# Medium and Message

In a somewhat unlikely Star Trek NG episode the crew encounters a race which speaks, unfortunately, entirely through cipher that is coded references to historical events. Blog, well, neighbor Eli is in a huff because some philosopher of science (Signorelli) offers that the “language of maths” isn’t sufficient for human experience. He offers as counter example not a cipher but a number substitution code and suggests that if you encode ordinary language with numbers you’ve translated text into the domain of maths. Well, sorry. That doesn’t it, the medium is not the message. That you are viewing this short essay which is encoded in ASCII and transmitted via HTTP protocols over 802.1 specified media, i.e., numbers. The message is not maths.

A possible line of argument that Mr Signorelli have more difficulty defending is whether is this possibly apocryphal anecdote whether the speaker at the funeral in his speech was getting off track or whether he was using the language of Maths (in the real sense) to express and work out his grief at a colleagues passing.

On the other hand I might suggest a better avenue to counter Mr Signorelli in somewhat smaller domains. There is an audience and a market for combining ones’ passion for maths with other more basic passions, such as the artist Bathsheba and her wares (which I recommend and am an occasional customer). Consider that “ora” which can be bought as jewelry suitable as a gift for your lover … is two interlinked tetrahedra in its self-dual symmetrical glory … and its pretty. For the right recipient there might be a message of maths (not as transmission technology) but which conveys “I love you.” I’ll also offer that when I was dating the woman who would become my wife, I sent her (in the very early 90s) a love letter written on an HP-48 calculator and transmitted using the same calculator to her via programs written on the calculator (and its serial port) to send the letter via FAX when I was traveling. That is a way in which the medium and the message mix a bit, in that computer geekery was used to transmit, well, passion.

Drop in on departmental lecture in your local university maths building. What you hear there is the language of maths. That is what Mr Signorelli is arguing is in sufficient to transmit the breadth of human experience. Basically, he’s right, except that for those passionate about and fluent in that language it can be used to transmit some of those human messages and experience. It is hard even for the maths monomaniac to begin with “let’s consider a function of one complex variable” to say in that language “Let’s get pizza tonight.”

**Filed under: **Mark O. • Offbeat Questions

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Mark, it looks like you’re arguing that math can’t be used to SYMBOLIZE human experience. But obviously this is false, as you yourself observe. I grant you that this is a different interpretation of Signorelli than mine, because in my reading he only wants a REPRESENTATION of human experience. But the punchline is the same: just because we

don’t oftenuse math that way doesn’t mean that wecan’t.This presents the following dilemma – which, incidentally, I brought up in the post to which you initially linked. Either we are saying that math is insufficient because it is FORMALLY deficient in some way that language is not, or we are saying that math is insufficient because we just don’t HAPPEN to use it in the way we use language. The first horn is a total waste of effort, for math is directly translatable to all languages (including not just vocabulary but syntax, grammar, etc.) and therefore its equal in formal expressive power. In theory, then, math can convey anything that natural languages can convey.

But what of the second horn? Like Signorelli, you seem to be fixated on this one. What we HAPPEN to be able to communicate in any particular way is very context-sensitive, as your own examples demonstrate (what with the calculator and the geometrical symmetry and all). And, yes, I admit that most people will not be able to construe math in this way. But there is a gaping hole in this argument: namely, nobody ever said that math WAS capable of this. When we say that math can represent the whole of human experience, we mean that math can in some way explain or be identified with human experience. Whether or not math works IN PRACTICE to say “I love you” has nothing to do with the fact of where the “I love you” comes from. To draw a relevant analogy, if I sent you a very detailed brain scan of me thinking “I love basketball,” you would have in your hands a direct representation of my thought that I love basketball – but you would almost certainly not be able to identify it as such. What we are looking for when we talk about math representing human experience is the former of these, not the latter. Choosing the second horn of the dilemma, then, means completely misunderstanding the subject at hand.

The only way out of this is for you to argue that the two horns are actually related in some way, but that’s such an absurd idea that I don’t think you could even entertain the thought. So no, Signorelli was not basically right. He was entirely wrong, and you’re not improving on his position at all.

Eli, ” and so on to your waitress, she’d think (rightly) that you were nuts and not bring you any food.

I still think you’re missing the point. Look at a smaller claim. “You can’t use the ‘C’ programming language to replace ordinary human language.” You can in fact, write a browser, OS, and so on and use that as the

mediumto express things. But that is (as you say, trivial) and the problem is .. beside the point. The point is that you can’t use ‘C’ to express simple things, like ordering food at an eatery. If you started quoting “#includeUhm, that was what Signorelli said maths couldn’t do. And he’s right.

