Pythagoras' Theorem. Evidence of elsewhere or our ingenuity.

[Audley Strange]

Does this define something real or have we just used clever symbology to create a context in which it is always true?

If the former does, that not imply a level of reality that influences us directly yet is not attainable or alterable, the platonic realm of forms. If it's the latter then we have no reason to assume a constant, that we've just made it all up. Is the first not a religious thought, the assumption of extra-spatial phenomenon that shapes and guides the nature of a pre-determined universe? Is that assumption real, is mathematics a map of an invisible landscape or is it just a convenient fiction to explain things?

Does the question even make sense?

Send your answers to "Loose Women"

[pErvinalia]

I don't know what you are talkng about, Willis. Mathematics only defines anything so much as it fits within the axioms upon which it is based. I.e. it certainly describes something. Whether that is real or not is open to debate, but likely not answerable.

[Rum]

Well for starters there are no straight lines in nature. But you touch on a fascinating area - do 'maffs' exist in some objective reality or are we simply using symbols to represent complex systems which happen to work for us at an approximate level.

[Robert_S]

Define "exist".

Edit:

Let's define "real" too while we're at it.

[Audley Strange]

Yeah, there are no straight lines in nature. I'm sure there are some but the point is taken. Rationalism and science is all about such though eh? The mean, the average, the revelation of function. So I have no problem in considering that mathematics is the map of low level function. However part of me, the empiricist and cynic who laughed his way through one failed chemistry or physics experiment after another wonders if this whole endeavour is not simply leaving out real data to fit into platonic forms and if it is doing that who knows what we are missing. If it's not though, then it's little more than wizardy.

Which in itself is pretty groovy if you think about it.

[MiM]

Well for starters there are no straight lines in nature. But you touch on a fascinating area - do 'maffs' exist in some objective reality or are we simply using symbols to represent complex systems which happen to work for us at an approximate level.

A ray of light is a darned good approximation, though.

Is maths discovered or invented. Is that the question here? I for one have real difficulties to imagine, how at least basic things like countability of discrete entities could be any different (e.g. 1+1=2, 2+1=3...)

[Audley Strange]

Define "exist".

Edit:

Let's define "real" too while we're at it.

Okay, though I don't feel it necessary, such things tend to derail the conversation into a more complex one which given enough time is inevitable given the subject. Anway, just because you asked...

Real. That which exists.

Exist. To be Real.

[MiM]

Yeah, there are no straight lines in nature. I'm sure there are some but the point is taken. Rationalism and science is all about such though eh? The mean, the average, the revelation of function. So I have no problem in considering that mathematics is the map of low level function. However part of me, the empiricist and cynic who laughed his way through one failed chemistry or physics experiment after another wonders if this whole endeavour is not simply leaving out real data to fit into platonic forms and if it is doing that who knows what we are missing. If it's not though, then it's little more than wizardy.

Which in itself is pretty groovy if you think about it.

Chemists theorem: Any function can be fitted through two data points
Chemists corollary: Don't ever make more than two measurements

[Audley Strange]

Well for starters there are no straight lines in nature. But you touch on a fascinating area - do 'maffs' exist in some objective reality or are we simply using symbols to represent complex systems which happen to work for us at an approximate level.

A ray of light is a darned good approximation, though.

Is maths discovered or invented. Is that the question here? I for one have real difficulties to imagine, how at least basic things like countability of discrete entities could be any different (e.g. 1+1=2, 2+1=3...)

If maths has been discovered, what is it we have discovered exactly, is it a map? If so what of? Your point about numbers is an excellent addition. If they are entities where do they reside, in our neural pathways, externally, both at the same time? We see a single tree and know it is one tree, but what does that actually mean if anything?

[pErvinalia]

It's a pattern. There are no definitive (i.e. discrete) boundaries. Therefore numbers area an approximation. Also, numbers are only a very VERY small part of mathematics. Nothing much past that would appear to have an empirical basis as far as I can think (although, it's been a long time since i did any maffs).

[Audley Strange]

It's a pattern. There are no definitive (i.e. discrete) boundaries. Therefore numbers area an approximation. Also, numbers are only a very VERY small part of mathematics. Nothing much past that would appear to have an empirical basis as far as I can think (although, it's been a long time since i did any maffs).

So is it apophenia or revelation? Are we seeing a pattern that exists or are we creating it?

[MiM]

Could a mathematic system where addition isn't commutative (e.g. 2+3 is not equal to 3+2) accurately describe the reality? If you have two apples and add three more, the result would be different from adding two apples to your original three?

Now somebody will find a quantum experiment that doesn't abide to commutativity of addition.

[cronus]

Mathematical forms are a set of recipes that say do so and so and you'll have something useful. Proofs are a poison test. They only work whilst you are alive. There is no elsewhere. Only a end.

[MiM]

If you can assume that every intelligent enough species would have mathematics that are basically similar, I'd say that maths are discovered. If the assumption is that they would significantly differ, then it is constructed or invented.

Obviously things like the number base would be different, but that is notation.

[pErvinalia]

It's a pattern. There are no definitive (i.e. discrete) boundaries. Therefore numbers area an approximation. Also, numbers are only a very VERY small part of mathematics. Nothing much past that would appear to have an empirical basis as far as I can think (although, it's been a long time since i did any maffs).

So is it apophenia or revelation? Are we seeing a pattern that exists or are we creating it?

I dunno. Don't ask hard questions! Where's JimC?


We make patterns to explain what we see. The pattern is our creation based on what we see. I don't know where to go with that, though. Perhaps if we consider scale. Would bacteria recognise a human being as a discrete entity? I don't think they would (if they could). Would an alien the size of the sun recognise trees as discrete entities? Probably not.