The age of 17 was for Ramanujan a turning point in which he began to engage in pure mathematical research at the highest levels; Among other things, he studied a certain (and important) series of fractions and as a result he was also able to calculate Euler's constant up to 15 digits after the point.
When I come to write the history of a great mathematician, one goal comes to my mind, and that is to make the audience who is unjustly afraid of the world of mathematics understand that in order to succeed in this field in particular and others in general, nothing is required other than a true desire and love to speak. Galois, Tartalia, but וJermaine They tasted the bitter taste of severe poverty throughout their lives, but this did not prevent them from being among the first ranks of the greatest human minds that walked the face of the earth. They were never required to study beyond what their friends and neighbors learned, but it was only a strong will that led them to abandon all the lusts of life and devote all their time to studying mathematics and its development, and this despite the many difficulties heaped upon them by society that did not (and still does not always know) to encourage For a real genius who speaks a language of behavior different from the usual.
I will admit the truth because I do not think that the readers of this article are going to walk from Nablus to Nablus together with these giants even if they invest all their energy for many years, God forbid not out of disdain but from the understanding that these are individuals of virtue and as their name is - individuals. However, and this is a big point, these people are supposed to be a kind of model for us to imitate in the love and strong will power that were an inseparable part, apart from their minds being composed in a different way than that of ordinary people.
Mental ability is an innate quality - each person has the crown placed on his head, but willpower and love to speak are the lot of each of us - whoever wants will take as he wishes.
Will we reach the summit of humanity with the help of desire and love to talk? Most of us will not succeed in doing this, but the very existence of these principles is important, the study of mathematics (in this matter) is the summit to which we should strive and not the summit of this or that humanity; Be and this will be combined with this - you have won world fame.
When I told my father about the life of the Indian mathematician I will talk about, he said to me in a sort of question: "Indians have always been smart, he is not the only genius, there are many more like him in India." I answered him with a question: "So where are they? There are more than a billion people and only one emerges from all of them."
When I write these lines I understand that he was probably right, so there are quite a few geniuses like him, but in a country where a urine-soaked sidewalk serves as a comfortable bed for hundreds of millions of people while its leaders invest its treasures in financing and developing weapons of mass destruction - it will be difficult to find those special individuals.
The following article tells the story of a poor and rebellious genius who was born and died in India after making a big mark in the world of mathematics. It is not for nothing that he is called the greatest Indian mathematician (and not only the Indians in my humble opinion).
Srinivasa Ramanujan was born in India in his grandmother's house in 1887 to a housewife mother and a father who worked as a clerk in a small shop of cloth merchants. During his childhood he wandered between several elementary schools until at the age of 12 he placed himself in a post-primary school in his birthplace while successfully passing all the subjects he studied. Being only 13 years old, he began to study mathematics himself (which was at a much higher level than the one he studied at school) and mainly focused on the fields of geometric and arithmetic series. I will briefly explain that a series is any sequence of numbers that we can think of, but a geometric (engineering) series is one that fulfills a condition in which each number and the previous number have a certain relationship, for example 2,4,8 is a series in which the relationship between one member and the next before him it is multiplied by 2; An arithmetic series is one that fulfills a condition where between each number and the previous one there is a constant difference, for example 2,4,6 where the difference is 2. I would emphasize that I claimed that these are numbers even though this can be attributed to another type of "members" in the series.
Let's get back to his point - Ramanujan learned at the age of 15 the method of solving equations of the third degree (see an article on Tartalia) and immediately after that he found a new method to solve quadratic equations! As befits a true genius, Ramanujan continued to try and solve equations of the fifth degree, but he did not know that the mathematician but (Abel) has already demonstrated his inability to solve this and he did fail in his attempt. At the same time, Ramanujan continued to study mathematics from the book of a mathematician named CARR; While this book had a significant impact on his mathematical abilities for the better, it is the one that, because of its concise and special way of writing, led Ramanujan to the method of writing articles that he adopted in later years, something that he had to scorn among other mathematicians. The book contained theories and formulas but the proofs given to them were too short to serve as a "proper" explanation for the average mathematician.
The age of 17 was for Ramanujan a turning point in which he began to engage in pure mathematical research at the highest levels; Among other things, he studied a certain (and important) series of fractions and as a result he was also able to calculate Euler's constant up to 15 digits after the point. I will simply point out that a constant is a kind of special number that appears in all kinds of science, and Euler's constant in this case is a number (the more correct mathematical definition is "limit") that was created as a result of the series of numbers whose Nth place is the following number:
That is, a connection of fractions up to a certain point minus another part (natural logarithm) on which I will not expand. Just saying briefly that when N increases to a really large number, the result of this series should reach the number 0.577. Another important thing that Ramanujan tested (and discovered completely by himself) is Bernoulli numbers, which are also of great importance in number theory.
At the age of 17, he also began studying at the university in his birthplace and thanks to his excellent achievements in high school, he was awarded a scholarship which, unfortunately, was not renewed the following year, as he decided to focus only on mathematics and completely neglected the other subjects. This situation brought him to a serious financial problem and he decided to abandon his studies at the academic institution and instead immigrated to a distant city where he devoted all his time to studying mathematics while placing emphasis this time on a field called hypergeometric series (special series that can be used to formulate equations in a different way ) and the relationship between series and integrals. I will try to explain the connection between the last terms in a few words - a series, as I explained, is a sequence of numbers and the addition of the sequence of these members gives a sum; On the other hand, an integral is simplistically some area, we can think of an area that is actually an accumulation of smaller parts arranged in a way that maintains a connection between each part and the other as if these small areas were a series in itself.
An interesting personal detail in Ramanujan's life was at the age of 22 when his mother married him a suitable bride aged only 10, but Hela did not live a life of partnership with her until she reached the age of 12.
Ramanujan continued his innovative and numerous researches until in 1911, following a revolutionary article on Bernoulli's numbers, his name came before him as a genius and gained fame among the group of mathematicians despite his lack of academic education. In his words, the founder of the Indian mathematical community - Ramachandra Rao - gives a detailed description of the lift: "A short and unrefined figure, stout, unshaven and a little dirty, with big, bright eyes entered my office and was swimming under an old notebook; He was appallingly poor. He opened his notebook and began to explain to me the mathematical theories he came up with on his own, I immediately understood that this was an abnormal phenomenon, something I had never seen in my life, but I could not judge whether his words were nonsense or nonsense because my mind was short on these matters. I asked him what he wanted, and he asked me for a basic subsistence allowance so that he could continue to engage in his mathematical studies." Rao tried to get him such an allowance but was unsuccessful and Ramanujan decided to try and find a job as a clerk in the finance department of the university. A letter of recommendation from a professor of mathematics at this institution contained the following: "I highly recommend the convict, he is a young man with a mind full of mathematical knowledge and especially in the field related to number theory. He will surely be able to handle the calculations required in this position."
While working in the aforementioned job, he continued to engage in research and this time he decided through his friend who was a mathematics professor from London to send his works to regions overseas to discuss them with world-class mathematicians, but they all expressed their disdain for his writings since his style of writing was not "academic". To his delight, his following words eventually managed to fall on the attentive ears of a great mathematician named Hardy: "I never received a (full) university education but I studied formally at school and therefore the content and form of the things I wrote down are different from what is customary. After I finished school, I began to spend all my time studying mathematics, and the last things I discovered were described by local mathematicians as scary."
Hardy and his friend Littlewood deeply examined Ramanujan's words and writings and pointed out to him that there are indeed some profound and important discoveries that they would like to examine more comprehensively after he provides them with purely mathematical proofs. Some of the things Ramanujan wrote down were (unbeknownst to him beforehand) mathematical proofs previously given by great mathematicians such as Gauss (Gauss) and Kummer (Kummer), and they also had very important matters in number theory and especially about what is called Riemann's zeta function. The reason I emphasized this is because it is one of the most difficult and important problems (that have not yet been solved) that exist today in the world of mathematics and its importance to number theory in particular and to the scientific world in general is priceless.
Ramanujan wrote back to them (especially Hardy) these beautiful words: "I have found in you a true friend who treats my work with respect. I am all starving to death (due to his love of mathematics) and to preserve the faculties of my mind I need food of this kind (Hardy's good words).
In 1914, Hardy brought Ramanujan to the University of Cambridge so that they could work together, and indeed this act led to a close relationship that produced many important mathematical fruits, but so did the one that led to his untimely death; Ramanujan belonged to the Brahmin religion in India that advocated vegetarianism, while in England it was difficult to maintain this type of diet because the First World War made it very difficult to trade in the special foods he needed. Already at the beginning of his journey, problems with his health were discovered as a result of this reason.
Another problem arose from the fact that Ramanujan was not familiar with the form of mathematical writing and proof required in the academic world; Hardy asked his friend Littlewood to teach him this, and Hela explained the situation to him shortly after he began this craft: "It is so difficult, because every time I had to teach something to Ramanujan he managed to come up with fantastic mathematical ideas and it is simply impossible to go on like this that way ".
Ramanujan continued to get significantly ill because the winter was unbearably harsh, something he was not used to in his native land and his work was indeed delayed as a result. At the age of 29, only about 3 years after starting his studies at Cambridge, he earned a graduate degree in the study of sciences (today this degree is called a "Doctor of Mathematics") and two years later, he received the greatest honor of entering the list of the Royal Order of London (an English tradition from 1645, in which A limited number of scientists lead to a representative group of the elite of science at that time). This led to the fact that Ramanujan's frail health began to improve miraculously and Hardy's words explain this well: "We hope that he got on the road leading to full health, he gained weight as if he were a rock. Happily, we never saw any decline in his mathematical abilities, he did produce slightly more research but the quality still remained fantastic. I believe that when he returns to India, he will achieve a glory such as no Indian has ever achieved before, and I am sure that his country will give him the respect and facilities that are due to a treasure of this kind. He is extremely humble and it should be explained to him in the clearest way that he is indeed a success like no other."
Ramanujan sailed back to India in 1919, but his health again began to deteriorate and he died in Ibu at the age of only 32.
138 תגובות
thanks for sharing!
Who else do you hate?
Who else do you despise?
It is important that the public knows so that those who need it can beware of you!
Hello. I am a computer science student, and as such have taken several math courses.
Like anyone who studies mathematics and is amazed by its false beauty, I also went and read the book The Indian Clerk and became interested in all kinds of autobiographies about different mathematicians, whose lives were not that interesting, only their mathematics was worth something, and this is something that can only be understood if you study the This, that is, mathematics is a bubble, a separate world. A sort of bunch of realistic people who are not ready to stop insisting on the casual meaning of our existence in the world. Now I must say that I do not like your forceful and infantile approach to life. I hate how you insist on being serious and cold at first but immediately realize how childish you are after a minute or two. You hide all your life behind this bluff called mathematics, and you don't have the courage to go out into the real world.
Hi Michael
Thanks for the update on Perlman
I just wanted to let you know that the article
On Hilbert's sixth problem
which is now on my site
Will be submitted in about a week to the AIP journal
I met in Jerusalem for a few minutes
You are Laszlo Lobs, the president of the World Mathematical Union
And I gave him a copy of the article I wrote
Happy 2010
In one of the comments here Perlman was mentioned and it was said that he proved the Poincaré conjecture while locked in his house.
Today an article about Perlman was published in the "Haaretz" supplement and I decided to learn something about his life.
It turns out that the claim made here in his case is not true:
http://en.wikipedia.org/wiki/Grigori_Perelman
Michael:
I received the email, thank you!
In July 2000 I met a friend whom I had not seen for many years
It was during the preparations I made for the trip to the "Mahilbert Century" conference
He asked me if I solved one of the problems from Hilbert's list?
I told him no. It was while I was writing the book "Love Letters to Mathematics"
Since then I have been concentrating more and more on solving the sixth problem on the list
I will send you relevant material soon
I hope this will make us really want to meet
Moses
Moshe:
I sent you an email with my contact details.
I suggest that we start correspondence because the geographical distance between us is great.
Hello Michael,
Congratulations on publishing your article with the rectangles with the correct solutions!
As you can see on the website of "Gan Adam"
I created a reference to our discussion following Liran's article on Ramanujan
I am currently writing a new article on "organic mathematics"
for a journal following participation in a conference in Sweden in June
I would love to meet with you as an entrepreneur and mathematician to present it to you
Best regards
Moses
Michael
I must admit defeat, on the other hand I have never excelled at solving puzzles...among other things I lack the necessary perseverance.
