The word "is", maps to the logical "equals" operator. I agree with the example, but I don't agree it is relevant. There is no implies operator.
The statement "Math is Language", where A is Math and B is Language, maps to the logical assertion: "A = B".
If we are going to really be kinda twisty and non-standard, we could interpret the english "is" to be "is an equivalence class of". Which would map to your example pretty well: language is indeed an equivalence class of math, but math is not an equivalence class of language. Though, nobody is talking about implies operator or equivalence class here.. It's a "is" relationship, logical *equals*
You point out the "is a" relationship, not the "is" relationship, they are different. [0]
Find examples with two singular nouns and just the word 'is'.
The phrase in question: 'Math is language' is an example, or something like 'food is love' is too. I concede you could interpret those last few sentences with poetic license to be read more like: "A is a form of B", or "A is a B" - though that is not what was written and this is not a place to expect that much poetic license.
*edit*: a minute later, thought of a good example. "ice is water". True that "ice is a form of water", but strictly speaking no, "ice is not water". I'll concede there could exist an implied "is a", or an implied "is a form of", but that is poetic license IMO.
[0] Google AI summarized it pretty well: google "logical "is a" vs logical "is"
> In logic, "is" typically represents an equality relation, while "is a" (or "is of the type") represents an inclusion relation. "Is" indicates that two things are the same or identical, while "is a" indicates that one thing is a member of a larger class or set of things
> You point out the "is a" relationship, not the "is" relationship, they are different.
Well, what you reacted to was, let me copy'n'paste, "Math is a language". It was you who insisted that "is" in this sentence maps to "equals" relation, so thanks for agreeing that you were wrong.
I'm reacting to: "Math is language. 'Everything' is language. Language is the image of reality."
There are other discussions which say:
- Math is a subset of language, surely
- It's easily argued that languages are subsets of math.
Given that context, the distinction seems to be very important.
I find the following idea (paraphrasing) to be very interesting: "not only is math a subset of language, but the language and math are equal sets." I also think it's not true, but am curious how a person would support this assertion. So, my challenge is, because the logical "is" relationship is reflexive and the reflexive property does not hold here - how can this be true? The most satisfying answer has been (paraphrasing) "cause I'm using non-precise language and you should just infer what I meant." Which is fine I guess..
I literally copied "Math is a language." from your quote that started this subthread. Nobody here has typed "Math is language" - except you. Just open https://news.ycombinator.com/item?id=43873113, press CTRL+F and see for yourself. I can't fathom how can you still deny being so obviously wrong.
Honestly I don't think his point even stands. We were using English to communicate and English doesn't have the strict rules of mathematics. That's literally why we created math (which I'll gladly call "a class of languages"). He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection.
The problem here all comes down to seadan83 acting in bad faith and using an intentional misinterpretation of my words in order to fit them to their conclusion. I'm not going to entertain them more because I won't play such a pointless game. The ambiguity of written and spoken language always allows for such abuse. So either they are a bad faith actor "having fun" (trolling) finding intentional misinterpretations to frustrate those who wish to act in good faith or they are dumb. Personally, I don't think they're dumb.
> We were using English to communicate and English doesn't have the strict rules of mathematics.
Agree.
> He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection.
I agree. So, why can't either interpretation be valid? Perhaps, because one is obviously not true? Yet, it seemed like there was a clarification that the obviously not true relationship was the intended one!!!
Godelski previously wrote: "Coding IS math. Not "coding uses math".
I interpreted that clarification to mean you intended "is" to be a strict "is". Particularly given the other context and discussion of "is a" in other threads. I suspect now you were perhaps emphasizing "uses a" vs "is a", rather than "uses a" vs "is". Not a satisfying conclusion here. It would be a lot more interesting if the precision could have been there and had we been able to instead talk about whether all coding languages form an abstract algebra or not. Or perhaps use that line of reasoning to explain why all coding is a form of math. That would have been far more interesting..
Thinking about this a bit more.. I think I can refute your statement that "coding is math" and not "coding uses math".
I'm sorry the conversation got so caught up on pedantics.
Previously I would have quite readily agreed that at least "coding is a subset of math" - now I'd only agree in the sense that coding is an applied math, just like Physics is applied Math.
So, it does seem to be clearly a 'uses' relationship, and I'll support the assertion. To explain, coding is the act of creating a series of boolean expression (governed by boolean algebra) to create a desired output from a given input. To really explain, code is translated to assembly, which is then translated to binary, which then directly maps to how electrical signals flow out of CPU registers into a series of logical circuits. Assuming no faulty circuits, that flow is completely governed by boolean algebra. We therefore use boolean algebra to create our programs, we define a series of boolean operations to achieve a certain goal. We are _using_ boolean algebra to arrange a series of operations that maps a given set of inputs to a desired output. In the colloquial sense, coding is applied math, it is not pure math though. We use boolean algebra to create our programs, the programs are not boolean algebra themselves, but an application of boolean algebra.
Now, tying it all back to the article and implications. The data collected stated that the language parts of the brain are more responsible for whether we are able to learn programming. That seems to imply that the math part of programming is so far abstracted, that the parts of the brain which are used for math are no longer the most salient.
I wonder how the experiments and results in the article would have gone had the topic been electrical circuits and electrical engineering, which is far closer to the underlying math than coding.
It's such an absurd thing to argue about that I just assumed that some massive brainfart happened there. It happens to everyone, not everyone doubles down on it though.
But then again, isn't a good portion of this thread non-mathematicians arguing about what math is? I really thought ndriscoll put it succinctly[0]
> It's like trying to argue about the distinction between U(1), the complex numbers with magnitude 1, and the unit circle, and getting upset when the mathematicians say "those are 3 names for the same thing".
I fear the day some of these people learn about Topology.
> But then again, isn't a good portion of this thread non-mathematicians arguing about what math is?
No, a good chunk is clarification of "WTF do you mean?"
The abstract arguing I suspect we all find to not be interesting and absurd. Let's go to substance here..
The article has stated there is evidence that the math related regions of the brain are not nearly as heavily used when coding as compared to the language regions. The "mathematicians" seem to be arguing that this can't be true because coding and math are so closely related.
This is why the article and evidence are interesting. Coding and math are clearly and very closely related in many ways. Yet, the way the brain handles and interprets coding is more akin to pure language, than it is to pure math.
Which I suppose makes it all the more interesting that Math, Language, and coding are so related, yet (per the evidence and the article) - the brain does not see it that way.
There is no problem with A -> B ∧ B -/-> A
Here's an example. "I live in San Francisco" would imply "I live in the US". But "I live in the US" does not mean "I live in San Francisco".
Here's a more formal representation of this: https://en.wikipedia.org/wiki/Bijection,_injection_and_surje...