More importantly the way you suggest using maths (code or some such) is not “using maths.” Maths is more akin to “Let M be a simply connected compact finite dimensional manifold …”

Maths isn’t the technology of the modern world or a code. That maths to a few specialists can be used to convey meanings outside of the direct (as a eulogy or love token) for a very few doesn’t mean that generally maths can be used to cover ordinary human communications. It can’t.

Eli,

Oh, and I’m not sure I get the reference to the “horns” you’re talking about. I think I’m missing a sentence or two there setting up what you’re talking about.

“I still think you’re missing the point. Look at a smaller claim. “You can’t use the ‘C’ programming language to replace ordinary human language.””

Yeah, and I still think that YOU are missing the point. Nobody but nobody says that you can use C to replace ordinary human language. Signorelli, moreover, has no interest in debating that claim, because C is not the language of science. His goal, in his own words, was to show that science cannot “offer us the definitive accounts of human life, and general human practices like worship or law-following.” This has nothing whatsoever to do with whether or not C (or math) can be used in place of English.

“Maths isn’t the technology of the modern world or a code.”

And this is where you and he are wrong. Your computer runs on math. Computers encode language, color, sound, and (yes) emotions using math. Computers, in a real sense, ARE math. Please don’t tell me that you don’t know this, because if you don’t know this then you aren’t qualified to have this conversation.

Eli,

Wait. It occured to me. You wonder about “so you take Signorelli to mean X and I take Y. When you take X his meaning is trivially wrong. When you take Y it is trivially right. Why the heck would you then figure the meaning is the former not the latter?

Again, because he wants to disprove the idea that science (via math) can “offer us the definitive accounts of human life, and general human practices like worship or law-following.” If this is the idea he’s arguing AGAINST,

andif I’m supposed to take his meaning to be the trivially true one, then he’s arguing against a TREMENDOUS straw-man.Eli,

Stop being silly. You aren’t “doing” math when you’re typing on your computer or making a phone call or watching a movie (digital/dvd). Just because deep in the tech numbers are involved doesn’t make it maths. Again go to that lecture. That’s maths. Calling on your smartphone isn’t. You confuse medium and message.

And yes, I’ve written compilers. I know what a CPU, an ALU, FPU and MMU and all that stuff. But a CPU isn’t doing maths. This is math. If you figure ordinary human experience can be encoded in that language .. you’re wrong.

Eli,

Just because you find numbers in a place, doesn’t make it math.

No, *I’m* not doing math. The computer, however, *is* doing math. Please try to keep the two separate, because this goes to the heart of the confusion that you keep running into.

Yes, *I* could not consciously do all the calculations that my phone does, let alone fast enough to replace my phone. But when my phone calls someone else, it does the math for me. Whatever I am saying to them – whatever human experience I am expressing – gets mathematically encoded by my phone and then mathematically decoded on the other end. For a time, therefore, it exists ONLY as math.

Again, if you’re asking for *my* capabilities, then you’re not talking about what *science* can and can’t do. But if you’re asking about what *happens*, then you have to admit that language gets reduced to math all the time.

Eli,

The computer is doing arithmetic. It’s not doing math. Number!= math.

1 232 4334 55 3 333 21 is not math. It’s a string of numbers. Demonstrating that the set of prime numbers is infinite, to pick a trivial example, is doing math.

Okay, now you’re just screwing with me:

“The computer is doing arithmetic. It’s not doing math.”

From wiki:

“Arithmetic or arithmetics (from the Greek word ???????, arithmos “number”) is the oldest and most elementary branch of mathematics”

I mean, can you even take this argument seriously? “I’m not doing math, I’m just adding and subtracting numbers”? Is that how far you’re willing to go in order to defend this broken idea?

Eli,

OK. Then I’ve been screwing with my kids for decades, because I’ve been teaching them for all their life that “doing math” isn’t arithmetic computations.

I’m curious do you say you’re “doing quantum mechanics” when you play baseball? Because the reason atoms don’t collapse is tied to the Pauli exclusion principle.

Eli,

Or is quantum mechanics also “doing math” so that all life and existence is the act of “doing math.” Doing maths is doing maths, proof, theorem, conjecture, visualization. The language is, well, Gowers has been blogging elementary notions of the language of math … perhaps you’ve that on your RSS and have been following it? That’s the language. Is it universal enough to cover human experience. Not really, sorry. Keep trying.

“I’m curious do you say you’re “doing quantum mechanics” when you play baseball.”

