Do you think Math was discovered, invented, or both?

[tomilay]

@tomilay

In support of your point, mathematics is a formal language, and does differ from informal languages in certain respects.  However, if informal languages were not capable of adequately capturing the semantics of a formal language then we would not be able to use formal languages as there would be no way to communicate their meaning using the informal languages we share, whether they be English or Chinese.  So it seems necessary that an informal language such as English be capable of performing the same communicative function as the formal language of mathematics, or else one has a paradox that must be explained.

Once again we see theist arguments being used in a completely ad hoc manner, not because they have derived a conclusion from sound reasons, but because they have a conclusion and are only in hindsight looking for sound reasons to support it, often coming up with absurd and irrational notions in the process.  Not that I'm characterizing it that way, but that seems to be the whole substance of reformed epistemology: ordinary epistemology won't confirm your conclusion, so you invent a new epistemology ad hoc to serve that purpose.  It's wholly disgusting and a massive embarrassment for so-called "rational Christians."

Yep. It has more rigor.  

The semantics of the mathematical formulations are in fact always expressed in informal languages.

[SteveII]

As has been said elsewhere, mathematics is just a specialized language.  

It can be used to formulate what is observed as you point out.  When used in that fashion, it comes after, as opposed to preceding, the ideas in question.

It can also be used to facilitate new insights.  It's use in this fashion is predicated on formulations previously shown to have basis in the real world.

But it can also perfectly logically express things that have nothing to do with reality.  This is all consistent with a language.  It's similar to grammatically correct but untrue, even meaningless, ideas in everyday language.


E=mc^2 can also be described in plain English, as can the relationships that you mention.  Even the shortcomings of mathematical theories, such as when observations do not match predictions, can be expressed in English.


The same can be done in Telugu.


I don't understand unassigned meanings, but language in general can describe everything math can.

This part of your reply illustrates where the problem is. No, non-math language cannot describe these relationships between physical things. 

It seems we are in agreement that math is indeed a language.  It facilitates the expression of the relationships.  It's by no means the only language that can do it.  Think of it as a short-hand.

For example, what is the relationship between the radius of a circle and its circumference? Answer in non-math terms.

2 multiplied by the ratio of a circle's circumference to its diameter multiplied by its radius.  It can be even more verbose depending on the amount of vocabulary in a language.  Mathematics makes it easier to distill the relationships.

What is the relationship between mass and energy? Express that in non-math terms. Express any of these in their standard equations in non-math terms.

You can use a similar approach to the previous question.

Science and mathematics have filled huge gaps in our knowledge, but have also opened up new ones.  No, we do not have the code on how the universe works.  

It is not necessary to know how the universe works. EVERY physicist and cosmologist thinks the relationship between pairs of physical thing is mathematical though. Give me an example where the physical universe's relationships are not expressed mathematically or thought not to be able to be expressed mathematically.

All the relationships that are expressed mathematically in relation to the universe can also be expressed in plain English.  But we are not claiming the universe is intrinsically English, are we?

Wolfram's characterization isn't wrong.  Because, while math facilitates how we can convey information about relationships in the real world, it can also convey logical ideas that have no representation in the real world.

I'm not sure you understand the argument. 

I understand him to be saying that we use logic to make sense of reality.  I am saying reality may be logic, but logic is not necessarily reality.

I would say that reality is logical. I would never say logic is reality.

No one is saying that we do not express these relationship is a language of our creation. What I am saying is that there ARE relationships everywhere and that these relationships are something MORE than a simple description of physical quality x and physical quality y. 

What more are they?

The relationship is not invented, it is discovered.

I agree with that 100%.

Then you are not understanding my point. I am not talking about the words/symbols/sounds. I am talking about the relationships in the physical world that we can express with our chosen set of word/symbols/sounds. The concept of 10 shiny objects on the right and 8 more on the left give you a total of 18 is discovered--not invented. The relationship and physical constants I mentioned above are discovered, not invented. This is my only point in a thread that asks that exact question.

[adey67]

Maths can be super confusing though...



     

As someone with dyscalculia who required extra lessons to pass the math test for nurse training this gif is freaking me out how is this possible?? I'm guessing it's something to do with angles idk.