On the other hand, I have a tip for a possible solution:
Assume by the negative that there exists an integer dimensionless rectangle consisting of rectangles with one integer dimension.
There must be a minimum number of rectangles that make it up. As mentioned, such a rectangle cannot be composed of a single rectangle because one rectangle must have a complete dimension. Such a rectangle cannot be composed of two rectangles because there are only two ways to make a rectangle from two rectangles and the resulting rectangle has a whole dimension. Therefore, according to the negation assumption, a rectangle consisting of N rectangles with one whole dimension is not such. When it is not possible to find such a rectangle consisting of a number of rectangles smaller than N.
Assertion: It is not possible to find within such a rectangle a sub-rectangle (smaller rectangle), which consists of an integer number (greater than 1) of rectangles with one whole dimension.
If such a complete subrectangle can be found then:
1) If it lacks a complete dimension, this is in contradiction to the assumption that the large rectangle is the complete dimensionless rectangle consisting of a minimal number of rectangles.
2) If it is a rectangle with one complete dimension, then all the rectangles that make it up can be united into one rectangle and therefore we have reduced the number of rectangles that make up this large rectangle in contradiction to the fact that N is the minimum number.
This is basically where the basic idea ends.
Now it remains to prove that it will always be possible to find a subrectangle inside the large rectangle.
The algorithm I come up with is scanning the large rectangle using a vertical line and a horizontal line that move continuously so that they actually separate the large rectangle into four smaller rectangles.
The claim that I currently do not know how to prove is that in this way a subrectangle can always be found.
In order to be able to find a correct subrectangle, it is forbidden to divide a rectangle in its whole dimension so that a rectangle without a whole dimension is created (the same mistake you found in my previous idea). At the moment I do not have the proof for this last step.
Michael
Maybe later you will write about the more fascinating topic.
It is very interesting to read your insights on the matter.
Thanks.
Higgs:
The article I prepared is not about the general topic of solving puzzles but about a solution to the problem of the rectangles plus some surrounding insights.
The general topic of solving puzzles is perhaps the most fascinating topic that I can talk about, but somehow I feel that it is a topic that goes through a frontal lecture much better than in an article (I have already managed to give such lectures here and there).
Michael
Thanks for the postponement, I hope I'll be able to take advantage of it.
Michael
Your description of cracking a problem by throwing a rope. I really relate! The real problem is how to teach others to give them rules of thumb for solving problems. The problem of numbers from 1 to XNUMX is quite easy. It's a little hard to understand why it's difficult to solve it. Maybe it's because you don't use intuition correctly In this case. In any case, you are preparing to write an article about these things right away.
For "educational" needs? 🙂
LOL…
It doesn't matter, I'll think about it myself... I got to it once so there's no reason why I won't get to it again...
The skeptic:
The truth is that I prefer not to publish the solution too much yet because - as you saw - the puzzle is used for "educational" purposes.
You can ask my father to send me your email address and I will send you the solution this way (there were already some readers on the site who received the solution from me by email)
Yes that's the puzzle, thanks…
Unfortunately I don't remember my solution, I only remember that it was very simple...
Do yourself a favor and solve it too in your article 🙂
By the way - the above riddle has been solved by several people and the active Higgs here on the site also hinted at its solution.
The skeptic:
I guess you mean toThis puzzle.
Both bodies are made of an imaginary material that I call "topological material" - a kind of material that can be stretched or shrunk at will without it springing back to its previous state, but which cannot be torn, punctured or glued.
Michael, you once wrote a puzzle from Agniva (in which two rings were drawn if I'm not mistaken)
A short type of drawing - a puzzle...
I remember thinking I solved it but I couldn't find the article you published it...
Except that now I don't remember what the puzzle was and what my solution was
I would be happy to try to solve it again if you could kindly give the link to it again...
Unfortunately I don't really remember what it was, I think you posted it as a response to someone who claimed that imagination is not necessary in mathematics (or something like that, I don't really remember that either...)
Hope you understood my vague descriptions 🙂
correction:
I remembered that actually Lev Radziblovsky also solved the question with the pawn.
Moshe:
Here are a few things about your question about Behler:
http://213.8.106.62/leibowitz/files/bechler.htm
http://www.ifeel.co.il/page/3351
http://he.wikipedia.org/wiki/שלוש_מהפכות_קופרניקניות
http://213.8.106.62/leibowitz/files/elia.htm
Moshe:
It turns out that my words achieved their goal because we are finally starting to move forward.
You write:
"The question, in my opinion, is not whether there is room for mistakes in mathematical proofs (Ramanujan did not prove anything!) but whether the language of mathematics can expand to a new place (of consciousness / the way the brain works) where accuracy will be preserved and also a flexibility of thought that is not based only on the formal method will be developed .”
And that's exactly what I argued: you have a question and you don't have an answer to the question!
As long as you have not been able to develop this direct connection even with yourself - how confident are you that you will succeed (until 2010!!!) in developing it with someone.
I too am always surprised by the power of intuition - not Ramanujan's but mine (you, I have more experience) and I explain to people more than once that mathematical progress is not like climbing a mountain where each time you drive a new nail as a step, but rather one where tens of ropes are thrown meters upwards - to a place that you can't see at all - but with an inner feeling that you will be caught in something and only then do you start climbing the rope (and create the proof that you are indeed caught in something stable).
The point is that without climbing the rope - we don't have any confidence that he was really caught and certainly we can't convey this information (that even we don't know) to others.
I also allow myself to guess that the claim that you solved hundreds of such puzzles in your youth is more nostalgia than reality.
I'm sure you solved puzzles - but not these.
I can draw this conclusion based on two independent facts:
One is the statistics that I manage (not in an orderly way - but the small numbers in question do not need to be in order) on the various puzzle solvers.
I know a lot of professional and amateur mathematicians and I know exactly who among them solved the puzzles and who didn't.
For example - regarding the question with the numbers between one and a thousand - I do not know for sure that any of my acquaintances solved it, although I believe that Professor Nega Alon did solve it because he told me that he did.
Lev Radziblovsky - the coach of the Israeli national team for the mathematics competitions - also asked me for the solution after trying to deal with the question for many months without success (in fact, he asked me for the solution through his brother - Pavel - one of the coaches of the Israeli national team for the Physics Olympiads and Pavel was shocked by the fact that the solution was so simple I could explain it to him on the phone for about three minutes).
I know, of course, that I'm not the only one who solved it (because it came to me from somewhere - I didn't invent it).
Regarding the question with the pawn - I only know one person who solved it (besides me). His name is Yoav Raz and he lives in New York.
The question with the rectangles was already quite famous when I came across it, but everyone who knew it already heard some solution of hers (which is different from mine) and no one claimed to have solved it themselves.
It's about the stats on others.
Regarding the second fact - I allow myself to base myself on the mistakes I made in the previous proof attempts. Was your ability to spot errors better in the past? Maybe a little (age takes its toll) but probably not substantially.
Michael
Because I tried to establish, albeit unsuccessfully, the beautiful idea that Ehud brought up here for solving the rectangle puzzle, you don't have to bother at all and explain to me the importance of accuracy in mathematics. By the way, I spent my youth.. solving (of course I didn't always succeed) dozens and even hundreds of mathematical puzzles similar to the ones you present to us here in the discussion (and thank you for that).
In the context of understanding Ramanujan's unique method of creation, the question in my opinion is not whether there is room for mistakes in mathematical proofs (Ramanujan didn't prove anything!) but whether the language of mathematics can be expanded to a new place (of the mind/how the brain works) where accuracy will be preserved and A flexibility of thought that is not based only on the formal method will be developed. I also invite you to read the article "The Limits of Language" in the attached link, where I referred to Wittgenstein's book at the end.
http://www.snunit.k12.il/heb_journals/kimat2000/007038.html
Allow me to quote here from the book "Mi Michir Wittgenstein" published by Havrat Safarat" page 74
"falling in love again"
Shortly after becoming a lecturer, Wittgenstein fell in love with a young student who attended Trinity College, Francis Skinner, who became a permanent friend and an important partner in philosophical work. Skinner, the most promising mathematician of his generation, was a shy, handsome and very refined guy who was clearly destined for an academic career. Under the influence of Wittgenstein, he gave up university and became a mechanic in a factory.
I would appreciate it if you could send me a suitable reference for Zeev Bechler's opinion on Wittgenstein II
sympathetic:
I grabbed my father and we agreed on postponing the publication to Monday.
Moshe Klein:
I allow myself to say that Wittgenstein (in his second term, because in the first he was still normal) simply talked nonsense.
You should read what Zeev Bakhler writes about him.
Of course, the issue of future wars is irrelevant.
What does belong is that in mathematics questions have unequivocal answers that are not based on sociology.
It is customary to say that mathematics is not a science and practically it is true, but philosophically it is definitely a scientific theory based on basic assumptions that have not been tested by any person but by evolution and have stood countless tests.
Without the basic assumptions that are used by us in mathematics we cannot think at all and certainly we cannot converse.
I have not the slightest doubt that none of this will change.
Sure - we will discover new sentences and maybe we will also find here and there errors that we have made, but we will continue to use the logical theory that evolution instilled in us both because we have no escape from it (it is part of our humanity) and also because it just works perfectly.
A mathematician has to be able to wear all of de Bono's hats at the same time.
He should be creative, of course, but he should also be critical and refer to the data.
I really hope that the mathematicians of the future will not try to sell solutions that do not pass the test of criticism.
Note that it is very difficult to deal with a wrong proof of a true sentence because the sentence is true and finding examples that disprove a wrong reasoning on the way to proving it is sometimes an almost impossible task, but someone who can give a wrong proof of a true sentence can also prove a false sentence in the same way and his math is simply unbelievable (And I emphasize: in my opinion - contrary to what is implied in some of your words - there are things that are true and there are things that are not true and this is not about a sociological result but about things that can be tested even in an experiment. As I said before - a proof is a proof, an experiment is an experiment and its result is its result).
Michael
Yes I see the flaw now
that you voted for in Ehud's proposal.
I'm already curious to see
your solution to the problem.
FYI, normal mathematics is also sociology
It is based on assumptions and hidden agreements of the community of mathematicians
That is why the philosopher Wittgenstein convened the seminar
Discuss the foundations of mathematics at Cambridge
This was before the outbreak of World War II
Regarding the ability of the tals built with normal mathematics
You must know Einstein's answer to the question
What will they fight in World War III?
He replied that he did not know how to answer
But in World War IV
They will return to fighting with sticks and stones
Moshe Klein:
Your proposal has the same flaw I pointed out in Ehud's proposal.
Think again.
Regarding what you call new mathematics - it is not mathematics - it is sociology.
I wonder how you propose that the rockets that are sent to the moon according to certain calculations take into account all opinions.
Following on from Ehud's idea. The small rectangle that has a corner on the right and left side of the main rectangle has at least one side that is complete. We will continue its incomplete side further until we reach the side of the main rectangle. On the way we may cross existing bricks. Now we will omit this whole part (it's a shame we can't draw here) and we will get a new main rectangle but smaller in size. When we cut perpendicular lines along the way, then we will inevitably also add new bricks that were not there but will be in front of them in the area where we omitted the same amount of bricks. Therefore the total number of rectangles in the newly created rectangle will be at least one less than the number of rectangles that were in the main rectangle. Because in addition we omitted the small creating rectangle. Therefore the induction described earlier in the proof can be applied. This is after we checked the cases n=1,2
The new mathematics, inspired by Ramanujan's work, assumes that a point and a line are atoms that are not derived from each other. She sees mathematics as a dialogue and creation of living interaction and not of a single creator. Therefore, the other person's opinion will always be important. in every present moment.
sympathetic:
First of all - the fact that I am right is not a reason to be sad 🙂
Regarding the publication date - we were thinking about Mochash, but I will try to talk to my father (I tried right now and didn't catch him) and maybe it will be possible to postpone it.
Michael
Unfortunately you are right...
I think I can fix the solution also against such cases but then it already becomes ugly
every.
I have at least two more ideas for a solution but I don't have time to develop them right now
I hope you don't present the solution before Monday.
sympathetic:
Instead of being cynical, think again.
If you still don't understand, ask and I'll explain why what I said is true.
Michael
It seems to me that even amateur mathematicians should know that: a whole less a whole gives a whole
And a rational number that is not an integer cannot be turned into an integer by subtracting an integer from it?
Cutting and then gluing the parts does not change the properties of the rectangle (a whole minus a whole equals a whole number)
A non-whole rational number minus a whole number equals a rational number.
If you have a problem with the cutting, you can simply delete each time the corner row or column and continue this way until you reach a single rectangle.
