# You know more math than you think: non-decimal numbers

Yes, you do. If you are a frequent reader of this blog, then you probably already know about binary numbers, hexadecimal numbers, and sundry non-decimal numbers. You know, the kind we nerds know about. The ones that make us confuse thanksgiving and christmas because `oct(31) == dec(25)`

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But how about normal people (or as I like to call them: people)? Well, they may look at you confusedly if you tell them that they use way more exotic things every day.

Let's start with the time. When you say "it's 10:30? well, that's a base-60 number.

If we add days, it gets harder, because days are base-24. So "2 days, 10 hours and 30 minutes" is just a difficult way to say `2*24*60 + 10*60 +30`

minutes. It's a numerical system with *two different bases*.

Sure, it doesn't do the cutesy thing hex does of having extra symbols, like A meaning 10, but it's exactly that, except 20 is written "20" or "8PM".

And how about January 11th, at 5:20 PM? Well, that is also another way to express a number of minutes, in an even *more* complicated mixed-base system!

January = 0 months = 0 days = 0 hours = 0 minutes 11th = 11 days = 251 hours = 15060 minutes 5PM = 17 hours = 1020 minutes 20 = 20 minutes Total: 16100 minutes

That way to express a date uses a mix of base 60, base 24, and base 365 (if we can, please, ignore leap years) or maybe base 60, base 24, base ~30 and base 12

I don't know if numerical systems with non-fixed bases have a *name* in mathematics, yet you use them, random non-math-person!

And you can even do arithmetic on them! Yes, you! You know what exact time it will be at "Jan 9th 2:10 + 12:15". You can even do multi-base arithmetic *in your head*.

And I have not mentioned seconds (base 60 again), years (multiple base 10 digits) and second fractions.

Yet, when hex and binary are explained to people in school, it's incredibly hard to make them "get it". And once they get *that* if you try to explain, say base-3 numbers, it's confusing again.

y la gente se sorprende cuando uno tiene un reloj binario, como si una mancha más al tigre lo haría tanto más manchado... jeje

je

y la "hora de internet" tenia segundos o era la "hora atomica oficial" alguien se acuerda?

http://en.wikipedia.org/wik...

Once you get through the concept of bases and powers (you can explain them using coins and stacks, rocks, or even fingers) explaining how a specific base works follows naturally. I think other concepts are even more complicated, like modulo arithmetic, but they become more obvious to people if you use the right analogies and strip them from all the noise.

I have succesfully explained octal numbers to 5-year olds using floor tiles.

Bueno, tampoco se usa de manera correcta la base 24. Cuántas veces escuchaste que nos juntamos "a las 12:30 de la noche" (24:30 es menos común escuchar).

Eso es porque son unos quesos para aplicar módulo :-)

"Well-optimized modern definitions have unexpected advantages. They give access to material that is not (as far as we know) reflected in the physical world. A really “good” definition often has logical consequences that are unanticipated or counterintuitive. A great deal of modern mathematics is built on these unexpected bonuses, but they would have been rejected in the old, more scientific approach. Finally, modern definitions are more accessible to new users. Intuitions can be developed by working directly with definitions, and this is faster and more reliable than trying to contrive a link to physical experience...rank and-file mathematicians can use the new methods confidently and effectively, while success with older methods was mostly limited to the elite"

-- A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today http://www.ams.org/notices/...

Sí. La idea de entender definiciones y sistemas axiomáticos como separados de la realidad y sólo sujetos a su lógica interna esunamuy buena idea.

No te ayuda a calcular cuando tenés que poner para el asado, pero es una buena idea.