[tomilay]

No one is saying that we do not express these relationship is a language of our creation. What I am saying is that there ARE relationships everywhere and that these relationships are something MORE than a simple description of physical quality x and physical quality y. 

What more are they?

The relationship is not invented, it is discovered.

I agree with that 100%.

Then you are not understanding my point. I am not talking about the words/symbols/sounds. I am talking about the relationships in the physical world that we can express with our chosen set of word/symbols/sounds. The concept of 10 shiny objects on the right and 8 more on the left give you a total of 18 is discovered--not invented. The relationship and physical constants I mentioned above are discovered, not invented. This is my only point in a thread that asks that exact question.

I understand it and agree with it.  

But you have also made the wrong assertion that these relationships cannot be expressed in non-math language.

[SYZ]

As someone with dyscalculia who required extra lessons to pass the math test for nurse training this gif is freaking me out how is this possible?? I'm guessing it's something to do with angles idk.

It's a Photoshop "trick"...



Note that the two bottom-most triangular fragments don't match in size—which
they should of course in order to shift one into the other's position on the block.

Try it in real life, and it won't (can't) work.   

[adey67]

As someone with dyscalculia who required extra lessons to pass the math test for nurse training this gif is freaking me out how is this possible?? I'm guessing it's something to do with angles idk.

It's a Photoshop "trick"...



Note that the two bottom-most triangular fragments don't match in size—which
they should of course in order to shift one into the other's position on the block.

Try it in real life, and it won't (can't) work.   

Thank goodness it's an illusion because I couldn't work out how it could be done and was kicking myself for being a math retard and unable to work it out or understand it.

[tomilay]

As someone with dyscalculia who required extra lessons to pass the math test for nurse training this gif is freaking me out how is this possible?? I'm guessing it's something to do with angles idk.

It's a Photoshop "trick"...



Note that the two bottom-most triangular fragments don't match in size—which
they should of course in order to shift one into the other's position on the block.

Try it in real life, and it won't (can't) work.   

I noticed the padding of the bottom blocks at the point that the moving chunk hits the right edge.  I assumed that had to be the explanation.

[SteveII]

I'll have to think about this before giving a more substantive answer, but it seems that these relationships exist because things in the universe have some degree of order and regularity.  First of all, there are only two possibilities here, either there is no order in the universe, or there is some order in the universe. [1] That the human mind can pick out things resulting from order in the universe doesn't overwhelm me, nor does trying to suggest that something which may be dependent on the mere existence of order, such as mathematics here seems to be, strike me as anything more than something of a bait and switch.  I'll elaborate more on that if you like.  The bigger problem is that according to Ramsey theory, there will exist "pockets" of order in any random or chaotic set, so even if the universe were completely random and chaotic, we would still expect there to be pockets of order within it, and therefore relationships, and if relationships are all that is required for mathematical truth to exist, then it will necessarily exist whether or not the universe is or is not completely random and chaotic. [2] So, rather than picking out anything meaningful, it seems that, if relationships == math, as you seem to be suggesting, it's simply an inevitable consequence of the fact that things exist.  If all that what you're suggesting is reducible to the proposition that things exist and that proposition is objectively true, then I have some serious reservations about your claiming that you have shown that mathematics is discovered and not invented [3]. I also have to add additional reservations given that in order to form a consistent set of mathematical truths, some rather arbitrary decisions need to be made and so the given set of mathematical truths we choose to embrace is highly suspect as a supposedly found object.  And further, Godel's theorems leave us questioning whether a consistent set of mathematical truths without any arbitrary or subjective inclusions in it can even exist.[4]

1. I think there is a third: that the entire universe is ordered. Even if you introduce QM indeterminacy, the net effect on the macro world is an order well beyond the accuracy threshold to discover and test such order.
2. We do not see "pockets" of order. The entire universe seems to be ordered--from the very large to the very small. From physical relationships to spacial and temporal relationships. From stealing 3 shiny objects from someone who has 10 and leaving her 7.  
3. Order of this magnitude cannot be considered random and it is quite warranted to infer that the order is baked into reality. We do not invent this order, we discover this order. The order would be there for the next mind to evolve to understand.
4. Do you have to prove mathematics to discover that the universe is orderly and can be expressed in mathematical relationships? That does not seem to be a necessary condition to discover the relationship.

