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Amar Hadzihasanovic (Jun 15 2020 at 10:48):Intuitively, I would think that the difference is on the lines of:
mathematics is one of few disciplines that are entirely defined by their methodology, not at all by their subject of study;
in a certain sense it belongs better together with the “performing arts”, ie one “performs maths” the way one “performs music” or “performs dance”;
with philosophical logic/foundations/philosophy of maths being to maths as music theory is to music, which is why it is somewhat at the boundary (it may incorporate the performance of maths but not always).
I'm sure that someone has already expressed this thought better than I am now...
Amar Hadzihasanovic (Jun 15 2020 at 10:48):Whereas “computer science” is more traditionally defined by the broad subject of study.
Amar Hadzihasanovic (Jun 15 2020 at 10:52):A discipline which is defined by its subject is “open” in the sense that it can possibly incorporate all sorts of “performances” as long as they are related to the subject.
With a discipline which is defined by methodology/performance, you may push the boundaries of what “counts” as a performance (like ready-mades counting as art...) but you cannot cross the boundaries between different performing arts. Like, you will never be able to sell a musical performance as maths (at most the piece of music, eg if you're Xenakis...)
Amar Hadzihasanovic (Jun 15 2020 at 11:08):The other examples of “performing arts” that I can think of in the sciences, beside “mathematics”, would be
Interestingly like there are “professional mathematicians” there are also “professional builders” and “professional arguers”, so these are arguably also disciplines like maths is, but I don't think there's such a thing as “professional experimenters”.
Amar Hadzihasanovic (Jun 15 2020 at 11:09):As in, someone who studies how to be “an experimenter in general” and could go work in a physics lab, or a medical lab, or whatever. But maybe I'm wrong.
Jules Hedges (Jun 15 2020 at 14:13):Amar Hadzihasanovic said:
Intuitively, I would think that the difference is on the lines of:
mathematics is one of few disciplines that are entirely defined by their methodology, not at all by their subject of study;
in a certain sense it belongs better together with the “performing arts”, ie one “performs maths” the way one “performs music” or “performs dance”;
I LOVE this idea
Jules Hedges (Jun 15 2020 at 14:13):This is the greatest hot take I have ever seen, and it's not even on twitter
Amar Hadzihasanovic (Jun 15 2020 at 15:11):Jules Hedges said:
This is the greatest hot take I have ever seen, and it's not even on twitter
I'll turn it into a twitter thread, I'd be curious to see what other people think of it.
(=_=) (Jun 15 2020 at 15:22):Jules Hedges said:
Nah, it's only twitter. Disagreement drives the analytics more than anything else
Talk about a perverse incentive. Is there a sheaf for this?
John Baez (Jun 15 2020 at 15:27):To get a lot of twitter hits, if you're an academic, slam an entire field by saying something like "mathematics is culturally "closed world" - there is a fixed-for-all-time list of things that "count" as mathematics. Whereas computer science is culturally "open world"."
Jules Hedges (Jun 15 2020 at 15:32):Pro tip: If you pick on mathematics then most mathematicians will fight back. But if you pick on philosophy then most philosophers will join in
(=_=) (Jun 15 2020 at 15:33):Amar Hadzihasanovic said:
Like, you will never be able to sell a musical performance as maths
But why would you shortchange a performance by doing that? Maths doesn't sell, as much as some would hope otherwise. If it did, people would be scalping tickets to lectures, not concerts.
In any case, this linkage of performance with maths reminds me of this book, which is book II of Mazzola's newly expanded The Topos of Music.
(=_=) (Jun 15 2020 at 15:34):Amar Hadzihasanovic said:
As in, someone who studies how to be “an experimenter in general” and could go work in a physics lab, or a medical lab, or whatever. But maybe I'm wrong.
They're called lab technicians.
(=_=) (Jun 15 2020 at 15:36):Amar Hadzihasanovic said:
mathematics is one of few disciplines that are entirely defined by their methodology, not at all by their subject of study
What about "science"? I heard they're defined by their methodology as well.
John Baez (Jun 15 2020 at 15:41):Yeah, that's another one.
(=_=) (Jun 15 2020 at 15:43):John Baez said:
Yeah, that's another one.
So according to Amar and Jules, science is culturally "closed world" as well. Which does make sense, in a kind of way, but maybe not what was originally intended. :upside_down:
Amar Hadzihasanovic (Jun 15 2020 at 15:44):Rongmin Lu said:
Amar Hadzihasanovic said:
As in, someone who studies how to be “an experimenter in general” and could go work in a physics lab, or a medical lab, or whatever. But maybe I'm wrong.
They're called lab technicians.
I don't think what I am talking about describes lab technicians. A “pure experimenter” would be someone who takes some theoretical input and then designs an experiment, runs it, and does statistical analysis on the results.
Amar Hadzihasanovic (Jun 15 2020 at 15:44):Of course they exist ... but branching off other subject-defined disciplines.
Amar Hadzihasanovic (Jun 15 2020 at 15:45):You go study physics and then become an experimental physicist, medicine and then become a medical lab researcher, etc.
Amar Hadzihasanovic (Jun 15 2020 at 15:45):You don't go study “experimental science” and then become an applied experimenter in physics, medicine, etc.
(=_=) (Jun 15 2020 at 15:46):Amar Hadzihasanovic said:
You go study physics and then become an experimental physicist, medicine and then become a medical lab researcher, etc.
But we all know they'd then make a hash out of it, and we'll have to bring in the lab techs to baby-sit them and the statisticians to clean up the experimental design.
(=_=) (Jun 15 2020 at 15:47):Oh, and the professional software developers to write any code properly, because as it had become apparent elsewhere, scientists apparently don't believe in clean code.
Amar Hadzihasanovic (Jun 15 2020 at 16:15):Rongmin Lu said:
Amar Hadzihasanovic said:
mathematics is one of few disciplines that are entirely defined by their methodology, not at all by their subject of study
What about "science"? I heard they're defined by their methodology as well.
