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An Animated Introduction to Ontology: Is a Copy the Same as the Original?

Questions of equality and equivalence are of fundamental importance in mathematics and computer science. In everyday use we are usually comfortable with a vague definition of equality, but in programming for example, two objects may be identical in one instance and different in another. This is usually a great source of confusion for inexperienced programmers. In mathematics, equality has multiple meanings and uses and even basic subjects like high school geometry introduce the notions of similarity and congruence that represent two different levels of equality.

Of course, equality and equivalence are also part of the branch of philosophy called ontology. In the following classic animation, John Weldon presents the topic as a fun thought experiment that asks the question: what does it mean to be? Watch it and be amazed by the philosophical nuances of existence.

Is Mathematics Real? A Thought-Provoking Discussion for Any Math Class

Mathematics is so frequently put into the same category as the sciences that students often assume that it is one of the many scientific disciplines, just like physics, chemistry and biology. This can become a problem when students try to understand the reason for studying mathematics. Most students can immediately see that biology is the study of living organisms and the immediacy of that subject makes it both instantly appealing and comprehensible. In mathematics, however, as soon as the studied objects become sufficiently abstract and far removed from everyday experience, students fail to see their significance. As layers of abstraction are added, visualizing mathematics becomes even harder than picturing microscopic cells.

When confusion arises about the nature of mathematics, it can be helpful to introduce a few ideas from the philosophy of mathematics. That is exactly, what the following PBS Idea Channel video does. The question of whether mathematics is a science that studies objects that exist in this universe or is a mental construct that is aesthetically elegant and just happens to be the best language we know for describing nature, remains unanswered, but the discussion is important. Without it, students may never suspect that mathematics plays a unique role in human history and that it spans almost all disciplines. For those who want a deeper take on the nature of mathematics, Eugene Wigner’s classic paper on The Unreasonable Effectiveness of Mathematics in the Natural Sciences will provide much more food for thought.