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Maths do not have a why.

by hhlbf 5y ago

horsawlarway 5y ago
I find this answer to be true, but misguided. In particular, this type of answer was the exact thing that turned me off of math for YEARS. Maths DO have a why - We needed way to describe and model the world around us, and math was a requirement to do that. Now - once the model and rules are put in place - Fine, you can bugger off and be as self-referential and contained as you'd like - "There is no why!"... But lets be clear - there ABSOLUTELY is a why, and the second the world around you no longer matches the model of your maths, we start debating whether or not to throw the thing in the trash and make new rules (see set theory as the classic example...)
ecshafer 5y ago
Yes they do. At minimum Mathematics have a why in that it is something that is arrived at logically, and provable. But when you learn mathematics, whether it be algebra or geometry and trigonometry or calculus or discrete, there is another why added, that of real life solutions. Why do we care about geometry? Well it ends up being useful in optics and physics. We like Trigonometry because it can help you build a building or bridge or shoot a cannon and take down said building or bridge. Calculus has innumerable uses in engineering and physics and finance and biology and everywhere.
vangelis 5y ago
If maths don't have a why, then programming languages don't have a why. They're both abstractions.
- iammisc 5y ago
  Programming languages do not have a why. The turing machine is an arbitrary model of computation, as is the lambda calculus, as is horn clauses. The 'why' is deciding which one is most convenient to solve a particular problem. Given that very good computer scientists come up with very different means of solving the same problem, it's clear there's no universal agreement upon which paradigm is better and that there's a lot of subjective reasoning as to why particular models are better.
iammisc 5y ago
You are being downvoted but you're correct. Consider the natural numbers. There is no 'why' behind them. There are axioms behind them, and -- given those axioms -- there are statements about the natural numbers that can be logically reduced to the axioms, but the axioms have no why. Moreover, it is provable the axioms have no why, because they cannot have a why, because the axioms cannot be proven except in relation to themselves. If you're so convinced the axioms have a why, please prove me and Godel wrong. The 'why' behind natural numbers is a social one, and one of convenience. The natural numbers make it easy to solve and communicate about certain problems, but they are not the only way to solve those problem nor are they the only way to communicate about these problems. For example, another way to deal with basic arithmetic, is to talk about numbers as sets. Now you can define certain operations on them, and completely ignore the axioms of the natural numbers. This model is way better than others for certain problems. However, you now have a new set of axioms.. and oh yeah, actually the most obvious ones are completely self-contradictory, so you'll need to choose Zermelo-Frankel or something else. Or if you want to be even more general, you can simply talk about the lambda calculus, but good luck trying to 'prove' the lamba calculus theorems in itself, because you'll quickly hit the halting problem. Of course you can then say... well let's get rid of that and use the typed lambda calculus, but then oh yeah you can't do anything interesting. Why are these choices made? Can the choices be justified in the systems themselves? No of course not. The idea that you can use 'logic' to derive these systems is also ridiculous because formal logic is itself a system with axiom (and a very controversial system at that). But if you look at the lambda calculus, ZF set theory, and the natural numbers as simply models and systems that are sometimes useful, then it makes sense as to 'why'. But the 'why' exists independent of them and is not provable in them and is social and cultural in nature. It is certainly not mathematical as in order to 'do mathematics' (symbolic manipulations) you first need axioms. Mathematics education in this country has been replaced by rote dogmatism which is why many Americans cannot handle this ambiguity. What must be explained is that mathematics is a language and in order to communicate with other educated humans about these abstract concepts it behooves everyone to speak the same language. It is the same reason the word for 'dog' in English is taught as being spelled D-O-G. There is no why behind it. It's just the result of thousands of years of culture. Except mathematics is a more global language and more useful for different kinds of manipulations.
inglor_cz 5y ago
A lot of math has a practical motivation and some people learn better if they are acquainted with it. I would consider it hostile to your students if you were a maths teacher and withheld practical applications from your students on purpose.