Sigh – we’ve been over this already. This is the difference between me doing math when I talk on the phone and my phone doing math when I talk on the phone. Please try not to go in circles.

“Doing maths is doing maths, proof, theorem, conjecture, visualization.”

This, again, is clearly another topic than what Signorelli was talking about. I’m willing to play along with you in using this definition, but only if you recognize that it’s completely separate from the question of whether science can explain things like consciousness. Computation is included in what Signorelli was talking about because it’s included in (really, is essential to) science, so either you’re going to have to come around to the terminology used in the conversation or you’re going to have to admit that you’re talking about something else.

“Is it universal enough to cover human experience.”

Ah, but this is a canard. English isn’t universal enough to cover human experience, so I have no notion at all of why that would be the standard. This only goes to show the absolutely magical properties you ascribe to language.

Eli,

At least try to argue honestly. That was the problem with your whole argument. The medium is not the message (hint: it’s the title of the blog post).

I knowthat, it’s the problem with your argument. You confuse the matter insisting that you are doing math when your phone does math.Oh please. You can order pizza in English. You can’t do it in Maths. Your pizza delivery service is going to be confused at “Take a function of one complex variable …”

Huh?

Uhm, … what? I’m talking about the notion that “talking math” is not a universal subset of language. That you can’t say “anything” in maths speak.

“You confuse the matter insisting that you are doing math when your phone does math.”

When did I say that, let alone insist on it? Seriously: where are you getting this from? I’ve never said this. Talk about arguing honestly…

“You can order pizza in English. You can’t do it in Maths.”

Oh – so ordering pizza is the whole of human experience? Good to know.

And – for now the fourth time – what you’re talking about is NOT what Signorelli was talking about. I also can’t order a pizza in Latin or Greek or Russian, but that tells us jack shit about what Latin or Greek or Russian can do.

“you can’t say “anything” in maths speak.”

But you can! Whether or not you can be understood is a separate matter, but your computer “says” EVERYTHING you say only it says it “in maths speak.” It literally could not work otherwise. This is simply false.

Eli,

You know when you want to deny you’re confusing medium and message you shouldn’t make the same bloody mistake in the same comment. Your “but you can” paragraph is insisting that when your phone does math (which it isn’t doing as you acknowledged above) you are. Either you’re not arguing honestly or you’ve got more cognitive dissonance than a schizophrenic.

Nope. Ordering pizza is just one part of the things we do with language. One you can’t do in maths there are just a few more (actually

mosthuman language cannot be expressed in maths-speak.Sorry, only in your head dude.

From your quote:

OK. You peruse a Hilbert text book or Wigner or even Euclid. Let me know where you find “my anger is justified” in those texts. Try (for the Nth time) to recall that you aren’t doing quantum mechanics when you throw a baseball or doing maths when you use a computer to send an email (and encoding a document into ASCII by hand isn’t “doing math” either). You granted that. Stop saying things like “yes you can” when you granted you can’t.

Now, perhaps Signorelli’s argument breaks down when he brings this statement into statements about consciousness and language. So what? He’s right that maths isn’t a universal language. My point wasn’t that Signorelli was right about consciousness, but that you’re mistaken in finding the flaw where you do. Your whole coding as proof he’s wrong is not the error you think it is. Your grinding your axe on the wrong flaw.

“Your “but you can” paragraph is insisting that when your phone does math (which it isn’t doing as you acknowledged above) you are.”

No, it’s not. This isn’t even close. What makes you think this? Where are you getting this from?

“Ordering pizza is just one part of the things we do with language. One you can’t do in maths there are just a few more (actually most human language cannot be expressed in maths-speak.”

No: ALL human language can be expressed in maths-speak, which is why you can talk over phones and type into computers. Most human language can’t be UNDERSTOOD when expressed in math-speak, and that is entirely different.

“Stop saying things like “yes you can” when you granted you can’t.”

This is simply pathetic, and rather beneath you, Mark. Just because I AM not doing something does not prove that I CAN’T do that thing; again, I’m not typing this in Latin or Greek or Russian, but I daresay that I could. And, for now the fifth time, THIS IS NOT WHAT SIGNORELLI WAS TRYING TO PROVE. You are wasting my time with this trash.

“Your whole coding as proof he’s wrong is not the error you think it is.”

No: my coding as proof that he’s wrong was aimed at one very specific thing he said, as I identified it in the original post. (The relevant quote, in case you’ve forgotten, was that “mathematics [is not] capable of representing whatever language is capable of representing.”) The rest of it has its own set of arguments, which you’ve been doing your best to disregard for the length of this comment thread.