Steve, I'll get back to you on this, as I don't want to spend time on detailed explanation, and will defer full explanation and reply to your points until then.  In the interim, I'll simply point out that, if we grant, ex hypothesi, that the universe is completely and perfectly ordered, any change would result in a partially and not completely ordered universe.  So if the universe is perfectly ordered at time T, then it will not be so at time T+1. It is therefore impossible for change and complete order to exist over time.  The law of entropy tells you quite plainly that this is the case, and so your arguments here involve some confusion and conflation of terms, a serious misunderstanding of what I was saying regarding the nature of order in the universe (as well as a lack of imagination regarding such), as well as a rather ridiculous and prima facie false claim about order in the universe.  Stop pulling my leg Steve.  Give me a real argument.

I don't remember saying "perfectly" ordered. Even taking into account entropy or things like the randomness in radioactive decay, that does not mean there is not an order, it just means there is an average of the state of molecules for that particular feature and you represent that in an equation as an average. While we might no know which molecule will heat first, we can calculate how long it will take for the glass of ice water to get to room temperature.

There are no surprises at T+n in a purely physical system. As proof, you can reliably rewind the tape from any point with a great deal of accuracy to any earlier states (even if a thermodynamic system, you have an average). That level of accuracy is sufficient to support my position that mathematics are discovered, not invented.

[SteveII]

What more are they?


I agree with that 100%.

Then you are not understanding my point. I am not talking about the words/symbols/sounds. I am talking about the relationships in the physical world that we can express with our chosen set of word/symbols/sounds. The concept of 10 shiny objects on the right and 8 more on the left give you a total of 18 is discovered--not invented. The relationship and physical constants I mentioned above are discovered, not invented. This is my only point in a thread that asks that exact question.

I understand it and agree with it.  

But you have also made the wrong assertion that these relationships cannot be expressed in non-math language.

You defined my term 'non-math language' as 'something that was not language'. That seems to not even be possible. Are we to chirp and beep when communicating math concepts? For example, you said above "2 multiplied by the ratio of a circle's circumference to its diameter multiplied by its radius." Almost every word you used represents a mathematical concept. Now, we have shorthand for that C=2pi®, but simply saying those characters does not convey the meaning that your English sentence did. So, did you really use non-math language in your sentence? I think obviously not.

[tomilay]

Then you are not understanding my point. I am not talking about the words/symbols/sounds. I am talking about the relationships in the physical world that we can express with our chosen set of word/symbols/sounds. The concept of 10 shiny objects on the right and 8 more on the left give you a total of 18 is discovered--not invented. The relationship and physical constants I mentioned above are discovered, not invented. This is my only point in a thread that asks that exact question.

I understand it and agree with it.  

But you have also made the wrong assertion that these relationships cannot be expressed in non-math language.

You defined my term 'non-math language' as 'something that was not language'.  That seems to not even be possible. 

Can you provide a link to where I made that definition?

Are we to chirp and beep when communicating math concepts? For example, you said above "2 multiplied by the ratio of a circle's circumference to its diameter multiplied by its radius." Almost every word you used represents a mathematical concept. 

Yes, mathematics is a short-hand for concepts that can be expressed in other languages.  It stands to reason that mathematics and those languages can express the same concepts.

Now, we have shorthand for that C=2pi®, but simply saying those characters does not convey the meaning that your English sentence did. 

What's the meaning that my English sentence conveys?

So, did you really use non-math language in your sentence? I think obviously not.

I used English.

[Mark]

I understand him to be saying that we use logic to make sense of reality.  I am saying reality may be logic, but logic is not necessarily reality.

I would say that reality is logical. I would never say logic is reality. 

I think evolution would ensure that any creature's cognition is going to map onto reality to some degree, those whose reach extends to logic included.  But don't worry, Steve.  Fundamentalists will get there too someday.

Show ContentSpoiler:

Totally.  Pulling.  Your.  Leg.

Want it back now?