Moshe:
Didn't the mathematicians of the new generation know how to point out the flaws I described in Ehud's proof?
And as for the direction you suggest:
You won't know if your induction step will work until you set it up.
There is nothing to ask the opinion of others about an indefinite thing.
sympathetic:
You were understandable.
That's basically what I thought you meant and that's why I said I'm guessing the idea is wrong.
When you remove the row, you disrupt the properties of some of the inner rectangles and it is possible that after cutting these rectangles do not have any complete dimension.
Therefore, the rectangle after the cut lacks the property of "being tiled with rectangles that have at least one whole dimension" and that's what I meant in response 100.
Moses
In my opinion, my proof is not cumbersome, only my attempt at description is cumbersome. Graphically things are much simpler. As for induction, my proof is that there is no reverse induction.
How about a generalization of induction if for all rectangles consisting of k rectangles with integer dimension such that k<n
It holds because they have an entire dimension and the claim is also true for k=n Is the claim true for n=k+1 Now the claim can be proved by "deleting a row or column of the rectangles connected to the corner rectangle. The deletion is done perpendicularly
to the full extent. Prepares that the properties of the large rectangle have not been changed by the deletion and since it now contains
Fewer rectangles (at least less than one rectangle) because even the rectangle we started with n=k+1 had a whole dimension.
Hi Ehud
At first glance it seems a bit awkward.
I try to improve your first proof a little differently using induction on the number of rectangles n that make up the main rectangle. If n=1 then since the rectangle has an entire side it follows that the main rectangle which is the same as it also has an entire side. If n=2 the two rectangles must be completely contiguous on one side. If the common side is complete then it is also a side in the main rectangle and we are done. If not, then the two perpendicular sides are necessarily whole and their sum is also whole and this is the side of the main rectangle, so we are done. Let's assume that the claim is true for n=k and we will prove the claim for n=k+1.
Do you think the induction phase will work in this case?
First I apologize for the hasty description of the solution, I was just short on time
To Moshe I am glad that you found my solution to be elegant and simpler about it later
For Michael, this is a very simple idea, all that needs to be understood is that the algorithm does not change the nature of the rectangles, so it is correct.
I will repeat the proof again in a detailed manner before several definitions:
For a rectangle with 2 pairs of sides, I will call the short sides height and the long sides width.
Now for the proof:
Assume by negation that there is a rectangle composed of rectangles with an integer dimension so that it itself does not have an integer dimension.
We will run the following algorithm:
We will go along the height side of the large rectangle and check which rectangles make up this side. We choose those rectangles that have an entire dimension along the side (their entire dimension is parallel to the side) we delete the entire row adjacent to this rectangle, that is, the rectangle itself and all the rectangles and parts of the rectangles that are within the two rows across the width of the large rectangle, the rows are created by extending the sides that do not have an entire dimension of the rectangle The above on the side.
Since we did not change the nature of the large rectangle in this operation, the resulting rectangle is also apparent
missing a whole dimension. We will continue to perform the operation on all the complete rectangles that make up the height of the large rectangle. It cannot be possible to do this for the entire height because then we would have reached the contradiction of the rectangle
has a whole dimension. Therefore, at some stage it will not be possible to find on the height a rectangle of a complete dimension that is part of the height of the large rectangle. At this stage we will move to the width of the rectangle and find those rectangles that make up the width and have a whole dimension over the width. We will delete these rectangles and
All the rectangles and the parts of the rectangles lying between the two columns created by extending the incomplete sides of the rectangle to the height of the large rectangle. Now we will continue this operation until we have a single rectangle left. Why a single rectangle? You can always look at the corner rectangle, it belongs to or to the rectangle that makes up the getba we dealt with at the beginning so it is impossible and therefore it must be
A rectangle whose entire dimension is parallel to the width of the large rectangle and repeats (we always look at the corner rectangle) is finally left with a single corner rectangle and it must have an entire dimension in contradiction
to the initial claim.
I hope I was clear it's a bit difficult without drawing. If you have any questions about the proof, I will be happy to answer.
Shabbat Shalom,
sympathetic
sympathetic:
Your proof is at best missing important details and at worst wrong.
The truth is that in the way it was written it is not even defined because you did not specify whether the line you download has the full dimension or the one that is perpendicular to this dimension (and this is assuming that it is quite clear what a line is, even though this was not precisely defined either). In any case - you must prove that the remaining rectangle has the properties defined in the problem (because as Moses said - new rectangles are created inside it).
That's why I also answer Moshe:
Obviously, as it is written - the solution is not correct.
Since the solution is not fully described I cannot say at the moment if the idea behind it is correct (my initial impression is that it is not).
sympathetic
I liked your elegant approach to solving Michael's rectangle puzzle
Note that if you cut the rectangle you can create new rectangles that were not there before
Therefore, in my opinion, a short explanation is missing in your approach as to why we will end up with one rectangle
In any case, I would of course like to hear Michael's opinion on the solution you propose
Michael
Assume by the negative that there is no such rectangle. In other words, there exists a rectangle with an incomplete dimension consisting of rectangles for each
One of them is a whole dimension.
Now we will run the following algorithm:
At least one of the sides has a side of a rectangle with a whole dimension. We will delete the whole line (or cut it)
along this rectangle. The rectangle now obtained also cannot be a rectangle with an integer dimension. We will continue the process
until finally we get a single rectangle. Since by definition a single rectangle has a whole dimension we have reached a contradiction and therefore
Our assumption that there is a rectangle that does not have a whole dimension and yet is composed of rectangles that have a whole dimension is not correct.
Moshe:
It is difficult to formulate things in a way that will satisfy everyone.
The use of the word length will confuse people who perceive the rectangle as having two dimensions, one of which is length and the other is width - that's why I chose the word dimension.
I hope, in any case, that after the discussion that took place here, everyone will understand the intention.
Hi Michael
This question is very beautiful!
Why do you call it the dimension of a rectangle?
You mean of course along the side of a rectangle.
If so then the use of dimension may confuse readers
In the meantime I checked for a tiling of the large rectangle
in the number of rectangles 1,2,3,4 and I was able to prove in these cases
In any case, I would love to read the article you publish about this puzzle.
By the way, Aryeh, thanks for your question.
I am also happy that I decided to publish the riddle in advance because thanks to this fact and thanks to your question I corrected the wording of the riddle in the article.
The new wording is:
It has been proven that a rectangle that can be tiled using a collection of rectangles each of which has at least one whole dimension (that is, the size of that dimension is a whole number of measurement units), must have at least one whole dimension (in the same measurement unit).
It means that the size of the dimension is a whole number in some unit of measurement.
For example - if the unit of measurement is centimeters and all the rectangles have at least one dimension that is a whole number of centimeters long, then the outer rectangle also has a dimension that is a whole number of centimeters.
Michael - I don't understand what it means that the rectangle has at least one whole dimension. After all, a rectangle is an area and has two dimensions, and if it has less then it is not a rectangle and what is an incomplete dimension anyway? And sorry for the ignorance. The thought of N-dimensional boxes now made me imagine the famous body which is a three-dimensional layout of a four-dimensional cube. Looking forward to your article.
Friends:
I will not post solutions to the questions I presented in response 75.
Regular readers already know that these are questions from a stockpile of questions that I use when it is necessary to put someone in their place.
Their advantage over other questions is that I have never come across any publication - in the literature or on the Internet - that contains solutions to these questions, and therefore the chances are higher that whoever presents a solution to them has solved them himself who solved the questions but the chance that someone from the group who knows the solutions is friendly enough with someone from the group of pretenders to help him face the challenge is not high).
On the other hand, these are questions that are beautiful to me and I feel a little sorry that honest people who read the discussion read them and don't get to see a solution.
I decided, therefore, to try to atone for the matter a little by presenting a beautiful (but somewhat more familiar) question, the solution of which I have no interest in hiding.
In the coming days, an article of mine presenting the solution to the question will be published on the website, but in the meantime - those who are interested can start thinking about it.
the riddle:
Prove that a rectangle that can be tiled by a collection of rectangles each of which has at least one whole dimension must have at least one whole dimension.
Continuation puzzle:
What about N-dimensional boxes with K integer dimensions?
at the police station
------
I was standing in the main square of the city near the municipal offices. Across the road I saw the police station. Something in me that was at that time drew me closer to this station. When I stood at the entrance of the station I saw policemen sitting on a bench drinking coffee together. They looked at me and tried to understand what I wanted from them. I asked if I could talk to one of them. The deputy station commander stood up and told me to come with me. He took me to the inner room of the station and asked me to sit down. He took the station log in his hands and asked me to tell him about the incident that happened to me.
I told him that there was no need at all for him to write down my words in the diary. He asked me in amazement why? I answered him that this was a case that happened many years ago. Actually, it didn't happen to me and it also happened in another country. The policeman was very surprised. Despite my words, he asked me to continue the story. I answered him that it was a suicide attempt. The policeman was impressed and asked me to give him more details. It happened in England in 1917. A great mathematician tried to jump on train tracks when the train arrived at the station. And what happened? The policeman asked me. The train stopped near his head. Well I understand said the policeman so why did you come here today? It turned out to me that Scotland Yard took the mathematician they called Ramanujan to the police. At that time, attempted suicide was considered a crime in England. One mathematician he worked with named Hardy came to the police and gave false evidence about him. He told the police that Ramanujan was the best mathematician in the world and was a member of the Royal Society.
Why do you think this is a lie? the policeman asked me. Because Ramanujan was indeed elected to the Royal Society but it was only after his suicide attempt. It was already in 1918.
How can I help you ? asked the policeman. I replied that I was looking for a way to get to the file of this case at Scotland Yard. I wanted to find out if the police could help me get this material.
The policeman thought for a moment and answered me that the guard would not go to Scotland Yard to look for the material.
Anyway, he thanked me for the story and wished me success in my further search. I told him that soon in August 2010, the world conference on mathematics will open in India, the country where Ramanujan was born, and this is a good opportunity to try to understand the motivation of the best mathematician in the world to try to end his life. In any case, he died about 3 years later at the age of 32.
In the meantime without sufficient evidence, those of us who really love Ramanujan and draw inspiration from him for our mathematical creation will have to use our imaginations to try and answer this vexing question about Ramanujan.
” .. Cambridge began to resemble a prison. Ramanujan was used to the freedom that life in India afforded. The warm climate allowed people there to spend most of their time outdoors. At Cambridge he had to hide within the thick walls of the college to protect himself from the lashings of the freezing North Sea wind. The social segregation meant that there were only a few connections beyond the official interactions of academic life. He also began to feel that Hardy's insistence on maintaining mathematical rigor prevented him from letting his soul roam freely in the expanses of the mathematical landscape.
The music of the initial numbers page 213
"... In 1917, Ramanujan was already depressed in a way that was getting worse. The horrors of the First World War gripped Britain. And at Trinity they did not choose Ramanujan as a member of the staff. Russell's membership in the college faculty was revoked due to his opposition to the war. And the college could not afford to agree with Ramanujan's own pacifist position. He may have finally learned how to push his usual paws into the western shoes and have fun in the academic cap and the waves, but his soul remained in South India..."
Marcus Zo Sotoi - page 213, in the book "The Music of the First Number" published by Yediot Books
It was indeed my mistake, I didn't notice that it says the "minimum" common multiple, sometimes it is advisable to pay attention to the details
sympathetic:
I don't understand what you were trying to show in the numerical example.
I hope you didn't try to claim that what I said can be proven to be untrue because then you must be wrong.
Regarding the claim that it is better to avoid determinations based on a single case - I agree with you, but I did not do it.
I actually gave a single case as a counter example to your claim that was based on zero cases.
Ehud, please note that in your example 300 and 600 years are greater than 251 but their common denominator is less than 1000 therefore you cannot add the inverse of both and there are many more such pairs
Nevertheless, it is advisable to avoid determinations based on a private case.
Here is an example:
If you examine the question: "Given a group of natural numbers in the range between one and a thousand.
Given that in this group the least common multiple of any two of the numbers is greater than a thousand.
Prove that the sum of the inverses of the numbers (the inverse of a number is one divided by the same number) is less than 1.5"
If we choose 2 then even if we choose all the numbers greater than 500 so that their product will be greater than 1000
The sum of the inverses will be less than half and another number less than 1 which is the sum of 499 numbers each of which is less than 1/500
This is a private case, on the other hand, if we choose 4, then the sum of the inverses of the 749 numbers greater than 251 is greater than 1.3, we add 0.25 to that and we get that the sum of the inverses is greater than 1.5.