Yes, people say that, but I don't think it really fits the bill -- if we're talking about science as in “natural science”, it is usually implied that it's about the natural world. As for its method, it's a compound: part mathematics, part experimentation...
Amar Hadzihasanovic (Jun 15 2020 at 16:18):There's a certain idea of being “about anything at all”, at least in principle, in what I'm talking about with the “performing arts”.
Amar Hadzihasanovic (Jun 15 2020 at 16:19):I can do maths about a counterfactual world, I can do dance and paintings about a counterfactual world, but by definition I can't do science about a counterfactual world (unless it's really just maths).
Tomáš Gonda (Jun 15 2020 at 16:26):Amar Hadzihasanovic said:
Yes, people say that, but I don't think it really fits the bill -- if we're talking about science as in “natural science”, it is usually implied that it's about the natural world. As for its method, it's a compound: part mathematics, part experimentation...
I mostly agree, I would just point out that classifying it as a compound of math and experimentation is probably more simplistic than helpful. A bit more nuanced characterization is that science is a dialectic of model building--prediction generation--experimental testing (which then feeds back to the model). Quasi-fixed points of this feedback loop are often called theories in science. Mathematics is used throughout the process as a language mediating this dialectic mostly because it imposes some sort of internal logical coherence.
Tomáš Gonda (Jun 15 2020 at 16:28):Funnily enough, there is probably a version of this dialectic internal to mathematics, which is why "theory" in mathematics doesn't mean the same thing as "theory" in science, when viewed through a common lens.
Amar Hadzihasanovic (Jun 15 2020 at 16:50):Agreed, but I would be a very bad applied category theorist if I didn't think that a compound can be much more complicated than the sum of its parts :)
(=_=) (Jun 16 2020 at 00:59):Amar Hadzihasanovic said:
if we're talking about science as in “natural science”, it is usually implied that it's about the natural world.
No, we're not. By "science", I mean a systematic study of something using the scientific method. Despite the replication crisis, there's lots of good work done in good faith to study the social realm. Arguably, it's still about the natural world, but the social realm is more of a layer on top of that, and incorporates "non-natural" entities like ideas.
(=_=) (Jun 16 2020 at 01:05):Amar Hadzihasanovic said:
by definition I can't do science about a counterfactual world (unless it's really just maths).
Have you spoken to a string theorist lately? :upside_down:
Depending on how you define a "counterfactual world", there are things you can study about that world that can be done using the scientific method. If you accept that MMORPGs are counterfactual worlds, then people have studied the economics of those worlds, for example. It's not "really just maths", since these studies would usually involve observation and experimentation as well.
(=_=) (Jun 16 2020 at 01:10):Tomáš Gonda said:
A bit more nuanced characterization is that science is a dialectic of model building--prediction generation--experimental testing (which then feeds back to the model).
Yup, and it can in fact be applied to a counterfactual world that's amenable to that process: that's how you could do maths in a counterfactual world, which is implicit in your observation that "there is probably a version of this dialectic internal to mathematics".
I don't think that process is unique to science: creating a good narrative could be modelled by that as well. This is why you can have bad instances of narrative: the author has simply generated predictions (the narrative) that haven't been properly tested (exposed to a suitably critical audience to gauge their reaction) yet.
(=_=) (Jun 16 2020 at 08:59):So Amar had a couple of tweets on the topic he raised here that I'd like to discuss. Let's start with "a calculation starting with 0=1 is still mathematics":
Under classical logic, the principle of explosion means every calculation that starts with a contradiction like 0=1 is clearly not mathematics, because the concept of truth or falsity has become trivial. Even if you weaken the contradiction, and say that "0=1" means you're talking about the field with one element, that took a lot of work to set up.
@sunnya97 Whereas a math calculation which starts with 0 = 1 is still mathematics!
- Amar Hadzihasanovic (@amar_hh) (=_=) (Jun 16 2020 at 09:02):And that's the thing that's bothering me: Amar wants to assert that a counterfactual world is somehow necessarily inconsistent (or maybe paraconsistent). That's not the case, however: any sufficiently interesting counterfactual world, even for artistic purposes, is internally consistent. Assuming that "counterfactual => inconsistent" trivialises the work of so many people who work hard to build counterfactual worlds
(=_=) (Jun 16 2020 at 09:10):Consider the example in the other tweet of pretending some fizzy drink is fairy blood and doing a blood count. If your counterfactual world is inconsistent (e.g. assume the bare contradiction 0=1 and proceed from there), of course it's "just" an experiment, because perhaps your way of "doing a blood count" involves doing something that may be consistent with "the real world", but is inconsistent with the counterfactual world. But if you have a consistent counterfactual world in which "real world" fizzy drink is fairy blood (for the mathematical analogy, assume Borger's notion of ), then you would have a way of "doing a blood count" in the counterfactual world that would be scientific within the counterfactual world.
@sunnya97 I pretend some fizzy drink is fairy blood. I do a blood count on it. It's an experiment. It's not science. I'd say something is science only if it's about learning something about the real world.
- Amar Hadzihasanovic (@amar_hh) Amar Hadzihasanovic (Jun 16 2020 at 09:11):That's not what I wanted to assert at all. My example of starting with 0=1 was maybe misleading (of course that equation can be consistent in an appropriate world)
(=_=) (Jun 16 2020 at 09:12):I just feel that you have a rather crude notion of what a counterfactual world is.
Amar Hadzihasanovic (Jun 16 2020 at 09:14):I think the problem with these discussions especially on twitter is that one uses crude approximations to avoid writing a 200-page essay and then is taken to the same standard as the writer of a 200-page essay.
Amar Hadzihasanovic (Jun 16 2020 at 09:16):But there's nothing that remotely looks like "a counterfactual world is necessarily inconsistent" in what I wrote, so I think you are attacking a straw man and I do not feel like responding.
Amar Hadzihasanovic (Jun 16 2020 at 09:26):I think that you have a good point about MMORPGs, or simulations in general, on the other hand. It does show that my approximation of science being about the "actual world" was a crude one.