Maths do not have a why.

by hhlbf 5y ago

Maths do not have a why.

I find this answer to be true, but misguided. In particular, this type of answer was the exact thing that turned me off of math for YEARS. Maths DO have a why - We needed way to describe and model the world around us, and math was a requirement to do that. Now - once the model and rules are put in place - Fine, you can bugger off and be as self-referential and contained as you'd like - "There is no why!"... But lets be clear - there ABSOLUTELY is a why, and the second the world around you no longer matches the model of your maths, we start debating whether or not to throw the thing in the trash and make new rules (see set theory as the classic example...)

ecshafer 5y ago

Yes they do. At minimum Mathematics have a why in that it is something that is arrived at logically, and provable. But when you learn mathematics, whether it be algebra or geometry and trigonometry or calculus or discrete, there is another why added, that of real life solutions. Why do we care about geometry? Well it ends up being useful in optics and physics. We like Trigonometry because it can help you build a building or bridge or shoot a cannon and take down said building or bridge. Calculus has innumerable uses in engineering and physics and finance and biology and everywhere.

vangelis 5y ago

If maths don't have a why, then programming languages don't have a why. They're both abstractions.

iammisc 5y ago
Programming languages do not have a why. The turing machine is an arbitrary model of computation, as is the lambda calculus, as is horn clauses. The 'why' is deciding which one is most convenient to solve a particular problem. Given that very good computer scientists come up with very different means of solving the same problem, it's clear there's no universal agreement upon which paradigm is better and that there's a lot of subjective reasoning as to why particular models are better.

iammisc 5y ago

You are being downvoted but you're correct. Consider the natural numbers. There is no 'why' behind them. There are axioms behind them, and -- given those axioms -- there are statements about the natural numbers that can be logically reduced to the axioms, but the axioms have no why. Moreover, it is provable the axioms have no why, because they cannot have a why, because the axioms cannot be proven except in relation to themselves. If you're so convinced the axioms have a why, please prove me and Godel wrong. The 'why' behind natural numbers is a social one, and one of convenience. The natural numbers make it easy to solve and communicate about certain problems, but they are not the only way to solve those problem nor are they the only way to communicate about these problems. For example, another way to deal with basic arithmetic, is to talk about numbers as sets. Now you can define certain operations on them, and completely ignore the axioms of the natural numbers. This model is way better than others for certain problems. However, you now have a new set of axioms.. and oh yeah, actually the most obvious ones are completely self-contradictory, so you'll need to choose Zermelo-Frankel or something else. Or if you want to be even more general, you can simply talk about the lambda calculus, but good luck trying to 'prove' the lamba calculus theorems in itself, because you'll quickly hit the halting problem. Of course you can then say... well let's get rid of that and use the typed lambda calculus, but then oh yeah you can't do anything interesting. Why are these choices made? Can the choices be justified in the systems themselves? No of course not. The idea that you can use 'logic' to derive these systems is also ridiculous because formal logic is itself a system with axiom (and a very controversial system at that). But if you look at the lambda calculus, ZF set theory, and the natural numbers as simply models and systems that are sometimes useful, then it makes sense as to 'why'. But the 'why' exists independent of them and is not provable in them and is social and cultural in nature. It is certainly not mathematical as in order to 'do mathematics' (symbolic manipulations) you first need axioms. Mathematics education in this country has been replaced by rote dogmatism which is why many Americans cannot handle this ambiguity. What must be explained is that mathematics is a language and in order to communicate with other educated humans about these abstract concepts it behooves everyone to speak the same language. It is the same reason the word for 'dog' in English is taught as being spelled D-O-G. There is no why behind it. It's just the result of thousands of years of culture. Except mathematics is a more global language and more useful for different kinds of manipulations.

inglor_cz 5y ago

A lot of math has a practical motivation and some people learn better if they are acquainted with it. I would consider it hostile to your students if you were a maths teacher and withheld practical applications from your students on purpose.