YOUR MONDAY MATH with Mathematician KP Hart - What Does the Infinite Look Like?

Here’s Mathematician KP Hart’s Math Question and Answer for Monday, February 1st!

Why can’t I imagine what the infinite looks like?

When I think of the infinite then I do not get any images. Can people do this, and why can’t our brains deal with this?

In some sense, this question is a case of `question begging’: the question assumes that an earlier question, “What is the infinite?” already has an answer. Quite often the counter question, what one means by `the infinite’, is answered by a circular definition like that in the very first edition of the (well-known) Dutch dictionary Van Dale (1864):

finite: adj and adv. having an end.
infinite: adj and adv. without end;

or in a more recent version

finite: having an end; that which is bounded; antonym: eternal, infinite
infinite (wrt. extent or multiplicity) having no end; antonym: finite
the infinite: the unbounded space (of the universe); also without reference to space

What these definitions have in common is that they replace the terms finite and infinite by synonyms that explain basically nothing.

In that same dictionary, Van Dale, I found this sentence: mathematics is sometimes defined as the science that tries to get a command of the infinite by finite means. And, indeed, in mathematics we have an unambiguous definition of `infinite’, see this earlier post. That definition describes something that we certainly would call `infinite’ and that we can work with very well. After a while the term `infinite’ makes you think at once of that definition and that an image will form in your mind of what an infinite set is and does.

The mathematical answer to the question will be a question and exhortation: “Did you already think about what you mean by `the infinite’?” and “Define what you mean and really think that through”.

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Read all of KP Harts math questions here!

About Dutch Mathematician KP Hart: In the beginning of this year the Dutch government opened a website, The Dutch Science Agenda, where everyone could post questions that they thought were of scientific interest. This was an attempt to involve the whole country in determining what the Dutch science agenda should be in the coming years.

I looked through the questions and searched for terms like `mathematics’, `infinity’ … to see what mathematical questions there were and I noticed various questions that already have answers (and have had for a long time). On a whim I decided to post answers to those questions, in Dutch. For your edification I will translate these posts into English.