Amar Hadzihasanovic (Jun 16 2020 at 09:26):My point was that the act itself of writing an equation is mathematics, independent of purpose and motivation. But there's no pure "act of science". The same act may be science or not depending on various factors.
Amar Hadzihasanovic (Jun 16 2020 at 09:26):But I wanted to avoid trying to give "definitions" of what things are, because it's a rabbit hole.
Morgan Rogers (he/him) (Jun 16 2020 at 11:18):This paper by Mario Bunge opens with a more nuanced definition of the content of science, and may be of interest. The rest of the article lacks some context, but is an entertaining read nonetheless. I would observe that his definition lends support to the point @Rongmin Lu made about it being defined by its methodology.
On @Amar Hadzihasanovic's original "hot take": I don't really understand why you separate out 'experimenters' in your list on the basis that any experimental science is specialised. The same is surely true for the other subjects you specified: the idea that professional mathematicians are "mathematicians in general", for example, is a misconception. Sure, someone with mathematical training will be able to pick up an unfamiliar topic faster than someone without that training, but similarly someone with experience in one lab setting will adapt faster to new lab settings. In either case further training is required.
Amar Hadzihasanovic (Jun 16 2020 at 11:24):Hi Morgan, that part is entirely about how these categories are “socialised” and what the path to becoming a specialist is, not about the outcome.
Amar Hadzihasanovic (Jun 16 2020 at 11:25):What I am saying is that the way one becomes an experimental scientist is that one goes to study a specific subject, and receives the training to become an experimenter on the way to becoming a physicist/chemist/geologist/whatever.
Amar Hadzihasanovic (Jun 16 2020 at 11:26):It is not unconceivable that the same could have happened with mathematics.
Amar Hadzihasanovic (Jun 16 2020 at 11:26):That there is no community of “mathematicians” but only, say, “theoretical scientists”. Everyone learns only the mathematics of their subject (with different degrees of specialisation).
Amar Hadzihasanovic (Jun 16 2020 at 11:32):And in reverse, it is not unconceivable that we could have degrees in “experimental science”, and a culture of people who identify themselves as “experimenters” in the way that we identify as mathematicians. They would share an aesthetics of “beautifully designed experiments”, ones that best get rid of confounding factors, biases, various kinds of errors, etc.
And labs could hire an “experimenter” who is not necessarily a specialist of the field, just someone who is good at consulting on whether an experiment is 'actually' going to prove/disprove what the specialists want it to, and suggest how to improve it.
Amar Hadzihasanovic (Jun 16 2020 at 11:38):Statisticians fulfill that role in part, and I think quite recently they have started being “socialised apart” from mathematicians. But that only covers part of what “experimental science” is.
Morgan Rogers (he/him) (Jun 16 2020 at 11:39):The idea about general, hopefully unbiased experimentalists appeals to me a lot.
I can't resist noting the mild irony in you presenting a vision of science in a counterfactual reality like this, though, given the earlier discussion.
Amar Hadzihasanovic (Jun 16 2020 at 11:43):Again, the lines would be very blurred the way that they always are... I remember a professor in my undergrad insisting that “I identify as a physical mathematician, not as a mathematical physicist.” It's hard to separate the two and it's mostly a matter of self-identification.
(=_=) (Jun 16 2020 at 11:43):And all this because Jules Hedges was grousing about apparently not being able to be hired into a maths department...
Let me add more context. I consider ~3/4 of my own published work (plus my thesis) to be mathematics. Currently I'm in a (pretty non traditional) maths institute, but I'm moving from and to informatics institutes. I believe I am unhireable to most maths departments https://twitter.com/_julesh_/status/1272115707367604225
- julesh (@_julesh_) Amar Hadzihasanovic (Jun 16 2020 at 11:43):So you would probably have “chemical experimenters” who are very similar to “experimental chemists”...
Morgan Rogers (he/him) (Jun 16 2020 at 11:44):Right, the premise of this discussion is not constructive. Science and mathematics are not defined independently of the people who practice them, and different people in those communities have different ideas about their content, and about what these subjects/disciplines "should" be. For a practitioner of maths or science (or any of the other things that have been mentioned) these ideas are intimately tied to their sense of identity.
Presenting strong opinions about someone else's identity, especially ideas about 'what they are not' or 'what they cannot do', is rarely going to yield positive reactions.
(=_=) (Jun 16 2020 at 11:44):To be honest, I don't think Jules' hot take about open and closed worlds is really justified.
Amar Hadzihasanovic (Jun 16 2020 at 11:45):[Mod] Morgan Rogers said:
Right, the premise of this discussion is not constructive. Science and mathematics are not defined independently of the people who practice them, and different people in those communities have different ideas about their content, and about what these subjects/disciplines "should" be. For a practitioner of maths or science (or any of the other things that have been mentioned) these ideas are intimately tied to their sense of identity.
Presenting strong opinions about someone else's identity, especially ideas about 'what they are not' or 'what they cannot do', is rarely going to yield positive reactions.
I'm sorry, is that in reaction to something that I said?
(=_=) (Jun 16 2020 at 11:45):Could be in reaction to mine...
Amar Hadzihasanovic (Jun 16 2020 at 11:48):My “working definition” of mathematics was the most inclusive possible, down to “kindergartener counting apples and getting it wrong”.
(=_=) (Jun 16 2020 at 11:48):[Mod] Morgan Rogers said:
Right, the premise of this discussion is not constructive.
I agree. The premise is, based on Jules' most recent tweet about this, that maths departments are "closed world" or exclusionary, because they require publications in maths journals, whereas CS departments are "open world" because they're okay with publishing in conference proceedings. I'm not sure I buy that.
(=_=) (Jun 16 2020 at 11:53):For example, at Macquarie University in Sydney, which is the HQ of Australian CT, quite a few CT people were actually hired to the CS department there, before shifting over to the maths department. There's also at least one CS person who does a lot of CT and is still in the CS department. It's really a function of curation, as someone else had mentioned on Twitter. If you've published mostly in CS venues, the natural places to hire you are CS departments. I don't think there's anything bad about that, and I don't think it justifies the "two worlds" take.
