Like this blog?- New webpage at www.vadimkulikov.org March 24, 2017
- (Ir)rational Behavior of Calculation October 18, 2011
- The Product of Topological Spaces Does Not Obey Cancellation October 12, 2011
- Wild Embeddings October 11, 2011
- Progress October 4, 2011
- Class-metric August 24, 2011
- Intellectual Lazyness August 22, 2011
- Time Limit: One Minute! August 17, 2011
- Douglas Hofstadter: I Am a Strange Loop. August 15, 2011
- 0.999999……=1? (continuation) July 10, 2011
- Walks on Planets July 5, 2011
- 0.999999….. = 1? July 3, 2011
- Prisoners’ problem 6 June 29, 2011
- I am back! June 28, 2011
- A non-associative “group” March 21, 2011
- Why I haven’t blogged March 21, 2011
- Doodling with Fractals and Persistent Worms. January 2, 2011
- Five groups November 23, 2010
- Splitting A Rectangle November 17, 2010
- Sphere November 10, 2010
Category Archives: Philosophy
Intellectual Lazyness
My friend gives private mathematics lessons to young pupils, mostly high school students who need some help in their curriculum math. Here is a story about a student of him. My friend asks him: how much is 5+6? The guy … Continue reading
Posted in Education, Philosophy, Popular
4 Comments
Douglas Hofstadter: I Am a Strange Loop.
Two weeks ago I finished reading Douglas Hofstadter‘s 2007-book I Am a Strange Loop. I haven’t read other Hofstadter’s books and I want to write this review before I read any. My next Hofstadter-book is going to be Gödel Escher … Continue reading
Posted in Book & Article Reviews, Logic, Philosophy, Popular
2 Comments
0.999999….. = 1?
The question in the title is constantly discussed on web forums and at our department’s corridors; sometimes even by professional mathematicians and is in fact already quite seen and banal. In our department this question is often raised by the … Continue reading
Posted in Calculus, Education, Mathematics, Philosophy, Popular
5 Comments
Can Mathematics Solve Philosophical Problems?
This post is not an attempt to answer the question of the subject, but merely to discuss related topics. The idea dates back to the time when I first learned what is the likelihood function in probability theory. When one … Continue reading
Posted in Philosophy
2 Comments
Prisoners’ Problem 5
There is a famous class of problems concerning public announcements. There is a philosophical (sociological) appeal in these problems. Can a public announcement change the behaviour of the citizens? Of course, if it is for example a news article about … Continue reading
Posted in Combinatorics, Mathematics, Philosophy, Recreation
Tagged Prisoners' problems
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The Most Important Relation In Mathematics 1
Part 1: Basics In this and few following posts I will argue that not only in mathematics, but in all human reasoning, the role of equivalence relations is crucial. The notion of an equivalence relation is the key to any … Continue reading
Posted in Education, Foundations, Mathematics, Philosophy
3 Comments
Pinocchio Is Omnipotent
Please visit my new website at www.vadimkulikov.org to find more about mathematics, science, cognitive science and art!
Posted in Logic, Mathematics, Philosophy, Recreation
15 Comments
Continuum Hypothesis III
Suppose you pick randomly a real number. What is the probability that it equals to 1? The probability is zero. Suppose [tex]X\subset [0,1][/tex] is a countable subset of the unit interval. What is the probability that a randomly picked real … Continue reading
Posted in Foundations, Mathematics, Philosophy, Probability, Set Theory
Tagged Continuum Hypothesis Trilogy
2 Comments
Continuum Hypothesis I
This is the first part of the forthcoming trilogy in four parts. The trilogy will be devoted to the understanding of the Continuum Hypothesis by looking at some statements that are equivalent to it. In this post I just expose … Continue reading
Posted in Foundations, Mathematics, Philosophy, Set Theory
Tagged Continuum Hypothesis Trilogy
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The Monkey and the Balls
I heard this story here at Mittag-Leffler institute from someone who heard it from someone else, who probably also heard it from someone else. (And so on.) What is the probability that I heard it from someone else? Just kidding. … Continue reading
Posted in Mathematics, Philosophy, Probability
2 Comments
A liar’s paradox
I will hereby argue that I am the Pope. Consider the following sentence: If this sentence is true, then I am the Pope. It is an implication, i.e. a sentence of the form [tex](A\to B)[/tex], where A is “this sentence … Continue reading
Posted in Philosophy, Recreation
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