it is a little bit of both. For everybody who is living in the modern era, particularly in North America, it is easy to see how fast we are growing technology-wise. I should also mention that, although there has been several technological jumps, the gaps between the jumps were never filled. That’s why we have many gadgets and softwares each of which suffer serious problems and restriction. I believe, it is mainly because technology is not about providing service (anymore) than making money. Hence, the amount of hours one has to invest to perfect a device, or an app, or a software, does not worth the money.

Now, let me briefly mention what I mean that we became dumb recently.  Over the course of the last century we have more turned to become a man of repetition rather than a man of creation, invention, or exploration. Our educational system combined with our work environment have been designed in such a way to diminish the differences between us while strengthen our similarities (why? look here). If we look at our everyday life, we see that what we are doing, can also be performed by a machine, but for the moment we are less expensive than a machine. So to speak, we are converging to a machine life, where intelligence is replaced by algorithm and ideas are replaced by mere data. The bottom line is that from top to bottom of our daily life, our brain solely performs a given algorithm and controls our involuntarily movements.

The very surprise of this year fields medal.

Let me begin this post by congratulating Maryam Mirzakhani for receiving the equivalent to Nobel Prize in Mathematics this year. I imagine that everybody has heard about the recent big achievement made by the Persian mathematician who is the first Iranian and also the first woman ever won the fields medal. I was going to send something earlier; however, I was trying to explain (or find an explanation) in layman terms what the award is for, which was not possible yet. I may post on that, later.

I, myself, got interested to mathematics in early years of high school and started reading different books on geometry, number theory, graph theory, and combinatorics. I was really enjoying solving problems of those books. It was when I first came across the name of Maryam Mirzakhani through a yellow book on number theory (if I remember correctly). Since then, I was sure that these mathematicians will flourish in future years.

As an Iranian individual working on mathematics and physics, I am very proud. I am also reminded of my dreams for which I left the country. It further reminds me how the societies and governments can be so cruel to people, particularly in academia, in stopping them from following  their dreams, particularly for international students. These days, not everyone has the luxury of following up on his/her own ideas; you can easily get busy with idiocy and unrelated daily issues, which is no good for anyone. Not to mention the outside pressure from funding agencies.

I am very proud that a Persian mathematician could break into the list of top mathematicians, and I have no doubt that in coming years, we will have more Iranian mathematicians in the list. Since, I believe, mathematics is still one pure field which rely less on technology and more on intuition which ancient nations such as Iran are full of it. Intuition is one treasure we have, and we should cherish.

 

If the process of scientific discoveries is reproducible?

Reproducibility is one of the main principles of a scientific method, that is, the entire process of a given experiment should be reproduced independent of the experimenter. Now, imagine a given scientific discovery, for example quantum mechanics. It starts with some observations, then some ideas and finally formulation based on some mathematical proofs. Now, the question is: if this process, from idea to formulation, is reproducible? More precisely,  are the results independent of the people who contributed in formulating quantum theory, such as Planck, Einstein, Heisenberg, Bohr, and many more?

My short answer to this question is “No”. For example, it is not clear that how Planck came up with his role of quantization in his 1900 paper, and if it was not suggested by him, probably this could still remain as a mystery for many more years to come. Or, it is not clear that how Heisenberg came up with his matrix formulation of quantum mechanics. See this reference, in which possible derivation of the 1925 “magical” paper of Heisenberg is discussed. The same is true for Born probabilistic interpretation of quantum states. So, as it is clear, all these steps depend highly on the genius of the people who contributed to the field. These derivations are not reproducible, hence, the process of scientific discoveries itself is outside of the realm of science, surprisingly.

In the ancient eastern science there were two methods for obtaining knowledge. The first method, which matches with the definition of the modern science, is by extrinsic observation and speculation and is called “obtainable” science. I call this method an algorithmic method. It means that, there is an algorithm to obtain that knowledge. The second method  is derived by a deep intellectual intuition and it depends on the individual intellect and its level of awareness. I call this method an intuitive method.

Almost all of the mathematical and geometrical proofs belong to the second method of obtaining knowledge, that is by deep intuitions. Actually, this is the part which distinguishes human from machine, and this is the part which I believe can not be simulated by AI (artificial intelligence). Solving an equation, or winning games like chess, all belong to the algorithmic method, so the higher the power of computation, the easier to solve or win. But proving a mathematical or geometrical problem does not require a computational power; it requires ingenuity or a deep intellectual intuition.

The second method is strongly criticized by the modern science, however, ironically, the process of scientific discoveries belong to the category of the intuitive method. In the eastern science, there is a long history of how to improve awareness and intellectual intuition accordingly [1]. This is, in fact, what is missing in the modern science.

[1] The procedure of improving awareness, actually, is the source of different religions in the east. Each religion came up with an answer to this question, as this is also the only way one can go beyond the material world, if there is any. That’s why whence the modern world started to criticize the religions, it also denies the second method totally without paying much attention to aforementioned subtleties.