Morgan Rogers (he/him) (Jun 16 2020 at 11:56):Amar Hadzihasanovic said:
I'm sorry, is that in reaction to something that I said?
Partly, yes: from my perspective, this discussion has been about the idea of what "counts" as a particular discipline, such as the tweet of yours that was quoted about a particular act "not being science". And my argument is partly that this discussion can't be separated from the identities of the people who consider themselves to be doing those subjects, which is why you end up with people identifying themselves "as a physical mathematician, not as a mathematical physicist.”
Amar Hadzihasanovic (Jun 16 2020 at 11:59):I think “running a blood count on coca cola (knowing it is coca cola) is not science” is a degree of controversy that I am willing to accept.
(=_=) (Jun 16 2020 at 12:02):[Mod] Morgan Rogers said:
people identifying themselves "as a physical mathematician, not as a mathematical physicist.”
This is partly about methods, and partly because "physicist" is an insult amongst certain mathematical circles. Actually, the two are intertwined: a physicist is allegedly fond of indulging in "non-rigorous" reasoning, and so is an object of ridicule amongst some mathematical circles in the past. So the difference between the two is that:
You can see how it's rather silly, because the boundary is rather porous. I don't think people say "physical mathematician" much these days, because a lot of physics is now yielding to rigorous methods.
Amar Hadzihasanovic (Jun 16 2020 at 12:06):For the record, I don't think that any of these distinctions in self-identification is silly. I have identified in many different ways over the years. Only that they are extremely “intensional” and not “extensional” distinctions, to use CS jargon: it may be impossible to distinguish a mathematical physicist from a physical mathematician just by observation.
(=_=) (Jun 16 2020 at 12:06):Amar Hadzihasanovic said:
I think “running a blood count on coca cola (knowing it is coca cola) is not science” is a degree of controversy that I am willing to accept.
Yeah, and I was critiquing the "knowing it is coca cola" bit when I said you're asserting that a counterfactual world is necessarily inconsistent.
In the real world, running a blood count on coca cola is not science. That isn't controversial.
What I disagreed with is your assumption that in a counterfactual world, where coca cola is fairy blood, that the "you" in the counterfactual world would "know" that it is coca cola, and that thereby running a "blood count" (in the sense of that counterfactual world) is "not science".
(=_=) (Jun 16 2020 at 12:08):Amar Hadzihasanovic said:
it may be impossible to distinguish a mathematical physicist from a physical mathematician just by observation.
For what it's worth, I think John was happy to call himself a mathematical physicist, even though he's never been in anywhere but a maths department. There are also respected mathematical journals with "mathematical physics" in the title, which probably helped as well.
Amar Hadzihasanovic (Jun 16 2020 at 12:12):@Rongmin Lu I think there is a mismatch between “external” and “internal” in the way that we are referring to the 'counterfactual world'.
Let's put it this way: I am suggesting that whether something is science depends on the purpose of who is doing it. So something is not science unless the person doing it, is doing it to learn something about (some) 'reality'.
Amar Hadzihasanovic (Jun 16 2020 at 12:13):So it does not matter whether one is dealing with “a counterfactual to the real world that is out there”. It matters whether one thinks something is counterfactual.
(=_=) (Jun 16 2020 at 12:14):Yeah, now that is really confusing to me. There are two parts to your argument there. I'll have to deal with them separately.
Amar Hadzihasanovic (Jun 16 2020 at 12:15):Trying to measure a property of the luminiferous aether is science if I think there is or may be a luminiferous aether. Trying to film a ghost is science if I think there's a chance there are ghosts.
Amar Hadzihasanovic (Jun 16 2020 at 12:15):But I would say that “make-believe” experiments are not science.
Amar Hadzihasanovic (Jun 16 2020 at 12:16):Even though they may follow all the rituals.
Amar Hadzihasanovic (Jun 16 2020 at 12:16):I think this is a much more inclusive definition of science than most people accept, btw. String theory is easily in.
(=_=) (Jun 16 2020 at 12:17):Amar Hadzihasanovic said:
But I would say that “make-believe” experiments are not science.
Wouldn't "trying to film a ghost" be considered a "make-believe" experiment externally by people who don't believe there's a chance there are ghosts?
(=_=) (Jun 16 2020 at 12:18):Anyway, your current argument confirms to me that the view you're advancing of what a "counterfactual world" means is rather basic.
Amar Hadzihasanovic (Jun 16 2020 at 12:19):What can I say, I am a shallow guy.
Amar Hadzihasanovic (Jun 16 2020 at 12:19):I like my counterfactuals skin-deep at most.
(=_=) (Jun 16 2020 at 12:19):Simply considering a single counterfactual, like assuming 0=1, will lead to inconsistencies in the world you believe in. Of course this will, more often than not, lead to a system of beliefs that isn't scientific.
(=_=) (Jun 16 2020 at 12:21):That is what I was critiquing. For me, a "counterfactual world" is one that has internal consistency. If coca cola is fairy blood in a counterfactual world, then "running a blood test" will produce a meaningful result and cause the experimenter to learn something about the said counterfactual world. It will, of course, not lead to any new knowledge about our "real world".
Amar Hadzihasanovic (Jun 16 2020 at 12:21):I still really can't understand why you think my counterfactuals imply inconsistency.
(=_=) (Jun 16 2020 at 12:22):In the real world, running a blood test on coca cola is inappropriate, because a blood test will not tell you anything about stuff that isn't blood.
Amar Hadzihasanovic (Jun 16 2020 at 12:23):You are considering “the experimenter in the counterfactual world”. I am considering “the counterfactual world in the mind of the experimenter”.
(=_=) (Jun 16 2020 at 12:25):That seems to be the problem. You made references to performance and the arts, in which people routinely create and inhabit consistent counterfactual worlds, so I took it that you meant that.
(=_=) (Jun 16 2020 at 12:27):And of course string theory is a major example of maths being done in an a priori counterfactual world that string theorists have postulated to be factual.