Continuing the discussion of Ramanujan's mathematical legacy, you can read the following article:
Warning signs of a possible collapse of contemporary mathematics
On the website of Prof. Edward Nelson from Princeton University
http://www.math.princeton.edu/~nelson/papers.html
sympathetic:
True - but it is a more serious foundation than a conversation with zero scientists.
By the way - proof that such a person is not seen as eccentric is definitely here.
Michael
On a side note: I assume that you are aware that a conversation with one scientist is not a statistical basis.
As for the question of where is today's Ramanujan, I think we have exhausted it.
sympathetic:
Indeed, in my opinion, every talented scientist - all over the world - will find his way in the academic world and will always find someone who will listen to his words.
There are enough talented scientists and there is enough competition between them that the mere fact that one of them rejected the paper would actually encourage another scientist to check it seriously.
Of course, there may still be theoretical situations where this will not happen.
For example, if that talented scientist doesn't talk to anyone or if he happens to say things that are really at a level beyond what all the other scientists are able to understand, but the probability of this is extremely low (and this is a situation that you really can't blame anyone for except the scientist who didn't know how to clarify his words good enough).
By the way, Galua's story was mentioned here and it is worth noting that although it did not make it easy for his teachers at all (and it is interesting to read in this context the This review of his biographies) his works were submitted by his teachers as nominations for very important awards and only an unfortunate combination of circumstances (such as Koshi's death) prevented their importance from being immediately discovered in the entire academic community.
The fact is that even after Galois died (something that eliminated a significant part of the impetus behind the attempts to gain recognition for his works) 15 years were enough for them to gain the recognition they deserved (that is - if he had not been killed - and even if he had gone into a coma for 15 years, he would have woken up at the age of 36 and discovered that he was famous global!).
Regarding Einstein and the multiple worlds - I think you have not done a comprehensive enough study on the scientists' opinion on the subject.
I recently spoke, for example, with Lev Weidman - one of the senior quantum theorists at Tel Aviv University - and this is by definition the preferred interpretation for him.
No one thinks he's eccentric.
Michael
I did not give the answer to the question I raised. I still ask if something that is not from a leading academic institution or a world name can break into consciousness today? Does today's Ramanujan or Bose stand a chance? If you believe that the answer lies in the accessibility of information, then I would appreciate it if you could tell me about mathematical or physical discoveries made by unknown researchers who did not originate in the US or Europe... but you may be right and perhaps today it is easier to obtain scholarships and talented researchers at an earlier stage can Move to the rich western countries and get a better education.
Regarding the ability of science to filter errors here, I completely agree with you and we had no argument about this issue, the scientific method is built so that it can prevent errors. An interesting book on this topic is called:
Bad Science: The Short Life and Weird Times of Cold Fusion (Hardcover)
/Gary Taubes
The book tells about the two chemists who in 1989 claimed at a press conference that they had succeeded in achieving hot fusion. One of the reasons for the uproar that broke out is that the two turned to the media with their discovery instead of receiving scientific criticism when they had already received scientific criticism that denied their inventor it was too late.
Despite all this there are examples that misconceptions can take root in science for a while. Newton, for example, believed that light is made up of matter particles and this for incorrect reasons (today we know that indeed light is made up of photons). During Newton's time, experiments indicated that light is a wave, and Newton fought this idea to the bitter end. But this is an unusual example.
As mentioned, I have no argument with you about the high ability of science to prevent mistakes, but I do have doubts about the ability of things that are not according to the dominant example to take hold. Is there a chance for something that speaks a slightly different language, such as Ramanujan's letters to Hardy which included claims without formal proof, to be accepted and recognized?
Side note: I can assure you that Einstein would not have believed in the multiple worlds interpretation! Even in Israel the physicists advocating this interpretation are considered eccentric and it is considered a marginal approach. The elegance of this interpretation is that it assumes nothing but the laws of quantum mechanics, meaning that there is no need to assume a priori a world that fulfills the laws of classical physics. Mathematical elegance but the interpretation is clearly not physical (it does not contradict the laws of physics but it does contradict the spirit of physics!).
Ron:
I did attack you.
I did it consciously and I also explained why I did it.
I repeat and explain to you because of your difficulties in understanding: I attacked you because you attacked me. Capish?!
When someone talks from his ass, he is not entitled to a response from another organ, and yet I rewarded you with an answer that also has factual elements.
You preach to me "the degree of honesty requires me to say the least - I don't know how it happens." After you said it's a (definitely!) left hemisphere job.
Is it consistent with your demands from others?
But you should know: I actually do know what I'm talking about when I say it comes from the subconscious and I also know what the subconscious is.
The activity of the subconscious can be measured with devices. God's activity is impossible.
There are many more differences but you won't understand it.
The explanations you ask for different aspects of reality show that you should land on the ground of reality before you start talking about it.
This of course also includes the minimum requirement - that you have some idea of what it is to be a mathematician before you try to teach others how to be a mathematician.
http://he.wikipedia.org/wiki/%D7%A9%D7%99%D7%97%D7%94:%D7%92%27%D7%95%D7%A8%D7%92%27_%D7%A1%D7%A4%D7%A0%D7%A1%D7%A8-%D7%91%D7%A8%D7%90%D7%95%D7%9F
I was standing in the main square of the city near the offices of the municipality. Across the road I saw the police station. Something inside me pulled me closer to this station. When I stood at the entrance of the station I saw the policemen sitting on a bench drinking coffee together. They looked at me and tried to understand what I wanted from them. I asked if I could talk to one of them. The policeman who later turned out to me to be the deputy commander of the station stood up immediately and told me to come. He took me to an inner room and asked me to sit down. He took the station diary in his hands and asked me to tell about the incident that happened to me.
At the time I was completely upset by the discovery of Ramanujan's suicide attempt by jumping on railway tracks. What amazed me more was the false testimony given by Hardy to the police that Ramanujan was a member of the London Mathematical Society. It was only in 1918. I know that Hardy said this so that Ramanujan would not be arrested by the police, but something inside me wanted to understand more about what really happened there.
(Continuation may come..)
Michael, speak nicely, especially with you in the dialogue with Ishvani.
Instead of answering me - you attacked me.
Here you do it again
If I say you don't understand what you're talking about - does that have any persuasive weight? I do not think so.
Ramanujan claims that the goddess is whispering to him - not that he has a thought that anyone has given him.
The degree of honesty requires me to say at least - I don't know how it happens.
Although I am interested in knowing - but at the moment I do not have the tools.
Saying subconscious - it's like religious people say God - it's not very helpful
You have found a patent for running away from confrontation
First of all, explain to me how in reality 1 plus 1 is 2
If reality is one - there can only be half and another half equals one
Or a man plus a woman equals three - a child, here 1 plus 1 is 3
Actually, Ron:
One more reference.
I think you have no idea what you are talking about.
Goddess Namagiri does not reside in the right hemisphere and according to you it has nothing to do with reality.
Ramanujan did not know the workings of the mind and did not know what the subconscious was - so he treated the solutions that came to him unexpectedly as if the goddess Namagiri had planted them.
If he had grown up in a Jewish family, he might have said that Harbevich planted them.
Both claims had exactly the same validity and would express exactly the same misunderstanding.
You, instead of dealing with my arguments, chose to try to attack me personally.
This is the reason for my previous response.
My feeling was that for the purpose of formulating your responses you did not recruit the brain hemispheres but the hemispheres of another part of your body that is usually intended for sitting.
In my opinion, you don't even have a green idea about the topics of our conversation and you are welcome to try to refute this.
Here is a problem for your right hemisphere (but from my side - you will also use the left hemisphere and all the hemispheres in the heads and butts of all your friends and we'll see if you can handle it):
XNUMXD Faun has black wigs and white wigs.
The number of black wigs exceeds the number of white ones but no two black wigs share a common side.
It has been proven that such a pawn cannot block a ball.
And here is a more Ramanujan problem (more related to number theory):
Given a set of natural numbers in the range between one and a thousand.
Given that in this group the least common multiple of any two of the numbers is greater than a thousand.
Prove that the sum of the inverses of the numbers (the inverse of a number is one divided by the same number) is less than 1.5
demand me
Ron:
I allow myself to content myself with this reference to your nonsense.
Ramanujan claims that he gets the mathematical information from the Indian goddess Namagiri.
This is the intuitive right lobe
Why are you ignoring this?
I noticed that you usually rejected any reality that didn't fit into the Shabanite framework
And what did you build it with? With the help of one aspect of reality
Your comments are a desperate attempt to repel any justified criticism
I feel a lack of reading your responses together with the thought that your opinions represent the scientific world - I expected better and more inclusive answers
Too bad
And one more addition to the addition:
It is no coincidence that the story with the demand for sexual bribes in exchange for grades happened in the field of social sciences and not in the field of natural sciences.
It is much more difficult to give a bad grade to good work in the natural sciences, while in the social sciences the definition of "good" work is much more fluid.
Search the internet for phrases like Sexual favors for grades or related phrases and you will see that this is a statistically significant phenomenon.
This is just another testimony to the power of influence of the iron framework of experiment and proof.
Completion to Ehud:
There is a point that I have already presented before, but it seems to me that you do not appreciate its importance.
I mean the concepts of "mathematical proof" and "experiment".
Even if the scientists are not different as human beings from other populations (and I do think they are on average more honest, but let's assume that for the sake of the discussion) then the proof and the experiment put their actions into a rigid framework that has nothing but bad in any other community.
That is why the scientific community - in the end - is more open to changes (only changes for the better, of course - those that allow for better prediction).
And in relation to Einstein - as long as his thoughts were not disproved in an experiment - his words were completely legitimate.
Unfortunately - he did not get to see the rebuttal, but I have no doubt that he would have changed his approach if he had encountered the rebuttal.
Perhaps he was not yet ready to accept the cubes and would have preferred (like many physicists) the interpretation of multiple worlds, but there is no doubt that he would not have adhered to the claim that was disproved in the experiment.
sympathetic:
I see you answered the questions you asked yourself.
The global village prevents disasters like the one that happened to Ramanujan!
As soon as someone is talented enough - he will receive the proper education and get the most out of himself.
I don't think that Wales or Perlman are the Hermanujans of our time, but there's no point in arguing about that.
In my opinion they (as well as Ada Yonat) are more in line with the model of "obsessive genius" described in the book about Marie Curie
http://www.text.org.il/index.php?book=0505091
I think in a supportive environment, a person like Ramanujan might have developed into a character like Ardosh but this is just pointless speculation.
Moshe:
I am willing to look at a line both as an independent entity (opaque in your language) and as an infinite collection of points - all as appropriate.
Believe me when I come to solve problems in geometry I am not interested in the infinite collection of points.
When I do this then not only lines but also planes or sheets in general can function as "atoms".
A large part of solving problems in geometry is manipulating bodies in the imagination (right hemisphere) and coherently sewing the products of imagination into a solution/proof rule (left hemisphere).
The ability to treat lines as opaque is also the basis for the effectiveness of graphic illustrations.
Michael
You're right, let's leave Einstein out of this discussion.
I ask you a simple question:
What does the line consist of?
I would appreciate it if you could answer me.
Moses
Michael
Regarding quantum theory there is some confusion:
It is true that today there is no single interpretation of quantum theory. The accepted explanation until a few years ago was interpretation
of Copenhagen and there was no legitimacy to other explanations.
Einstein refused to recognize the quantum theory as a well-known (and worn out) physical theory, saying that God does not play dice and the sin is that a physical theory should be deterministic and not probabilistic. epr experiments
They "proved" that it is not possible that quantum theory is based on deterministic hidden variables (and maintain causality).
Regarding the education of scientists, it does not harm a person's ability to change his mind, but they do not add either
Talk about his ability to admit mistakes or change his mind.
These two topics are marginal. I will return to the topic of the article and the basic question about how science works.
The question is whether today a new Ramanujan can be revealed? Can today a scientist like Bose win the support of a world-renowned scientist? You will surely claim that today there is no problem for the scientist from India (in these examples) to upload his ideas on the Internet and gain wide circulation. He does not need a patron. If so, how many Ramanujans or bozos (or bozos) have you heard of? Is there anything today to break the scientific hegemony of the USA and Europe. Have you heard today of a scientist from a marginalized country who is gaining world fame? The US and Europe set the scientific tone and do not allow scientists who are not from the leading universities to have their say. The Internet in this case did not open doors, it only closed them. Today's Ramanujans are people like Andrew Wales or Gregory Perlman who come from within the system but break away from the mad race for papers to try the big, essential questions.