Eli,

What I fail to understand is how you can put these two statements together and not have neurons misfire.

I’m willing to go along and math=code doesn’t compute.

Just because a thing is a stream of numbers doesn’t make it math. You keep repeating a notion that it is, it isn’t. You’ve

saidit’s not what Signorelli was talking about, except given the words you quoted, it clearly is. “Mathematical statements” are not streams of random digits. Mathematical statements are what you read in math texts or hear in lectures and so on. Just because “computations” are used in science doesn’t mean Fourier transforms digitally recorded of sound oscillations can be transmitted and reproduced as music doesn’t mean that MP3 file is “math” in any sense of the word math. It isn’t. In the first chapter of that Princeton Compendium I linked Gowers (or contributors) give a quick rundown of the “language of mathematics” …thatis the language of math, not digitized text or sound.Representation of “I’d like a pepperoni pizza” in maths is not an Ascii byte-string. Something like “Choose one of the set {Pizza} with member {Pepperoni}” except the {Pizza} and {Pepperoni} don’t exist as maths constructs, which is why you can’t say that in maths. For Maths so represent

whateverlanguage is capable of it has to say each of those things, including ordering pizza. Your coding as proof is wrong because highly compressible streams of numbers digits isn’t math, or in other words the medium isn’t the message.I’m curious, in which maths class did you take in college where the professor just repeated random digits for 90 minutes 3 times a week?

Eli,

Look when you use maths to represent the real world, like using Path integrals for particle scattering or statistical models to represent gases. Those aren’t random digit streams. They are functionals and equations. This is how real world things are represented in maths. Not data, but relations and functions. In the language of maths. What your phone does and what Feynman path integrals do are worlds apart. The latter is what Signorelli was talking about. Not your coding crap (and yes it’s a trivial objection but it’s also clearly wrong).

Eli,

Look I took 10 years of Physics at school. All we ever did in Physics, when you get down to it, is get down to doing the best job we could at describing the real world using the language of maths. Guess what? We didn’t describe a whole lot of things that language can do. I won’t bore you with example, but I’ll bet you can imagine one or two topics not easily covered with the methodology and techniques in classical, statistical, and quantum mechanics, you know like expressing “my anger is justified” or “my behavior has been shameful.”

“Mathematical statements are what you read in math texts or hear in lectures and so on. Just because “computations” are used in science doesn’t mean Fourier transforms digitally recorded of sound oscillations can be transmitted and reproduced as music doesn’t mean that MP3 file is “math” in any sense of the word math.”

No: the MP3 file the input in the computation that leads to music. I think you’re still conflating representation and translation, which is another mistake Signorelli makes. Please note that I am not doing this. I’ve been very explicit – multiple times – about how I have distinct lines of reasoning, and you’re continuing to muddle them.

“…except the {Pizza} and {Pepperoni} don’t exist as maths constructs, which is why you can’t say that in maths. ”

And this is why your idea of language is magic. What, exactly, do “pizza” and “pepperoni” exist as except as language constructs? The analogy is as direct as can be.

“Your coding as proof is wrong because highly compressible streams of numbers digits isn’t math, or in other words the medium isn’t the message.”

You keep trying to straw-man me this way and I’m just not going to have it. The whole process is mathematical, yet the process is the thing itself. Ergo the thing itself – the song coming from my computer speakers, my communication over the phone, etc. – is just math. We have to output it into a format we can sense, but so what?

“Look when you use maths to represent the real world, like using Path integrals for particle scattering or statistical models to represent gases. Those aren’t random digit streams. They are functionals and equations.”

So is the stuff in your computer, Mark. So are all the programs that model language. This is how Siri works. This is how you get green underlines in Microsoft Word. This is how Google works. Everything that computes language works with “functions and equations” – including, yes, your phone. (Which, by the way: I thought that functions, being arithmetic, weren’t math…?) You can’t have it both ways.

“Guess what? We didn’t describe a whole lot of things that language can do.”

Great: paintings also express things that language can’t. Does that mean that reality is somehow ontologically connected to paintings? (Or music? Or scent? Or…?) Don’t be even more idiotic than you’ve been for the length of this conversation.

Eli,

Arrgh. A long reply lost. Hmm. Version 2 coming up.

Clearly with your code/encode “the process is the thing itself” you identify the coding process with a representation. It isn’t. Sorry. Nice try. But it’s trivially wrong.

from the point of view of the process (the math) the “song” coming from your computer speakers might just as well be a recording from a hog slaughterhouse. The encode/decode isn’t representation.