Amar Hadzihasanovic (Jun 16 2020 at 12:33):I'll try to rephrase what I mean again. Maybe it's not a very standard use of counterfactual. When I say “an experiment about a counterfactual world” it does NOT mean:
“an experiment on something which turns-out-to-not-be-actually-real-in-the-real-world-whatever-that-means”
it's
“a make-believe experiment, based on what I believe to be false, from which I do not expect to learn anything”.
And I would say that the latter is not science. But it's entirely relative to the state of mind of the experimenter and, as all such things, can be misread by observers.
For example a fraud mystic running a séance with the idea of faking contact with the deceased is not a “scientific experiment”, but may be misread as one by the victims of the fraud.
Amar Hadzihasanovic (Jun 16 2020 at 12:34):And it would still not be a scientific experiment even if ghosts happen to be real and show up during the séance!
(=_=) (Jun 16 2020 at 12:37):Amar Hadzihasanovic said:
And it would still not be a scientific experiment even if ghosts happen to be real and show up during the séance!
I'd say that's a successful falsification of the fraudulent mystic's mistaken belief, so it is scientific.
Amar Hadzihasanovic (Jun 16 2020 at 12:37):By the way I think it's ok to deal with some counterfactuals as a way of (hopefully) getting knowledge about the real world. One example would be studying anti-de Sitter space in string theory even if you believe, or know, that we are not in anti-de Sitter space: it's still science because you plan to learn things that you can then transfer to our universe.
Amar Hadzihasanovic (Jun 16 2020 at 12:38):Rongmin Lu said:
Amar Hadzihasanovic said:
And it would still not be a scientific experiment even if ghosts happen to be real and show up during the séance!
I'd say that's a successful falsification of the fraudulent mystic's mistaken belief, so it is scientific.
But would you say that the mystic is doing science?
(=_=) (Jun 16 2020 at 12:39):Amar Hadzihasanovic said:
When I say “an experiment about a counterfactual world” it does NOT mean:
“an experiment on something which turns-out-to-not-be-actually-real-in-the-real-world-whatever-that-means”
it's
“a make-believe experiment, based on what I believe to be false, from which I do not expect to learn anything”.
So you're assuming an inconsistency in your definition. What exactly about my "straw man" was wrong then?
Amar Hadzihasanovic (Jun 16 2020 at 12:39):“False” is semantic, “inconsistent” is syntactic, no?
Amar Hadzihasanovic (Jun 16 2020 at 12:40):I can think that God is not real even if I think she is not inconsistent.
(=_=) (Jun 16 2020 at 12:40):Amar Hadzihasanovic said:
Rongmin Lu said:
Amar Hadzihasanovic said:
And it would still not be a scientific experiment even if ghosts happen to be real and show up during the séance!
I'd say that's a successful falsification of the fraudulent mystic's mistaken belief, so it is scientific.
But would you say that the mystic is doing science?
The mystic did not intend to do science and may very well not realise the success of the experiment, but it would still be a successful scientific experiment to an impartial and competent external observer.
Amar Hadzihasanovic (Jun 16 2020 at 12:43):Ok, fair enough! So we disagree on whether the intent of the experimenter matters in judging what's science. That's ok.
(=_=) (Jun 16 2020 at 12:43):Amar Hadzihasanovic said:
“False” is semantic, “inconsistent” is syntactic, no?
Nope. What's inconsistent about the definition that "an experiment about a counterfactual world" means "“a make-believe experiment, based on what I believe to be false, from which I do not expect to learn anything” is that the "I" is doing an experiment while holding a belief that is in conflict with the premise of the experiment. That's the inconsistency.
Amar Hadzihasanovic (Jun 16 2020 at 12:43):I just find it a bit sad because it seems to accept fraud as science, if by accident the fraud happens to be on to something.
(=_=) (Jun 16 2020 at 12:44):Amar Hadzihasanovic said:
I just find it a bit sad because it seems to accept fraud as science, if by accident the fraud happens to be on to something.
A lot of fraud is done using very scientific methods -- that's how frauds succeed. It doesn't make it any less fraudulent.
Amar Hadzihasanovic (Jun 16 2020 at 12:45):Sure, in the end it's just about how we want to call things. Whether it's “fraudulent science” or “fraud, not science”.
(=_=) (Jun 16 2020 at 12:46):Amar Hadzihasanovic said:
Ok, fair enough! So we disagree on whether the intent of the experimenter matters in judging what's science. That's ok.
I'm not sure why the intent of the experimenter came into the picture here. I think you had in mind "pseudoscience", so why not just say it?
(=_=) (Jun 16 2020 at 12:47):Talking about "intent" tends to lead to very subjective and unproductive conversations.
Amar Hadzihasanovic (Jun 16 2020 at 12:47):No, I did not mean pseudoscience. One can genuinely believe in pseudoscience. I'm sure most homeopaths do.
Amar Hadzihasanovic (Jun 16 2020 at 12:48):I would call that bad science, pseudoscience, but not “not science”.
(=_=) (Jun 16 2020 at 12:48):I think I'm completely lost at this point now.
(=_=) (Jun 16 2020 at 12:50):@moderators Can we get an airlift to #philosophy please? I think that stream has been rather quiet lately, and would appreciate this lively conversation.
(=_=) (Jun 16 2020 at 12:51):Amar Hadzihasanovic said:
I would call that bad science, pseudoscience, but not “not science”.
I think a lot of scientists would want to disagree with you on this.
Amar Hadzihasanovic (Jun 16 2020 at 12:53):I think if you'd rather include frauds and exclude cranks from science, the priorities are wrong.
Amar Hadzihasanovic (Jun 16 2020 at 12:55):I'm sorry that you are lost, I thought we had reached something.
Amar Hadzihasanovic (Jun 16 2020 at 12:56):We disagreed on a specific situation that you would count as scientific and I would not. That seems like progress from just “not understanding the meaning of each other's words”.
Amar Hadzihasanovic (Jun 16 2020 at 12:57):It means the disagreement is definitional after all.