Ron:
I knew this lecture and read a lot of other material on the subject.
In all the material I've read - including this lecture (you should also watch it) - thinking in pictures, the ability to draw, etc. are abilities that come from the right hemisphere.
Moshe:
I don't know what Rudolf Steiner did with projective geometry.
I read some of his writings in the field of philosophy and was horrified by his stupidity.
I assume that even if he dealt with the subject - he didn't understand it, but it's just a guess because as mentioned - from the moment I read some of his nonsense, I stopped being interested in him.
You ask for accuracy but you describe Einstein who was accepted to higher studies and graduated as one as a clerk who was not accepted to higher studies.
What he had difficulty with was getting a job as a teacher, so he worked in the patent office at the same time as he studied for his doctorate, which he received in 1905.
It seems to me that this disruption of history stems from an agenda that is irrelevant to the discussion.
It is not clear to me in any case - why did you even tell about him and how the story advances us.
When I write ""But this concept of a line is the concept that every child learns in high school in geometry classes! The decomposition of the line into infinity points comes only later and only the students who learn about infinity become aware of it." That's exactly what I mean.
You learn about lines, you learn about points, you learn that two lines intersect at a point, you don't learn that a line is an infinity of points.
sympathetic:
My description of mathematics and science is not naive but factual.
When an experiment disproves a certain theory, it indeed disproves it, and so did Einstein - when he tried to deal with the results of quantum mechanics, he did not think of dealing with them by preserving the existing theory.
It should also be understood that quantum mechanics is an inappropriate example because we are not talking about Einstein or any other specific person - this is a theory that no one understands and all of Einstein's activity around the matter was an attempt to understand it.
He didn't argue about the results but about the interpretation and this argument continues to this day - precisely because the things that bothered him still haven't found their solution.
I was talking about scientists as human beings.
To the best of my understanding and experience - a person's studies do not harm his ability to understand reality, but the opposite.
That's why I allowed myself to also talk about the stages of their early lives.
It is clear that later - when they advance with the science itself and are not required to absorb the achievements of hundreds of years in a few years - they are required to change their minds at a lower rate but the fact does not change - they do change their minds.
I have already mentioned the fact that scientists are human beings and therefore they also have egos and sometimes it is difficult for them to admit that what they have been taught all these years is not true, but the scientific community is large and dynamic enough for an idea that describes reality better than others - to overcome them in the end (and even to cause the end of Something will come quickly).
There is no truth determined by expert opinion because science never claims to have discovered the truth.
There are issues where there is agreement (sometimes temporarily) and others where there is debate.
When a certain side of the debate makes a good argument - it cannot be swept away by authority.
Michael
In my opinion the sentence "in mathematics - a proof is a proof - is not a matter of fashion here.
In physics and other sciences - an experiment is an experiment and its result is its result - there is no matter of fashion here."
points to a naive perception of science. Science is not the results of an experiment but how we interpret them.
For example, Einstein was aware of the experiments that supposedly confirmed the quantum theory but refused to accept the theory as such...
The interpretation of experimental results depends on preconceptions. In addition to this, which experiments will be performed and which will not be influenced by fashion, what with the fact that nowadays science has become very expensive and requires multiple resources. So again the example of Ada Yonat who happened to be successful despite the obstacles that were put in her way. I think this is the exception that proves the rule.
Your claim that "many scientists have changed their minds - in fact almost all of them do during their studies" shows that when we are not talking about scientists we are not talking about the same thing. Scientists for me are researchers who have completed their training period and moved on to independent research and not students in their study stages.
There is a difference when a scientist admits in a private conversation that he accepted the opinion of something and a scientist who declares in Rish Gali that he was wrong. Science, like any other human activity, is not free from human flaws and I see no reason to think that it is superior to other human activities in terms of accepting differences, changing opinions. The naive view of science sees it as a democratic field where anyone can make a claim and if it is true it will be accepted in practice science is
In many cases it is hierarchical and the "truth" is determined by the opinion of the brains.
Hi Eddie
I received the material about the interesting project you are leading - thank you very much!
I will reply to you as soon as possible with a return email.
Hi Ron:
I would be grateful if you could explain here in Hebrew exactly in a few sentences what the discovery of the mathematician Kari Spulter was - I have never heard of her before?
Hi Ehud:
Referring to your words "..humans are not easily inclined to change their minds, I would be happy if you would show me scientists who criticize sin and point out that they were wrong. Many years are required for scientific revolutions and they usually end when the previous scientific generation retires from the world or at least retires." I wanted to add that George Spencer Brown is a specific and living example of a mathematician who made a real revolution already 40 years ago in his book Laws of Structure (1969). I heard about him by chance about a month ago. He is 86 years old today and they should hear more about him before he leaves us.
Hi Michael:
I know projective geometry. You probably know that Rudolf Steiner used it a lot.
(The clerk..who was not admitted to higher studies at the university) Albert Einstein leveraged the theory of relativity by discovering the hidden assumption of the Galilean transformation of the addition of velocities. He rejected this and chose instead the Lorentz transformation to preserve the principle of constancy of the speed of light.
So please, let's be precise in this important step: (of transition from left brain to right brain..)
What do you mean when you write: "But this concept of a line is the concept that every child learns in high school in geometry classes! The decomposition of the line into infinity points comes only later and only the students who learn about infinity become aware of it."
Hi Lyran
I hope you have already received the story "The Ramanujan Code" from my father
Moses
Michael, everything you described is a left brain function - which is in its place.
I think you will love and hate the above lesson
Regarding the functioning of the right and left lobes of the brain
Neuroanatomist Jill Bolte Taylor
had an opportunity few brain scientists would wish for: One morning, she realized she was having a massive stroke. As it happened — as she felt her brain functions slip away one by one, speech, movement, understanding — she studied and remembered every moment. This is a powerful story about how our brains define us and connect us to the world and to each other.
http://www.youtube.com/watch?v=UyyjU8fzEYU
By the way, projective geometry makes real sense in the use of line and point atoms and even talks about duality problems in which the roles of lines and points are exchanged
Moshe:
But this concept of a line is the concept that every high school kid learns in geometry class!
The decomposition of the line into infinity points comes only later and only the students who learn about infinity become aware of it.
Every mathematician worthy of his name activates the right brain as much as the left brain (if only because of the geometric aspects of the problems).
By the way, the cuts in school curriculums have fatally affected the study of geometry (for example - construction problems are no longer taught).
And another by the way: when I gave private lessons to high school and undergraduate students (many years ago) I liked to teach them pure geometric solutions to the problems they studied in analytic geometry.
Most of them were my original solutions - for example, to the theorem that claims that the tangent and the normal to the ellipse cross the angles between the lines connecting the launch point to the foci.
You should try it - it's just beautiful.
In the past, I asked several times about solving puzzles in different forums and showed them how graphic images simplify many solutions beyond recognition - again - using the right hemisphere.
By the way - an even more "organic" mathematician will also incorporate physical images into his solutions.
There is a huge variety of problems where this kind of imagery helps and I have a feeling that in this kind of solutions even a part of the motor system is mobilized for effort!
Moshe,
I watched the site and enjoyed it.
Bless you!
Hi Eddie
I am waiting for your email address in the meantime
You can tap my name in the comment
and reach the site of Adam's Garden
Michael
I'm glad you saw the video on my site
About the mathematical discourse program for kindergarten that I developed
I really enjoyed reading your beautiful article about language development
I agree that language is a derivative of brain development
Now it will be easier for me to explain to you my opinion about Ramanujan
And also the subject of a paradigm shift in mathematics
The accepted concept in mathematics
Assume that a line is a sequence of points
In this sense there is apparently
One atom which is a point
Because the line is made up of it
Now try to imagine
One new world that has two atoms
One is a point and the other is a line
If you understand this you really have a key
To create new mathematics!
Normal math is based on left brain activity
This is essentially serial thinking of points
Ramanujan thought in a different and parallel way
which is more suitable for the right brain
I'm glad you're great at solving problems
You might want to join the effort to improve the article
of George Spencer Brown
Regarding a solution of the Riemann hypothesis!
Moses
sympathetic:
It is so clear!
In mathematics - a proof is a proof - there is no matter of fashion here.
In physics and other sciences - an experiment is an experiment and its result is its result - there is no matter of fashion here.
Many scientists have changed their minds - in fact almost all of them do so during their studies (I don't think a child who hasn't studied would think of quantum superposition or time varying as a function of speed) but even after that it doesn't stop happening.
A famous example is the story of Hawking accepting Einstein's opinion, but in fact it just happens all the time.
In the article I wrote about the development of language I described a discussion I had with Dawkins that caused him to change his mind and accept my opinion.
For scoop reasons - many science news stories begin with the phrase "contrary to what scientists have thought so far..."
This is usually nonsense but many times it is also true.
Moshe,
Thanks.
Until now I have not been able to access the site, probably due to some technical fault.
Contact me via my email address.
Avi Blizovsky
There is a bug on this page, the margins are cut off after message 28
The discussion is very interesting
But unfortunately we don't see it
The whole message!
Michael
It is not clear to me what you are basing your claims on, because science is less vulnerable to human weakness
From other disciplines is it in the context of receiving correct ideas that stand in opposition to what the majority thinks?
I argued that it is not possible to prove theories only to validate them to show that the difference between theories or models
different is not necessarily done according to their truth, but according to fashions and the perception of the majority. Scientists like the rest
Humans are not easily inclined to change their minds, I would appreciate it if you could show me scientists who attack sin
and point out that they were wrong. Many years are required for scientific revolutions and they usually end when the generation
The former scientist retires from the world or at least retires.
Moshe:
The truth is that the video is the first thing I watched on the site and that's what excited me.
This is very similar to what I often do with children when I find myself in their company (within group trips or as a family) and I think it is very important to develop intuition and above all to preserve the love for the subject.
Personally - I have an excellent mathematical intuition and I would not exaggerate if I say that I am one of the most successful puzzle solvers I know, so my knowledge of the matter comes not only from looking at others but also from my own inner experience.
That's why I know exactly what you're talking about and everything I said in the previous comments takes this information into account.
Hi Eddie,
Thanks. I would love to cooperate. I asked my father Belzovsky to send me your email address
You are welcome to visit Gan Adam's website in the meantime http://www.omat.org.il
Michael, please watch the video of the work with the kindergarten children on permutations, divisions and the discovery of irrationality
Then I can explain to you more what is meant by paradigm shift in mathematics. In any case, the uniqueness of Ramanujan is not in the approximately 4000 formulas he discovered, but in the special way in which he arrived at these discoveries. Actually he couldn't explain it either.
Although the list of lecturers for ICM2010 is already closed, there is still a chance to invite George Spencer Brown.
Moses
sympathetic:
Did I talk somewhere about proven theories?
Why did you find it appropriate to quote something I say in almost every discussion?
Although a genius thinks in an unacceptable way (or speed), not everyone who thinks in an unacceptable way is a genius.
Most of those who think in an unconventional way are idiots.
I mentioned that the scientific society suffers from difficulties arising from being a human society, but that because of the scientific method and because of the level of the people who make it up, it suffers from these difficulties much less than others.
You can grumble about the fact that we are human, but it doesn't seem productive to me.
The scientific society recognizes geniuses much better than any other society.
There are examples of geniuses who were ahead of their time, but there are almost no examples of genius discoveries that were rejected in their time.
There were cases (like Mendel's) of discoveries that did not receive the resonance they deserved.
The chance of this today is smaller, but even in Mendel's time - no one in the scientific community contested his discoveries.
The scientific enterprise is not quantum mechanics.
It takes time for things to happen (it even takes time from the moment the genius conceives his idea to the moment he writes it).
Sometimes (very rarely!) this time lasts even beyond the life of the genius (although I can't recall at the moment any example of this kind) but in the end the method works.
In my opinion, there is no data that justifies the attempts to describe the scientific community as dogmatic and all defamations of this kind are nothing but defamations.
There are no proven theories except in mathematics there are correct theories for their time
The matter is simple
A genius is a person who thinks outside the conventional way and sometimes suffers from communication problems.
It is difficult for any company, including a scientific company, to deal with someone who is not
Speak in her language, especially if it is a case that goes beyond the statistics.
There are countless examples of geniuses who were ahead of their time, some of them were discovered by me
People there in their time and some not.
sympathetic:
I knew in advance that a comment of this kind would come, but it is also clear that I cannot provide data on what we do not know.