I begin to suspect you don’t know “how Google works.” This reminds me of a conversation I had in grad school. What is a physical theory? If you had a big book, which encoded a complete compendium of the results of every possible physical experiment that might ever be made would that be a TOE (theory of everything). String/M-Theory attempts to be a TOE, but in a different way, one which grants a model for understanding everything not just explaining it. Your encode/decode similarly “represents” all sounds and faithfully reproduces them, but without understanding. It provides no underlying model, unlike language.

When you or I hear the word (from language) “pizza” we will both identify with a very high degree of correlation a large number of culinary (and non-culinary) objects presented to us as Pizza/not-Pizza (alas I can’t quite say the same for function … as a digression … the word I had used was “functional” which isn’t a function and besides is this the sort thing you see as the same as 45+27=72 or arithmetic and that the latter is the same as the former?). But why does Pizza work for us the way it does. Because it refers to a model, it has semantic content, unlike the ascii table.

“When you or I hear the word (from language) “pizza” we will both identify with a very high degree of correlation a large number of culinary (and non-culinary) objects presented to us as Pizza/not-Pizza …But why does Pizza work for us the way it does. Because it refers to a model, it has semantic content, unlike the ascii table.”

I know that this is your argument, but it’s completely flawed. I am, however, very glad that you’re now (finally!) owning up to it.

“Pizza” does not just have semantic content. That is a wildly misleading way of saying it. Rather, we give “pizza” semantic content in virtue of a whole set of contingent and mostly arbitrary linguistic practices. I agree that equations and things don’t sit in the same kind of context: if I try to describe the mathematical processes that allow me to order a pizza via phone to the pizza guy on the other end of the phone, that ain’t gonna accomplish anything. All of that is correct.

However, all of that is also wholly irrelevant to anything that Signorelli or I was saying. If we seek to explain things like consciousness using scientific methods, it matters not one bit that I can’t order a pizza over the phone using math. Moreover, if we seek to understand reality in a thorough and rigorous way, it would be idiotic to fixate on the (again, arbitrary and contingent) limits of human cultural interaction. In other words, that language “provides [an] underlying model” is EXACTLY THE PROBLEM.

Eli,

Stop talking about “consciousness” that is completely off topic and irrelevant. It was never cited or mentioned in your original post. You offered a “trivial” counter example about mathematical example to which I partially objected (in that language elements normally not found in maths contexts like “I love you” and a euology might be said in maths speak in certain contexts). I offered to defend the argument against your trivial argument. I have done so.

Let me recap.

You cited an article that noted that you can’t represent ordinary language using a subset, i.e., mathematical language. As a counter example you cited simple textual/number code/encode as a “representation” of language. You then affirmed that the stream of numbers was not mathematical language … but backpedaled to claim that the conversion algorithm was a representation of language. Confronted with the problem that this code/encode algorithm treats garbage text with no difference than ordinary language means that this notion is problematic as a representation. You then cite Google’s MapReduce/Search, Word’s ability to parse grammar, and Siri. This is interesting … but in the first place,

nota code/decode algorithm … and has to confront the Big book of experiments vs model problem to which I alluded. You have decided to miss that point. It is where the argument (as I see it) stands now.You need to decide whether the “big book of experiments” is the goal of science or not. Does it represent an understanding or model of reality. If it does, then you would find a “perfected” Siri/MapReduce as a good model of language. If not, then it isn’t. In the argument we had then, we were not settled on whether the Big Book is the end (goal) of science or whether our project was to provide models to represent reality (the Physics/maths language goal).

There is no way I’m able to confront arguments off text, i.e., you are now trying to make an argument the context of which I am not privy. Keep to the topic, which is maths language is not a cover (which it needs to be to become a good representation) for ordinary human language, e.g., English.

“Stop talking about “consciousness” that is completely off topic and irrelevant.”

Oh – so you didn’t actually read the original article and you don’t know what I’m criticizing. That explains it!

I’m now going to stop commenting on this, because it’s not my job to make sure that you do your due diligence. If you want to keep on acting as though the context of my original post was irrelevant, you go right ahead. I’ve already lost more respect for you than I would’ve thought possible, so I’m done.

Eli,

I see, you shift goalposts … and if I object … you take your ball and go home.

Interesting.

Eli,

Actually, or more charitably, I think we’ve been laboring under a misunderstanding. When you asked “defend Signorelli” I took that mean to defend him in the context of the particular objection your raised regarding maths and language. You took that to mean, defend his whole thesis. I’ve been defending your particular “trivial” objection, which I did. You took me to be defending his entire argument, and accuse me of not doing “due diligence” which I didn’t do because it wasn’t required to the task I understood I undertook.