Notification Bot (Jun 16 2020 at 13:15):This topic was moved here from #practice: applied ct > What are Maths and Science? by [Mod] Morgan Rogers
Morgan Rogers (he/him) (Jun 16 2020 at 13:16):Rongmin Lu said:
@moderators Can we get an airlift to #philosophy please? I think that stream has been rather quiet lately, and would appreciate this lively conversation.
Done.
Morgan Rogers (he/him) (Jun 16 2020 at 13:20):Amar Hadzihasanovic said:
No, I did not mean pseudoscience. One can genuinely believe in pseudoscience. I'm sure most homeopaths do.
I have to say I'm a little confused too. If homeopaths believe that what they are doing is science, that makes it so?
And on the flip side, if someone performs an experiment that disproves the existence of something they had thought was real (eg the existence of the ether), was everything they did leading up to that point no longer science?
Morgan Rogers (he/him) (Jun 16 2020 at 13:31):Amar Hadzihasanovic said:
I just find it a bit sad because it seems to accept fraud as science, if by accident the fraud happens to be on to something.
If a hoax is presented/supported using scientific methods, the fraud lies in the falsification of the results of experiments. Whenever pseudoscience is approached with an unbiased scientific method, it either becomes self-defeating (the phenomenon is consistently disproven) or a genuine underlying cause for the apparent success of the pseudoscience is identified.
Amar Hadzihasanovic (Jun 16 2020 at 13:41):As I've said I'm not interested in defining what “proper” science is. I was trying to get to an agreement on what we can exclude from science under a maximally inclusive definition: one from which nobody will be offended by being excluded, if not in bad faith.
Amar Hadzihasanovic (Jun 16 2020 at 13:44):With the goal of supporting my claim that science is not purely about performance, in the sense that the same performance can be science or not science depending on its purpose. It seems that at least Rongmin disagrees with my example.
Amar Hadzihasanovic (Jun 16 2020 at 13:46):I think that “frauds acting in bad faith” are not doing science even under a maximally inclusive definition.
Amar Hadzihasanovic (Jun 16 2020 at 13:47):(The kind of definition that would include even the crank claiming to disprove “Einstien's equation” with an arithmetic error in the first line.)
Morgan Rogers (he/him) (Jun 16 2020 at 14:03):Amar Hadzihasanovic said:
As I've said I'm not interested in defining what “proper” science is.
How and why do you want to classify what a word or concept refers to without defining it? That is, why do you feel justified in marking out what "is" and "isn't" science when you're avoiding stating what you are interpreting science to mean? This is a Category Theory forum, definitions are pretty important to a lot of people here!
I personally subscribe (for the most part) to Bunge's definition of what (a) science is, as described in the article I linked earlier, which explicitly excludes pseudoscience, notably of the kind you are describing as fraudulent. It is not purely performative, in that it is required to include up-to-date knowledge and well-defined principles, and its description includes the community of people involved in its study. I would be interested to hear what you think of his take, actually, since we've moved this conversation to #philosophy.
Amar Hadzihasanovic (Jun 16 2020 at 14:37):I don't want to classify what a word or concept refers to! I've been tried to avoiding that from the start :D
Amar Hadzihasanovic (Jun 16 2020 at 14:38):All I need for the specific point I was making is to agree on an example of what is not science. That doesn't need a full definition!
Amar Hadzihasanovic (Jun 16 2020 at 14:39):You can agree that the discrete space with two points is not a connected space before we decide what definition of connectedness we're using.
Amar Hadzihasanovic (Jun 16 2020 at 14:44):I mean, that's the very way we develop definitions in mathematics! We have a bunch of examples that we want to include, and a bunch of examples that we want to exclude. Those come before the definition. In a sense they determine a space of allowable definitions.
Amar Hadzihasanovic (Jun 16 2020 at 14:44):So what I'm trying to say is: “here's an example of what for me should not be seen as science, whatever definition of science we're using”
Amar Hadzihasanovic (Jun 16 2020 at 14:50):Anyway, thanks for linking Bunge's article. I will try to read it. But I would like to check out of this debate for the moment, as I've spent too much time on it today.
(=_=) (Jun 16 2020 at 16:03):Amar Hadzihasanovic said:
I think if you'd rather include frauds and exclude cranks from science, the priorities are wrong.
I think I've been misunderstood. To be very clear, I certainly think that fraudsters and cranks should not be considered to be doing good science -- or good maths either! Does this mean science is a "closed world" culture? Yes, contrary to what you were arguing. But I think I've already argued the initial premise of Jules was not very well-founded.
About fraudsters: What I did say was that successful fraudsters are often perpetuating their fraud using methods that can be said to be developed on a scientific basis, otherwise they wouldn't be successful at all. The fraudsters going about their business using non-scientific methods are relying on luck for their success. The fraudsters that perpetuate fraud using a well-tested system are more likely to succeed.
As for excluding cranks, well, a lot of scientists would certainly agree with that. I don't see why you'd want to take me to task for that. The line between a crank and a fraudster can sometimes be very blurry.
(=_=) (Jun 16 2020 at 16:19):Amar Hadzihasanovic said:
As I've said I'm not interested in defining what “proper” science is. I was trying to get to an agreement on what we can exclude from science under a maximally inclusive definition: one from which nobody will be offended by being excluded, if not in bad faith.
I'm not interested in this maximally inclusive definition, because this discussion was kicked off by an ill-founded notion of what it means for a culture to be "open world" or "closed world". People have long held a "closed world" view of what science should be: it has long excluded "bad science", "pseudoscience" and things that are "not even science".
(=_=) (Jun 16 2020 at 16:26):In that sense, "science" is like "maths". Science, contrary to the argument you've presented, isn't an "open world" culture: in fact, you've already sought to make it a "closed world" by restricting its subject matter to "the real world", while I was pushing for it to include "counterfactual worlds".