The interesting thing is that to illustrate the counter claim it is impossible to bring confirmations even from the known information 🙂
Anyway - that's not the point.
Ada Yonat's correct theory was not rejected here.
All the heights and difficulties (few - it must be said, considering the duration of the research) that piled up in her path resulted from a different bet than hers on the unknown.
It is natural that at some point the environment will give up on the research while the one who has devoted his entire career to it will still stick to it.
I do not underestimate the power and importance of sticking to the goal, but as mentioned - the whole story (as well as the other stories) has nothing to do with someone's dogmatism.
By the way - you'll find out! It may even be that if Ada Yonet's research had been canceled, the saved funds would have led to an even more important discovery! I do not claim that this is the case, but if we are talking about hypotheses that can be raised without substantiation, then this is also an interesting hypothesis.
Michael Rothschild,
Thanks.
The amazing thing is that they didn't think of it before. Already today it is about 20% of the student population in Israel, and according to the annual growth rate of the sector's student population since 1992 (6.9% - 10.4%) there is going to be a national security problem here in 10 years, literally!
How fortunate that the top of the Ministry of Education understands the mess that has been made here for more than 30 years, and what a privilege it is to receive cooperation from excellent people and organizations such as 'All Education' (and you know who I'm talking about), Van Leer and the joint.
And only that the damned politics will not destroy (and indeed the deputy minister from the sector - supports)...
Michael
In the context of the academy's willingness to accept the different and allow it to create, I assume that you are clear that your objection (20)
"It is not even an exception that proves the rule because this situation of inventions by a person smart enough and famous enough in the system to be able to understand the innovation and give impetus to its publication almost always exists" she is problematic. After all
It is clear that we only hear about the successful cases and all the geniuses who were not accepted were thrown into the female abyss. Therefore, the borderline cases in which a world-renowned scientist finds leisure to refer to the claims of those who do not speak the formal language are
Lonely and in my opinion are only the floating tip of the iceberg.
The problem with an innovative genius is that he thinks in different language and concepts, which is often difficult for academia to accept
In addition to the fact that there is a lot of noise in the system, i.e. countless crazy people who think in a different way that does not lead to talk.
That is why it is rare that geniuses like Ramanujan, Bose, Galois, Einstein often find themselves in need of a patron. In the past there might have been time for the people there to read what was sent to them today with the flood of information the situation is different.
You mentioned Ada Yonat, she was indeed considered crazy, and if you listened between the lines to the interviews with her, she was at the stage
certain that her appointment was cut and she did not receive a salary from the Weizmann Institute. The successful geniuses are the stubborn ones who go against the basic resistance of the academic system to change and fight to the end until their rightness is proven.
I have quite a few more examples of similar cases but Ramanujan is definitely a representative case.
you mentioned
Eddie:
I am guessing which sector you are talking about.
Bless you!
Moshe Klein,
I just read Michael Rothschild's last comment and realized that you work to encourage children in the field of mathematics.
One of my ventures in recent months is related to the field of education of a certain sector, and it also has an aspect of locating gifted and gifted students among students in that sector, in the fields of mathematics and exact science. (Fortunately, the project is already supported by the Ministry of Education and significant organizations).
I would be happy if you contact me at my email (I assume you can get it from the system).
Avi Blizovsky:
Problem reading the comments in the current article.
The margins are clipped from 28 onwards
Moshe Klein,
I very much sympathize with your admiration and love for Ramanujan. I, too, am thrilled by this almost unique phenomenon in the history of mathematical mystical intimacy (it seems to me that only Pythagoras preceded him in the intimate, mystical connection with mathematical entities). Another person who claimed to receive mathematical divine messages is also not known.
In addition, hypotheses are also of great importance in mathematics, not only proven theorems.
The grief over the unbearable and downright disgraceful ease of not utilizing - and in fact losing - the man's unimaginable mathematical abilities, is truly enormous. It is very possible that if Ramanujan had lived longer, and had enough time to develop technically and also to produce proven theorems, mathematics would have been hired very much, just as it was hired from geniuses like Gauss.
But from here to the formulation of a claim about a 'completely new paradigm of mathematics of direct evidence' - the road seems long. After all, Ramanujan's phenomenon is a one-off, and is not a paved road for the rest of humanity, not even for the most brilliant of its generation (after all - who can argue that the Deity sweetens its mathematical secrets with him and whispers them in his ear? I guess even Perlman and Spencer and their ilk are far from that).
What to do, mathematics is usually a strong work of intellect, which involves quite a bit of luck (with a pinch of blessed luck), and the 'direct evidence' is far from it. It does not have a 'paradigm' of direct evidence, and there could not be one, except in a completely unique case, which teaches almost nothing about it.
Moshe:
I don't know what your claims are based on in the last response.
It is not clear to me why you claim that the 2500-year-old body of knowledge is definitive and in what sense it is definitive.
It is not clear to me what the claim is based on that Ramanujan represents the beginning of a new paradigm and as far as I know - there is no continuation after this beginning.
I certainly think that the qualities expressed in Ramanujan are important and I know that you work to encourage them in children.
I also, in a less institutionalized way, do this, but these qualities are not enough to promote mathematical knowledge - not only of the general but even of the individual!
Ramanujan may remain immortal as an object of admiration, but whenever someone tries to solve a mathematical problem, he will be forced to use knowledge created by other mathematicians - knowledge that Ramanujan would have created if he had grown up in a sufficiently developed environment.
Michael
Well, I probably wasn't clear enough so far in the discussion
I will try to be more focused
Ramanujan represents its beginning
of a completely new paradigm of mathematics
of direct evidence without the need for formal proofs
It turns out that the body of knowledge is 2,500 years old
Ever since Euclid's Book of Elements there has been finite existence
And it is Ramanujan who will remain immortal
May his spirit be and smile at the upcoming conference in India
Regarding Ramanujan's publication in the conference - I really searched in the content of the conference and not on the opening page.
It is only natural that the Indians are proud of him when they should have been ashamed that their academic environment could not allow him to realize the potential that was inherent in him.
Moshe:
But because of the fact that the body has a finite existence, all that a mathematician leaves to the world are his words and writings.
The scientific establishment was created to advance human knowledge and not to honor talents.
Honoring talents is only a means and as we know - Ramanujan's talent is also respected and respected.
Should I see in your words any resentment towards the organizers of that hypothetical conference?
Do you have a suggestion as to how they should have acted so that Ramanujan would enter and scavengers would not enter?
By the way: I looked for Ramanujan's name on the entire conference website and did not find a single mention.
Did I miss something? On what, apart from being an Indian Ramanujan, is the assessment that he will be presented there as one of the giants of mathematics based?
=============================================
So maybe you should read the entrance page to the conference website again
Here it is in front of you:
Welcome
India has a long history of engagement with mathematics. Ancient India had made impressive progress in Algebra.
* The place value system with the use of zero for representing numbers is an Indian invention.
* Mathematicians working in Kerala (in the South West of India) had anticipated many ideas that lie at the base of Calculus, some two centuries before Newton.
* In the more recent past - in the twentieth century, Ramanujan and Harish-Chandra blazed new trails in mathematics.
The Indian mathematical community is delighted at the opportunity we have been given to host the International Congress of Mathematicians in this country. We look forward to a very exciting congress which would help us widen our mathematical horizon.
We are happy to welcome our colleagues from around the world to the Congress. We hope that you will also be able to savor some of the touristic delights our country offers.
This page was last modified on October 14, 2009
Michael
You should understand that we speak two completely different languages.
In my opinion, the only common denominator between us right now is the use of the same letters
But mainly the profit between them...
In my world, a theorem in mathematics that has a proof
It is not necessarily true!
Ramanujan was the embodiment of mathematics in a living and breathing body!!!
incidentally:
I searched Ramanujan's name all over the conference website and did not find a single mention.
Did I miss something?
On what, apart from being an Indian Ramanujan, is the assessment that he will be presented there as one of the giants of mathematics based?
By the way, Moshe:
Do you know of any theorem of Ramanujan that will be presented at the conference?
How many such sentences are there?
Moshe:
I understand and also think it is justified.
For every such Ramanujan there are a million people who think the whole world should listen to them even though they are talking nonsense.
A criterion is needed to differentiate between those who have interesting things to say and those who do not have such things.
The ability to provide proof of your mathematical claims seems to me to be an excellent criterion.
If Ramanujan had been rejected because he did not provide proofs - he might have written proofs and been accepted to the next conference, but together with him all kinds of idiots who would not provide proofs would have been rejected and would have been rejected again in all subsequent conferences.
There is no evidence here of the dogmatism of the scientific establishment. Only his seriousness is expressed here.
To the editor Avi Blizovsky
The last comments are truncated and cannot be read
Michael
I got you. There is no argument between us.
In less than 10 months it will open in the city of Hidrabad
The world convention for mathematics with the participation of thousands of mathematicians
who will arrive there from all over the world. The link to the conference website is attached:
http://www.icm2010.org.in/
There Ramanujan will be presented with the most glory and honor as one of the giants of mathematics of all time.
And here we agreed in the discussion that if he had sent his discoveries
To the chairman of the scientific program of the conference then apparently
He would not have invited him to present them at the conference.
Do you understand ?
Moses
Liran
I'm glad you corrected the mistake in your article about Ramanujan's place of work. I agree with you that the committee of the World Mathematics Conference to be held in India in 2010 would not have invited him today to present his research. I think George Spencer Brown deserves to be invited to this conference because:
1) The book "The Laws of Structure" about the introduction of imaginary logic values into mathematics.
2) His pioneering work on solving the 4 color problem without a computer
3) The revised article (to the one already on the Internet) that will be published soon on the Riemann hypothesis.
I intend to act now to promote the issue. (By the way, the entry I wrote/translated on Wikipedia was deleted by the editors)
I will gladly read the new article you wrote about De Moaver.
Moses
Moshe Klein:
I don't know the statistics but, as I mentioned at the beginning of the response you refer to, "unproven theorems are not mathematical knowledge but hypotheses".
In this sense Ramanujan did not provide much new mathematical knowledge.
I'm not saying that he didn't know how to prove his claims, but it's clear that he didn't provide evidence for them and probably wouldn't have done so at such a conference.
The fact is that even today, despite the fact that the entire mathematical establishment recognizes his genius, one hardly ever comes across a mathematical theorem attributed to him.
"..with all due respect to Ramanujan - he hardly created any new mathematical knowledge (not through his fault but precisely because he was cut off from the scientific establishment) and therefore it was even justified not to accept him to such a conference..."
Michael
Do you really believe/think that the 4000 formulas that Ramanujan discovered on his own were known before him?
Moses
How Perry Spulter was Circassed
Peace,
At first (1911) he served in a temporary position in the Finance Department of the city of Madras in India, and then through a letter of recommendation from a famous professor named Middlemast from the Royal Academy of Madras, he was accepted as a clerk in the Accounts Department of the Madras Seaport. He started this work on the first of March 1912. What is surprising is that the big boss of the finance department where Ramanujan worked was a mathematician himself and even authored articles based on Ramanujan's research on the distribution of prime numbers. In this work he received all kinds of offers to send his articles to England.
Regarding the previous question, would Ramanujan be invited to lecture at the mathematics conference today:
Look, when Galois stood in front of the examiners of the Ecole-Polytechnique and solved the equations for them in a very short time and only by using their heads (and not on a page or a blackboard) they still didn't get it probably because Galois, like Ramanujan, was a different mathematician than those who tested him , who of course also had a serious stature. The difference is, as it has already been said here and so my high school math teacher also said, that there are mathematicians whose mathematical ability is intuitive, it sounds a bit vague but after you read biographies of people like Ramanujan and Galois and Gauss and on the other hand you read biographies of Koshi and Poria and the like - It is relatively easy to divide them into two types of geniuses - those who come naturally and those who have to work really hard. When Galois stood in front of the examiners, he came to them with an approach of intuition and they, for their part, were probably the type who were closed within the equations that their teachers taught them rigorously. It's not that I think their way is wrong, on the contrary, as I mentioned, in order to be a genius like Galois, you also need a brain structure different from that of an ordinary person and not just a particularly strong willpower, because it is not rational in any sense that someone at such a young age would study mathematics By himself and in such a short time he will reach insights that are no less than a mathematical revolution, this is not achieved just by studying a number. When you put such a person in front of people who think in a more fixed way, things can sound strange and incorrect to them, and therefore will also usually lead to disdain, because the person tends to disdain what he does not understand. Ramanujan would not have been invited to such a conference just as Gregory Perlman would not have been invited to this conference before he proved the Poincaré conjecture, because although mathematicians are strange creatures - these two are hyper-strange on such a level that it is very difficult to relate them to the general population.