[Dānu]

1. I think there is a third: that the entire universe is ordered. Even if you introduce QM indeterminacy, the net effect on the macro world is an order well beyond the accuracy threshold to discover and test such order.
2. We do not see "pockets" of order. The entire universe seems to be ordered--from the very large to the very small. From physical relationships to spacial and temporal relationships. From stealing 3 shiny objects from someone who has 10 and leaving her 7.  
3. Order of this magnitude cannot be considered random and it is quite warranted to infer that the order is baked into reality. We do not invent this order, we discover this order. The order would be there for the next mind to evolve to understand.
4. Do you have to prove mathematics to discover that the universe is orderly and can be expressed in mathematical relationships? That does not seem to be a necessary condition to discover the relationship.

Steve, I'll get back to you on this, as I don't want to spend time on detailed explanation, and will defer full explanation and reply to your points until then.  In the interim, I'll simply point out that, if we grant, ex hypothesi, that the universe is completely and perfectly ordered, any change would result in a partially and not completely ordered universe.  So if the universe is perfectly ordered at time T, then it will not be so at time T+1. It is therefore impossible for change and complete order to exist over time.  The law of entropy tells you quite plainly that this is the case, and so your arguments here involve some confusion and conflation of terms, a serious misunderstanding of what I was saying regarding the nature of order in the universe (as well as a lack of imagination regarding such), as well as a rather ridiculous and prima facie false claim about order in the universe.  Stop pulling my leg Steve.  Give me a real argument.

I don't remember saying "perfectly" ordered. Even taking into account entropy or things like the randomness in radioactive decay, that does not mean there is not an order, it just means there is an average of the state of molecules for that particular feature and you represent that in an equation as an average. While we might no know which molecule will heat first, we can calculate how long it will take for the glass of ice water to get to room temperature.

There are no surprises at T+n in a purely physical system. As proof, you can reliably rewind the tape from any point with a great deal of accuracy to any earlier states (even if a thermodynamic system, you have an average).  That level of accuracy is sufficient to support my position that mathematics are discovered, not invented.

What you said was ambiguous. I interpreted it charitably in the only way that it could make your argument work. If the universe is not perfectly ordered, then the universe is a mix of order and disorder and Ramsey theory applies. That being the case, your argument devolves to saying that math depends only on things existing, and because things objectively exist, math objectively exists. Like I said, I think that's a bait and switch. But if that's the argument you want to go with, let me know. Then language is also objective. Hell, I think you've just obliterated the object and subject distinction. That doesn't look like a good sign for what you're trying to say. (It seems that you're likely headed for a Waterloo with your assertions on free will down this path.)

Oh, and I'll follow up on your latter comment later. For now I'll just point out that you seem to be violating your earlier assertion that certain quantum processes are indeterminate. Though it's not at all clear what you're actually trying to say. Please rephrase in a way that actually says what you mean to say. And I don't see how or why you think that, which seems to be a clumsy way of saying 'determinism' supports your contention that math is discovered.

[Bucky Ball]

I would say that reality is logical. I would never say logic is reality. 

Science has clearly demonstrated that is false. 
Relativity : illogical; no one believed it until it was proven experimentally
Uncertainty : illogical; how is the double slit experiment results with ONE electron going through two apertures, "logical"
Dirac's tensors : illogical, (or non-intuitive). 

The problem is Stevie doesn't know shit about Reality. In fact 95 % of this universe is unknown.
We simply do not have enough information to make any statement on Reality at this point.

[Cheerful Charlie]

I was watching a documentary on mathematics and in it the filmmakers discuss the idea that there has been some debate over whether or not math was invented (by us), discovered (by us), or a combination of both. 

I added the “by us” in parentheses because apparently there are some theists such as William Lane Craig who are of the belief that since math is so useful (almost mysteriously useful) in describing the universe therefore god.  

Anyway, poll question and thoughts.  

It is simple.   Both.  There are basic principles that are discovered.  But that may not be enough to achieve anything useful in and of their selves.  Algorithms that allow us to use these basic principles to solve problems are invented.  But without understanding the underlying facts that have been discovered, it is hard to do that except for very simple problems.  Pi is an example.  On can empirically measure Pi, the ancient Egyptians did, but it took the Greeks,  Eratosthenes and his "sieve" to fully understand Pi and why it is as it is.  That was a discovery. Calculus was a set of procedures to solve problems.