You've now shifted the criteria to "intent", or whether a person is doing something in good or bad faith. As Morgan and I have pointed out, that is irrelevant to what science is about. The successful fraudulent mystic in your example would have used methods of a scientific nature to develop a system by which they could successfully defraud their victims. The good-faith believer in homeopathy is not doing science merely because of their good intent: any success can be attributable to the placebo effect, luck, or to the incidental adoption of scientific methods that produce results.
Thus, intent and the nature of the methods being used are two independent issues. You seem to be conflating the two in order to justify the ill-founded notion that "science" and "maths" somehow differ on their "openness". I've already pointed out where that flawed notion arose.
(=_=) (Jun 16 2020 at 16:32):Amar Hadzihasanovic said:
All I need for the specific point I was making is to agree on an example of what is not science. That doesn't need a full definition!
Firstly, I'm not sure what specific point you're making. Secondly, specifying what is not science does require working towards a full definition: this can be part of what a full definition is about.
(=_=) (Jun 16 2020 at 16:35):Amar Hadzihasanovic said:
You can agree that the discrete space with two points is not a connected space before we decide what definition of connectedness we're using.
No, I can't. Why can't a space with two points be connected? Is it because you've assumed discreteness? What is discreteness then? And so on.
Amar Hadzihasanovic (Jun 16 2020 at 16:48):Everything you just wrote is either irrelevant, or in contradiction with what I said, or I previously addressed it and you ignored it.
I have lost interest, please carry on without me.
John Baez (Jun 16 2020 at 17:15):Rongmin Lu said:
For what it's worth, I think John was happy to call himself a mathematical physicist, even though he's never been in anywhere but a maths department.
By the way, mathematical physicists have traditionally been in math departments: in the US, at least, a "mathematical physicist" is a breed of mathematician, despite the way the phrase looks.
The book Modern Methods in Mathematical Physics sets the tone: it's written by Barry Simon and Michael Reed, both in math departments, and it's full of theorems. I got my start on mathematical physics with Elliot Lieb and then Irving Segal, both in math departments.
The goal of mathematical physics - at least before Witten - was to rigorously formulate physical theories and prove theorems justifying what physicists do. It often involves a lot of analysis.
John Baez (Jun 16 2020 at 18:09):About the previous conversation:
John Baez (Jun 16 2020 at 18:11):I think internet discussions are most productive when everyone avoids criticizing each other personally and focuses on issues. As soon as I see phrases like this, I get worried:
John Baez (Jun 16 2020 at 18:12):"you have a rather superficial view"
John Baez (Jun 16 2020 at 18:13):"that is really muddled thinking" (not exactly personal criticism, but close)
John Baez (Jun 16 2020 at 18:14):"I think you're very confused here"
John Baez (Jun 16 2020 at 18:15):When people feel personally attacked, the conversation tends to change from "the play of ideas" to "a fight to defend oneself". Adrenaline and other biological responses kick in. People's ability to admit mistakes or simply change their mind drops.
John Baez (Jun 16 2020 at 18:16):So, it's great to catch oneself, whenever one is about to write a sentence attributing negative qualities to one's discussion partner, and rewrite it as a sentence about ideas.
John Baez (Jun 16 2020 at 18:17):It can be as simple as changing "you're wrong to say hydrogen is an inert gas" to "it's wrong to say hydrogen is an inert gas".
John Baez (Jun 16 2020 at 18:18):Or even better: "hydrogen is not an inert gas". Here the business of being "wrong" is not at the forefront!
John Baez (Jun 16 2020 at 18:20):It takes some training to notice that one is personalizing a discussion, starting to talk about the bad qualities of the other person instead of talking about ideas.
John Baez (Jun 16 2020 at 18:21):But if one looks at one has just written, before hitting "send", it's always possible to see the difference.
(Avoid using the "Press enter to send" button, since it eliminates this crucial moment of reflection.)
John Baez (Jun 16 2020 at 18:23):I find that after some years of practice I'm almost always able to avoid attributing negative qualities to my discussion partner. When it seems impossible I usually try to stop talking.
It seems to help a lot.
Gershom (Jun 16 2020 at 23:53):Rongmin Lu said:
Simply considering a single counterfactual, like assuming 0=1, will lead to inconsistencies in the world you believe in. Of course this will, more often than not, lead to a system of beliefs that isn't scientific.
Assuming 0=1 doesn't lead to inconsistencies. On the contrary, it, marvelously, makes everything consistent!
(=_=) (Jun 17 2020 at 07:32):Gershom said:
Rongmin Lu said:
Simply considering a single counterfactual, like assuming 0=1, will lead to inconsistencies in the world you believe in. Of course this will, more often than not, lead to a system of beliefs that isn't scientific.
Assuming 0=1 doesn't lead to inconsistencies. On the contrary, it, marvelously, makes everything consistent!
Making "everything" (i.e. every event, regardless of possibility) consistent tends to make things very uninteresting, which is counterproductive if the goal is to build interesting counterfactual worlds as backdrops to narratives.
(=_=) (Jun 17 2020 at 07:37):Amar Hadzihasanovic said:
Everything you just wrote is either irrelevant, or in contradiction with what I said, or I previously addressed it and you ignored it.
I have lost interest, please carry on without me.
My sentiments exactly. I'm glad we've agreed on something.
(=_=) (Jun 17 2020 at 07:40):John Baez said:
By the way, mathematical physicists have traditionally been in math departments: in the US, at least, a "mathematical physicist" is a breed of mathematician, despite the way the phrase looks.
I'm sure it is, but that hasn't stopped "physical mathematician" from being floated as a more "mathematical" alternative to "mathematical physicist" once upon a time. I thought that was pretty daft when I first heard of it.
The goal of mathematical physics - at least before Witten - was to rigorously formulate physical theories and prove theorems justifying what physicists do. It often involves a lot of analysis.
It's funny how we're now starting to realise there's more algebra to it than we'd expected.
Morgan Rogers (he/him) (Jun 17 2020 at 09:27):Amar Hadzihasanovic said:
All I need for the specific point I was making is to agree on an example of what is not science. That doesn't need a full definition!
I see what you're getting at. Just as we can often construct a supporting hyperplane for a function without perfect information about the values the function takes everywhere, we can give partial information about what cases a definition should include or exclude.