Regarding the second question:
Of course he deserves it. The best example is Karl Weierstrass, whose greatness as a mathematician did not come only because of his research contribution, but also and above all because he was a great teacher of mathematics, as it is customary to say - he challenged many students. Take another example - Eudomus a man from Rhodes who was not a very talented mathematician but was allowed to enter the pantheon because he wrote the first book on the history of mathematics, which was so interesting and fascinating that he made others study this field and develop it in a significant way.
By the way, two days ago I sent my new article about the French mathematician Avraham de Moaver, who also has a very interesting life story, and it will probably be published today.
Hi Lyran
Did Ramanujan work as a clerk in the finance department of the university or as a clerk in the port of Madras?
I forwarded to Abi Blizovsky in an email intended for you, the story I recently wrote "The Ramanujan Code".
Moses
Moshe Klein:
The scientific establishment deals with the creation of scientific knowledge.
Unproven theorems are not mathematical knowledge but hypotheses.
As humans (scientists or not) we tend to attribute more importance to the hypotheses of a person who has already proven himself (with hypotheses that he has also proven) than to the hypotheses of a person who has not proven himself.
The hypothetical Ramanujan you describe - the one who has yet to meet Hardy - would have fallen victim to this human trait rather than the paragon of the scientific establishment.
With all due respect to Ramanujan - he hardly created any new mathematical knowledge (not through his fault but precisely because he was cut off from the scientific establishment) and therefore it was even justified not to accept him to such a conference.
Ramanujan was recognized - not for the advancement of mathematics but for his qualities (qualities that would certainly have promoted mathematics if he had grown up in a more suitable environment) and Hardy's greatness was manifested in the recognition of these qualities.
Among the things that allowed Hardy to recognize the inherent potential in Ramanujan were also his personal talent and breadth of knowledge - which allowed him to understand that many of the hypotheses that Ramanujan made were correct.
I assume that as he heard Ramanujan, he also heard many people who made silly assumptions, whereas if he had adopted the wide open mind that Ron suggests - the one where the brain falls out of it - would have only caused harm.
Eddie:
Your words are true, but this is the reality I intended to describe.
I had to create a balance for the conspiracy theories I was responding to, and therefore I expressed myself somewhat decisively.
Every human system has faults but this is not the result of something in the structure of the system but of the fact that it is a human system.
Therefore the scientific establishment surpasses any other human system in its ability to identify useful and true information.
Certainly it surpasses the conspiratorial establishment within which Ron lives and from which the motivations for the reactions to which I responded are also drawn.
Hi Lyran
Did you update me about Galua's suicide attempt in prison? Do you have a reference to any source?
Please also read the testimony of the Indian physicist - winner of the Nobel Prize
Regarding Ramanujan and his suicide attempt:
http://www.tamil.net/people/andrew/subra.htm
It turns out according to his words that in 1917 Hardy gave false testimony to the police that Ramanujan was a member of the London Mathematical Society so that he would not be imprisoned. My impression, also after reading page 213 of the music book of the first numbers, is that Ramanujan is indeed considered the greatest mathematician by Hardy and Littlewood, but in the mathematics department at Cambridge he is seen only as a student of Hardy.
Regarding the work of George Spencer Brown - I am in telephone contact with him.
I will be happy to update later in the discussion
I asked the participants of the discussion: (Ofer, Michael, Ron, Eddie, Ehud, Liran and Anochi...)
1) If the anonymous Ramanujan (before his meeting with Hardy) had sent his unproven mathematical formulas to the organizers of the world conference in mathematics that will be held in India in 10 months! (There they will surely talk about him a lot) Would he have received from them the appropriate platform to lecture there?
2) Does a mathematician who managed to describe not the landscapes in Ramanujan's special mathematical land but the exact way how to get to this land, and create mathematics in it, deserve to be appreciated by the mathematical community and lecture at a conference that will be held soon in India?
Moses
I love how right you are
It seems that Michael unnecessarily takes this as a personal attack against him
Get an actual example:
Mathematician Carrie Spulter - have you heard of her? Probably not
Her revolutionary discovery is in the book
Gravitational Force of the Sun
Read two reviews of the book
Pari Spolter, who is not a physicist, argues based on experimental observations that the force of gravity is proportional to acceleration and not the fictitious quantity called mass. Furthermore, she argues from experimental observations that gravitation is quantized. These arguments invalidate the approximate theories of Newton's Universal Law of Gravitation and Einstein's General Relativity Theory when the scientific method based on the rules of logic is used. It is sad that science has degenerated into fads and political maneuvering to garnish government funds for research such that original thinkers such as Pari Spolter are largely ignored.
Charles Lucas – PhD Physics
Second review
Pari Spolter in 'Gravitation Force of the Sun' exposes scientifically and mathematically the farce of Newton's Law of Universal Gravitation and Einstein's theories of relativity both general and special.
Using current and accepted scientific references Spolter shreds our current beliefs about density, mass and gravity and brings us, scientifically, to what is really going on.
And what is really going on is that we have been hoodwinked by mainstream science to believe that gravity is proportional to the quantity and density of an inert mass of a celestial body.
If you are working on a degree or expecting advancement in the scientific community do not read this book.
However if you are searching for the truth no matter what the cost and you are willing to watch proven scientific data crumble before your very eyes buy a copy of Spolters' 'Gravitational Force of the Sun' and find a nice quiet place to read.
When you finish her book and understand what she is saying I can assure you, you will never be the same. But you will know the truth.
Scientific truth will spring forth in spite of the considerable and combined efforts of the military industrial complex who consider it their sole property.
Pari Spolter will be luckier than Giordano Bruno. Bruno got burned at the stake for supporting the Copernicus idea that the earth revolved around the sun.
All that will happen to Pari is that she will be shunned, denounced, excommunicated and insulted from and by the mainstream scientific community for her efforts to publish the truth.
John Lear
http://www.amazon.com/Gravitational-Force-Sun-Pari-Spolter/product-reviews/0963810758/ref=dp_top_cm_cr_acr_txt?ie=UTF8&showViewpoints=1
Ehud and Michael,
The truth is somewhere in the middle, perhaps more in Michael's direction, but the exceptions cannot be ignored either.
For example:
Every year 500,000 proofs of mathematical theorems are issued.
Among these there is a certain percentage of quite important theorems, which will not be known to the very large majority of the members of the scientific community for all kinds of reasons that have nothing to do with the objective value of those theorems: the fact that the mathematician is not placed in a suitable framework for appropriate publication and promotion, the vogue of subjects, just a lack of openness or Flight of the determining factors in the institutional 'procedure', personal factors, etc.
It is possible that the situation in areas with too much useful economic value is different. But it must be assumed that discoveries or innovations in the fields of science, which are not of a truly revolutionary magnitude of the order of magnitude of Einstein's theory of relativity or even Bose's theory of distribution (- but of a considered lesser magnitude, but still of significant importance -) will fall here and there in the trap of unconsciousness Regardless of their objective value. I suppose that if Bose had not been a little more militant - perhaps his theory of distribution would have appeared at a later stage, and perhaps attributed to someone else - more connected to the establishment.
And who knows how many cases of 'contempt' there have been and will be, who did not fight or will fight for their innovations, from all kinds of excuses, or who will not succeed in their struggle for recognition.
Sometimes it seems that the forces and motivations that work in the academies are really irrelevant. For example: the theory of the 'Eight Way' was attributed to Gell Man, for which he also received a Nobel Prize. This is why Yuval Na'aman published a similar Torah a few months before Gal Man, and the Swedes were indeed aware of this fact! It turns out that the difference between the two scientists was the institutional relationship: Gal Man Gova in a scientific establishment with tremendous lobbyism, and Yuval Na'am - not. Only the French dared to speak about the injustice openly, and the Americans tried in retrospect to compensate Naaman by honoring him with the Einstein Prize (I think Naaman was the first non-American to win the prize).
sympathetic:
Your words really do not belong to the matter and some of them are also not true.
Fermat's theorem occupied all mathematicians to the last of them until the moment it was solved.
No one saw it as an illegitimate occupation.
Wales was at it for a long time with a tenacity worthy of its name but no one underestimated him for anything he said.
At most they expressed surprise that he had not said anything for a long time.
Einstein was indeed not a member of the Academy, but it was not because of the theories he proposed, so it has nothing to do with dogmatism or mental fixation.
I don't know the real reasons for his initial rejection, but surely many factors played there, such as the tribal factor of standards.
The fact is that from the moment he opened his mouth and published successful theories - both he and he were received with applause, even though they completely crushed assumptions that were prevalent at the time of publication.
Bose was indeed a Torturer, but he too managed to publish his words in the end.
This is not even an exception that proves the rule because this situation of inventions by a person smart enough and famous enough in the system to be able to understand the innovation and give impetus to its publication almost always exists.
I don't know the history of research on superconductivity but it must have been funded and equipped by various universities and not conducted in some home kitchen. Here too - once there were clear results - they were accepted without any rejection.
There is also a difference between the encouragement that the academy may or may not give to the actual conduct of the research and its attitude towards its findings.
After all, Ada Yonat also received many raised eyebrows when she declared her intentions and the reason was that they did not think she would succeed.
Despite this, she received funding for many years - but this is also irrelevant because the topic discussed is not the encouragement given to investigate a certain topic, but the reference to the results that have been achieved.
Medicine is rightly very careful and we know that sometimes it is not careful enough (see thalidomide entry).
In any medical research, experiments are necessary to put the hypothesis to a strict test, and this is what happened with the ulcer as well.
Michael
Historically things are not that simple. Academia has a tendency towards fixation and fads and sometimes it is necessary to break away from it to reach achievements. A few examples that pop into my head right now:
Mathematicians:
Andrew Wales secretly worked to prove Fermat's Last Theorem he simply worked in his home for several years
(Seven if I'm not mistaken). One of the reasons for this was the lack of legitimacy in the academy to deal with this problem.
Gregory Perlman proved the Poincaré conjecture while locking himself in his house.
Galois who was not accepted into the French Academy and his ideas were rejected or simply ignored by the great mathematicians of his time.
physics:
Einstein was not a member of the academy when he came up with many of his discoveries, he was a clerk in the patent office.
Bose (similarly to Ramanujan) was an Indian who came up with the Bose-Einstein distribution and no one would listen to him and publish his paper until the paper reached Einstein.
The research on superconductivity at high temperatures was done in secret because there were fiscal proofs that this phenomenon could not be realized.
A much more established scientific field is medicine
The doctors were not ready to accept the fact that the boil was caused by a bacterium until the doctor heard this discovery and was forced to infect himself with the boil and cure the disease with antibiotics
And more and more
Ofer Ashkenazi:
The public has a completely unjustified tendency to see academics as a bunch of exemplary people who are unable to think properly.
What causes this perception is not the exemplary nature of the academy but the feelings of inferiority of the public.
Your words demonstrate this tendency in a number of places - starting with the strange claim that Ramanujan's mathematical ability was borrowed from his distance from professional circles (a conclusion that at least he himself disagreed with and voted against it with his feet when he could) and ending with the expression "Go use this figure...against a tough and exemplary academy ” - a phrase that ignores the simple fact that mathematicians never judge mathematics by its origin but only by its quality and the only support required for a mathematician's words is his mathematics.
This is also the place to point out that statistics by definition recognize exceptions and even predict their frequency and it is not at all clear what your contrary claim is based on.
We don't have many Ramanujans today.
There may be many with talents like his, but Ramanujan was not only talented - the fact that he was discovered by the academic world also stems from the efforts he put in and to be "another Ramanujan" you have to put in such efforts.
The demand for tolerance towards things that do not correspond to "academic culture" is also nothing but a part of the same postmodernist spirit of disdain for academia. The only academic culture that exists in the natural sciences and mathematics is the culture of honesty and logic.
Of course, there are those who deviate from it from time to time, but this is the exception and not the rule.
When someone proves a new theorem in mathematics there is no "cultural" force that can stop him.
This is also the case with the formulation of a new scientific theory (which is also the reason why many completely different interpretations of quantum theory manage to be generated in the scientific community in one fell swoop when all of them - until the last of them - seemed to all those involved in the subject - strange, to say the least).
I will read it soon, it really seems like a good book.