[EvieTheAvocado]

Both. In two different senses.

Mathematical truths were discovered but the process by which we discover such truths is an invention.

To do mathematics requires humans and human minds. But the truths themselves don't require humans. 2+2=4 is true in all possible realities with and without life.

[EvieTheAvocado]

I was watching a documentary on mathematics and in it the filmmakers discuss the idea that there has been some debate over whether or not math was invented (by us), discovered (by us), or a combination of both. 

Is it a Closer to Truth episode? Or another documentary about the same thing?

[Jenny]

I was watching a documentary on mathematics and in it the filmmakers discuss the idea that there has been some debate over whether or not math was invented (by us), discovered (by us), or a combination of both. 

Is it a Closer to Truth episode? Or another documentary about the same thing?

It was an episode on NOVA.  I don't know if it was part of that series as I found it online.

[EvieTheAvocado]

I was watching a documentary on mathematics and in it the filmmakers discuss the idea that there has been some debate over whether or not math was invented (by us), discovered (by us), or a combination of both. 

Is it a Closer to Truth episode? Or another documentary about the same thing?

It was an episode on NOVA.  I don't know if it was part of that series as I found it online.

This is the one I'm talking about:



I love Closer to Truth. There's also one about Consciousness and one about Free Will and many others.

My favorite philosopher is also interviewed on the show in a couple of episodes

[EvieTheAvocado]

Both for me as well. Seems like they discovered the principles, and then created a way to describe them.

Exactly.

[EvieTheAvocado]

It was definitely not invented. The relationship between the sides of a triangle are there regardless if someone is there to perceive it or not.

Math is not the relationship of a triangle. Math is the tool to describe the relationship of a triangle.

Mathematical truths are discovered and the mathematical process by which the discovering can be done is invented.

The key thing being: the mathematical truths would still be there to discover even if we never invented such a process of discovery which we call 'mathematics'.

[Deesse23]

It was definitely not invented. The relationship between the sides of a triangle are there regardless if someone is there to perceive it or not.

Math is not the relationship of a triangle. Math is the tool to describe the relationship of a triangle.

Mathematical truths are discovered and the mathematical process by which the discovering can be done is invented.

The key thing being: the mathematical truths would still be there to discover even if we never invented such a process of discovery which we call 'mathematics'.

In reference to the threat title i interpret "math" as "mathematics" (the tool) and not "mathematical truth". Maybe the OP should clarify.

[Jenny]

Is it a Closer to Truth episode? Or another documentary about the same thing?

It was an episode on NOVA.  I don't know if it was part of that series as I found it online.

This is the one I'm talking about:



I love Closer to Truth. There's also one about Consciousness and one about Free Will and many others.

My  favorite philosopher is also interviewed on the show in a couple of episodes

That wasn’t the one but I’ll definitely check it out-looks interesting! Thanks for posting!

[epronovost]

I would dare say neither. Mathematics was neither discovered or invented. It's just a feature of reality we experiment on the daily just like time or gravity or decay. We didn't discovered it or created it, we understand it progressively better and discuss it. We also invented a whole language to do so.

[Jenny]

Math is not the relationship of a triangle. Math is the tool to describe the relationship of a triangle.

Mathematical truths are discovered and the mathematical process by which the discovering can be done is invented.

The key thing being: the mathematical truths would still be there to discover even if we never invented such a process of discovery which we call 'mathematics'.

In reference to the threat title i interpret "math" as "mathematics" (the tool) and not "mathematical truth". Maybe the OP should clarify.

Mathematics.

[Deesse23]

Mathematical truths are discovered and the mathematical process by which the discovering can be done is invented.

The key thing being: the mathematical truths would still be there to discover even if we never invented such a process of discovery which we call 'mathematics'.

In reference to the threat title i interpret "math" as "mathematics" (the tool) and not "mathematical truth". Maybe the OP should clarify.

Mathematics.

Then i maintain my claim, we invented mathematics, we didnt discover it.