To Infinity and Beyond


Summer’s here and we ordered ice cream over the Net. When it arrived, my 6 year-old was thrilled to find not just the one box we’d ordered but two boxes. How come, she wondered. And then she saw the caption on the box saying, “Buy one, get one free”. Aha, she now knew why Christmas had come early.

Then she got greedy. So if we’d ordered two boxes, we’d have gotten four boxes, right? And if we ordered three, we’d get six?... Her enthusiasm in applying the multiplication table of 2 was in such stark contrast with her unhappiness in having to recite the same table while studying.

Continuing in that vein, she then announced, “If you’d ordered uncountable ice creams, we’d have gotten twice the number of uncountable ice creams”. And that’s how she got her first glimpse of infinity!

Ok, kiddo, looks like you’ve mastered the tables, so it’s time to move onto the Cantor infinities, the mind-blowing concept that there are multiple infinities and some infinities are larger than others… Just kidding. Or am I?

Comments

  1. Ramiah KumarMarch 14, 2018 at 12:16 PM

    Well, well, this fascinates me to no end (pun intended - see, infinity actually means "without end")!

    Now that little Aditi has managed a peep into the infinity, we look forward to Aditi becoming a mathematician one day who would rank with Cantor and Ramanujan!

    Cantor categorized even the seemingly endless infinities, through a clever idea of 'sets' i.e. some way of putting one to one correspondence. Ramanujan is sometimes referred as 'the man who knew infinity'! That should surprise no one who has seen some of the stunning equations of his (which an American maths professor describes as, "he pulled them out like magicians pulling out rabbits out of hats). In many such equations, one mind-boggling infinite series would be equated to two infinite series(es) multiplied or divided (twice more mind-boggling, no). That apart, the equations would be 'simple', in the sense they will only have a few full numbers like 3 or 7 or 253 etc. (not irritating decimal numbers like 2.763204) sprinkled into them.

    Anaadi and Anantam are Sanskrit words having the meaning "beginningless" and "endless", used as attributes of Brahman (Vedantic God) in Hindu spiritual literature. The same words also implied 'infinity', when Sanskrit was used for early Indian mathematics. May Aditi be the next master "who knew Anaadi and Anantam"!

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