Regarding Spencer Brown, I googled him a bit and found the Appendix 9 you mentioned as a PDF file. Write there that this is a proof and not a hypothesis for the Riemann theory from March 8 last year. Regarding the 4-color problem, I still haven't found any information about his way of solving it, but if he did prove the first theorem, it's something of global magnitude, for example, the summit of humanity that I talked about in the article. So what is actually happening with it right now? He submitted his solution to the researchers to verify it?
Liran,
You should thoroughly read page 213 about Ramanujan in the music book of the first numbers.
In any case, in 1939, a Ludwig Wittgenstein seminar on the foundations of mathematics was held at Cambridge University in England (exactly where Ramanujan worked in 1914-1918). This was following Godel's incompleteness theorem (1931). Wittgenstein tried to essentially lead to the creation of a new mathematics. About 20 years later, George Spencer Brown arrived at the same university. Inspired by Wittgenstein and Russell, he wrote his book "Laws of Form" which was published in 1969. A fifth edition of the book will be published soon. The book turns the liar's paradox into a positive value in mathematics by defining an imaginary logical value (in analogy to i, the root of -1). According to my understanding, this book will lead to a revolution in mathematics on the scale of Einstein's theory of relativity. George Spencer Brown is 86 years old today. At the age of 83!! He came up with an idea that may also lead to the solution of the Riemann hypothesis (using Dango's equivalence theorem regarding the Mbius function). It will appear in the ninth appendix of the new edition of his book. Also, one of the appendices in the book will present Spencer Brown's approach (from 1976!) to solving the 4-color problem without using a computer. By the way, I only heard about him by chance in the last month and I have been doing mathematics for decades.
Moses
It's interesting that your first image is about the mathematician
The one I want to talk about here is precisely that of a murderer
Hello friends,
Ramanujan's wonderful intuitive talent rests mainly on the fact that he learned mathematics by himself and with himself and not in any formal setting. In this way, I think his intuitive ability was preserved. What's more, when he was asked about the source of his knowledge by Hardy (who had a hard time dealing with the fact that Ramanujan didn't bother to prove the formulas he was coming up with at a dizzying pace), he simply replied that in his dreams an Indian goddess appears to him whispering the formulas in his ears... and now go use this data to support In your words, in front of a tough and exemplary academy 🙂
This is also the place to point out that when one chooses to examine reality through the lens of statistics (normal distribution and standard deviation), one tends to forget a simple fact related to the science of statistics, which is that statistics are not able to refer to a single case but only to an accumulation of events. When you look at the world through the channel of statistics there is no room for medical miracles or extraordinary one-time geniuses. In other words, the mere use of statistics eliminates any possibility of the existence of Ramanujan or the development of a new contemporary manifestation... and the main challenge of the modern era is to learn how to use the wonders of science and scientific theories (including statistics) without it hiding and elevating from us the unlimited range of possibilities present in this world at any given moment.
In this context I will mention an article published in the New York Times in 1903 which explained that it is possible to build a machine that will be able to fly in the air. But, for this purpose, the author of the article stated that he would require a meeting of all the top technicians and mathematicians in the world (then physics was in an inferior position compared to mathematics... before Albert Einstein shone and revealed to all of us the theory of relativity), and in any case, the author of the article concludes that the time it would take to build a machine of this kind would be between million and 10 million years. The special thing is that on the same day of the publication of her article, a guy named Wright wrote in his diary 'today the second shipment of the new machine arrived'... and a few months later, the first motorized plane in the world took off!!!
Ramanujan died many years ago ... today there are quite a few geniuses who are waiting to be discovered ... and for this reason the academy as it is, and the statistics along with it should show more patience and patience even in cases where the theories presented do not correspond to the recognized and accepted academic culture today.
Success for all of us
Ofer
Hi Moshe,
I didn't say there couldn't be the next Ramanujan, I only claimed that the chances of that happening were extremely low.
One of the main goals of the articles I write, as I have already mentioned before, is to make people wake up from the nonsense they are familiar with in many areas of life, among others in mathematics. I am an ardent supporter of the proposition that willpower cannot guarantee you certain success but it is certainly much better than depression and lethargy that will lead you to certain failure. If following these articles people realize that anyone can pick up a book and study for themselves out of genuine interest, just like the mathematicians I talked about did, they will discover many surprises, some of which will be about themselves and their ability to succeed. Again, as I wrote in the article, don't ask yourself to achieve goals of the magnitude of Ramanujan because he is one of a kind, your goal should be study only (in the case of mathematics) and if it is combined with a superhuman goal that you will achieve - then what is good.
Secondly, who is today's Ramanujan living in England? Can you give a name or a link?
And it is important that you remember - there may be some other geniuses like Ramanujan, but don't forget that in order to be remembered you have to leave a mark in the field in which you are successful. Ramanujan not only had a strong intuition for mathematics, but he associated himself with the right and deserving people and put his abilities to work so that others could also enjoy the fruits.
Reminds me of an article that Amnon Levy did in his show about an Israeli mathematical genius who lived in prison for life and developed a device that could predict heart attacks or something like that. So it's true, they say he's really a genius, but what does that help him and what does it help us? His device doesn't work at all, and he murdered a human being in cold blood. So what do you say about that? True, he is very smart, so what? What does he do with this wisdom? How did it manifest itself as Ramanujan manifested it?
Do you really think that the man you mentioned in point 4 is the type who will go down in the history of mathematics?
Hi Ofer - I invite you to join the discussion about the interesting article written by Liran about Ramanujan.
Do you have any idea how he managed to discover his formulas?
Moses
Hi Michael
Thanks ! You are welcome to contact me through the details on Gan Adam's website.
Hey Liran
1. If I am not mistaken Ramanujan died in 1920.
2. Page 214 of the music book of the first numbers:
".. After a partial recovery, Ramanujan, who was still depressed, tried to commit suicide by jumping in front of the London subway. He failed thanks to the intervention of a guard who brought the train to a halt right in front of Ramanujan's helpless body. In 1917 suicide was still considered an offense against the law in England. But through the intervention of Hardy, the charge was dropped on the condition that Ramanujan stay in a hospital in Derbyshire under full medical supervision for twelve months.
3. Do you mean that Ramanujan cannot appear next?
Would you like to prevent him from reading your article?
4. By the way, the next Ramanujan lives in England today!
Moses
Hi Moshe.
1. He arrived there in 1914, after 3 years he finished his degree, i.e. in 1917, after two years he joined the order, i.e. in 1919, and then in the same year he died.
2. Look, almost every mathematician of Ramanujan's stature has several biographical versions, each adding something new or different. I have two sources from which I draw the information and that is of course only after I have read both to the end. I don't include all the biographical details because I still need to summarize a bit, the articles should be as accurate as possible and I really hope they are like that. I intentionally omit details such as formulas (and in the next article I deviated from this for a moment) so as not to confuse the average reader with real mathematics. I mentioned that I might have heard and suggested that it was some sort of tumor found in Ramanujan's head, I skimmed that through a reference from another place and didn't give it too much thought.
By the way, you said he actually jumped on the train, I really didn't hear that anywhere. Regarding the music of the numbers, I have the book right here next to me in the closet, but I haven't had time to read it all, so if there is more information, I would love to hear it.
3. Regarding the second message, you made a claim but did not explain the reason for this claim, I am talking about message number 8 that you did not like the line. Look, as I wrote I'm trying to bring these great people to the average people so that they understand that with willpower you can achieve a lot and that's the only thing that should motivate you in life.
Regarding the other thing, let's ask like this, how many people do you know in the world who have reached the mathematical level of Galois and at such a young age? Or Ramanujan's? I follow such things and I have not seen a phenomenon of this magnitude. The reason for this is that people of their kind are unique, there is a normal distribution of intelligence level in humanity and they are far from the accepted standard deviations. you ask why For one reason, because their brains are built in a different way, or rather the parts of the brain that are responsible for their mathematical ability are tens of times more developed than mine and yours and this is an innate thing that cannot be achieved even through intensive study, like it or not it is nature and we play with the cards we have by hand
This is why I also said that I do not say this out of disdain, but out of a clear understanding that the chances are zero of finding anyone among the readers who can reach this level as they reached it, and therefore I recommend not trying to imitate Galua's way of working or eating or sleeping, but to try and adopt the psychology that stood Behind what he did, that is to say to yourself that for you mathematics (or anything else) is the easiest and you are going to be the best at it, and you can be sure that this is what he always thought, not out of arrogance but out of an understanding that only with the help of a good thought and willpower can you achieve anything . He specifically achieved much more than anyone else, but that doesn't stop others from doing the same.
Best regards,
Liran Zeidman
Moshe Klein:
I went to your site and it turned on.
Well done!
one more thing
I didn't like this sentence of yours:
"I will admit the truth because I do not think that the readers of this article are going to walk from Nablus to Nablus together with these giants even if they put all their energy for many years, God forbid not out of disdain but from the understanding that these are individuals of virtue and as their name is - individuals. However, and this is a big main point , these people are supposed to be a kind of role model for us in the love and strong willpower that were an inseparable part apart from the fact that their minds are made up in a different way than that of ordinary people."
Hey Liran
Thank you for your consideration of my response
1. Ramanujan did receive a bachelor's degree in science in Cambridge in 1916
But referring to your words, it is considered a doctoral degree
Only after his death in 1920.
2. If you have already heard about Ramanujan's suicide attempt in 1917
In jumping over train tracks, then in my opinion it would be worth maybe you study a little more
before you write the article about it. This is an important point
For a true interpretation of his human and mathematical character.
There is little material on this in the music book of the prime numbers
And of course the Indian clerk's book.
I hope that the world conference on mathematics that will open in August 2010
Will shed more light on this issue that remains in my opinion without a solution.
What was the real motive for this attempt?
I'd be happy to send it to you by email, if you'd like
A short story I wrote called "The Ramanujan Code"
The draftsman to clarify this issue.
Best regards
Moses
By the way, a Hebrew translation of a book called "The Indian Clerk" by: David Levitt was recently published. The book tells about Hardy Littlewood and Ramanujan, but in my opinion it is not a particularly good book, not for math enthusiasts. The book focuses on the historical period and on Hardy's personality. He emphasizes his being a homosexual (by the way, I am not sure that this fact has a historical basis).
Hi Moshe, thank you very much.
1. Not a bachelor's degree but a science graduate. The degree system abroad is different from the one in Israel, the level he reached is what is called a doctor abroad, and this is definitely a very high level considering the fact that he never received a formal academic education before. Note that two years after that, that is, after 5 years of study, he was accepted into the royal order; In the same way you (more or less) can think of a bachelor's degree student in mathematics in Israel who after 5 years of studies received the Israel Prize.
2. I think I heard something about it. Do you mean the time he was sick and they thought he had a tumor?
In the same context, Ehud wrote in the previous comment about this discovery. Indeed, I wanted to write it down and I reminded myself of it before I started writing, but after 3 straight hours (that's the average time it takes me to write an article) it just slipped out of my head, what's more, the sources I took the material from didn't mention it for some reason.
By the way, this is also the problem of defining a human being as a genius, both Hardy and Ramanujan were mathematical geniuses by supreme grace, but one had unprecedented mathematical intuition and the other did mathematical works on the scale of a true genius.
And another thing, Will Hunting is definitely an excellent movie.
Liran
Nice article! The next world conference will be in 2010 in India, Ramanujan's country.
Two comments:
You wrote: "Only 3 years after he started working in England, he received a bachelor's degree.."
In my opinion, this is a somewhat strange statement about a genius of Ramanujan's stature
You also did not mention in the article (did you know about it?) Ramanujan's suicide attempt in 1917
Moses
An amusing anecdote about Ramanujan is related in the number 1729 which is now called the Hardy-Ramanujan number.
According to the story, Hardy came to the hospital to visit Ramanujan and to amuse him he told him that he traveled in a taxi with the number 1729 and that he had never come across such a random number. Ramanujan immediately responded with astonishment, "This is an amazing number. It is the smallest nail given to its author as the sum of two numbers, each to the third power:
1*1*1*+12*12*12= 1729 וגם 10*10*9+10*9*9=1729
This context shows the essential difference between these two great mathematicians: Hardy is known as a formalist who takes care to formulate his theorems well, while Ramanujan had an intimate acquaintance with numbers as if he knew each and every number and knew its properties. Ramanujan was an intuitive mathematician who claimed that some of his discoveries were given to him directly by the goddess Nagiri (if I'm not mistaken in the name of the goddess with her forgiveness)
Another anecdote
The main character in the film The Good Will Hunting is partially based on the character of Ramanujan
A genius genius, but still starving himself on a strict diet for his religion. His God rewarded him for that.
Excellent article