Morgan Rogers (he/him) (Jun 17 2020 at 09:27):I'm sorry that this discussion went the way it did. Thanks for the wisdom, @John Baez.
Fabrizio Genovese (Jun 17 2020 at 09:48):Amar Hadzihasanovic said:
Rongmin Lu I think there is a mismatch between “external” and “internal” in the way that we are referring to the 'counterfactual world'.
Let's put it this way: I am suggesting that whether something is science depends on the purpose of who is doing it. So something is not science unless the person doing it, is doing it to learn something about (some) 'reality'.
This makes it very clear for me what science can have in common with arts in your view. I think what you said here is exactly one of the most defining features of contemporary art. What makes art art is, indeed, the artistic purpose. This is why a can of beans is just a can of beans, unless someone (e.g. Warhol) puts it in a gallery, giving it an artistic purpose that makes it art.
Fabrizio Genovese (Jun 17 2020 at 09:49):I agree this is VERY hard to digest for people that are unexposed to contemporary art, and the ultimate reason why many of those people "don't understand it" or "believe it is a fraud, or meaningless".
Fabrizio Genovese (Jun 17 2020 at 09:51):Still, the presence of purpose is one of the few things that really 99% of art forms since the first paintings in caves have in common. The Venus of Willendorf had artistic purpose. As Michelangelo's frescoes, as a painting by Borremans, as a performance by Abramovic or Cattelan's banana.
John Baez (Jun 17 2020 at 19:33):Rongmin Lu said:
John Baez said:
By the way, mathematical physicists have traditionally been in math departments: in the US, at least, a "mathematical physicist" is a breed of mathematician, despite the way the phrase looks.
I'm sure it is, but that hasn't stopped "physical mathematician" from being floated as a more "mathematical" alternative to "mathematical physicist" once upon a time. I thought that was pretty daft when I first heard of it.
I've heard it, but almost nobody uses it. Another little-used classification is "theoretical mathematician", proposed by Jaffe and Quinn as a way to distinguish rigorous mathematics from the kind of work Witten and others do, using physics to come up with new mathematical ideas. Their paper was met with an outpouring of scorn from Michael Atiyah, Benoit Mandelbrot, René Thom and others - quite amusing to read.
Fabrizio Genovese (Jun 17 2020 at 20:06):John Baez said:
Rongmin Lu said:
John Baez said:
By the way, mathematical physicists have traditionally been in math departments: in the US, at least, a "mathematical physicist" is a breed of mathematician, despite the way the phrase looks.
I'm sure it is, but that hasn't stopped "physical mathematician" from being floated as a more "mathematical" alternative to "mathematical physicist" once upon a time. I thought that was pretty daft when I first heard of it.
I've heard it, but almost nobody uses it. Another little-used classification is "theoretical mathematician", proposed by Jaffe and Quinn as a way to distinguish rigorous mathematics from the kind of work Witten and others do, using physics to come up with new mathematical ideas. Their paper was met with an outpouring of scorn from Michael Atiyah, Benoit Mandelbrot, René Thom and others - quite amusing to read.
Lol, some of those answers are priceless!
(=_=) (Jun 18 2020 at 06:24):Fabrizio Genovese said:
This makes it very clear for me what science can have in common with arts in your view. I think what you said here is exactly one of the most defining features of contemporary art. What makes art art is, indeed, the artistic purpose. This is why a can of beans is just a can of beans, unless someone (e.g. Warhol) puts it in a gallery, giving it an artistic purpose that makes it art.
I agree this is VERY hard to digest for people that are unexposed to contemporary art, and the ultimate reason why many of those people "don't understand it" or "believe it is a fraud, or meaningless".
I enjoy contemporary art and I get (but disagree with) what Amar meant, but I wasn't the one who raised the scenario of fraud (in this case, a fraudulent mystic defrauding gullible victims).
I don't see the relevance of the "intent" of the practitioner in this conversation, which seems to have been equivocated with the "presence of purpose" in a work of art in your recent comment. The nature of the practitioner's "intent" is very hard to discern and can be feigned, so it is very unhelpful to talk about whether or not something was done with "scientific intent". That's why, when people actually consider what "science" is, a lot of focus is placed on the methods, not on some nebulous and inaccessible internal mental state of the practitioner.
John Baez (Jun 18 2020 at 06:29):Fabrizio Genovese said:
Lol, some of those answers are priceless!
Yes. And Jaffe and Quinn deserved it. Some of what they said was simply outrageous, like blaming Poincare for the "slow start" of algebraic topology - sort of like blaming the Wright Brothers for the slow start of modern aviation.
John Baez (Jun 18 2020 at 06:30):According to them he should have conjectured less and proved more.
(=_=) (Jun 18 2020 at 06:33):Fabrizio Genovese said:
Amar Hadzihasanovic said:
Rongmin Lu I think there is a mismatch between “external” and “internal” in the way that we are referring to the 'counterfactual world'.
Let's put it this way: I am suggesting that whether something is science depends on the purpose of who is doing it. So something is not science unless the person doing it, is doing it to learn something about (some) 'reality'.
This makes it very clear for me what science can have in common with arts in your view. [...]
This is the origin of the subsequent disagreement. When I used the word "internal" in the preceding discussion, it was by analogy with what "internal" means in CT. That is to say, if in a counterfactual world, a "fizzy drink" has been identified with "fairy blood", then it is inconsistent to argue that a "blood test" in that counterfactual world, which presumably will give some sort of result with things of the type "blood", will not give any result with a "fizzy drink" that is identical with 'fairy blood" in that world.
(=_=) (Jun 18 2020 at 06:43):Let's consider a more timely example to illustrate why this is inconsistent.
Suppose travel between parallel Earths is possible and a traveller arrives from another Earth that differs from our Earth by some key political fact, e.g. X isn't the leader of country Y where they're from, but W is. From "our" perspective, the proposition A:= "leader W is the leader of country Y" is a counterfactual; to the traveller, that is a fact on their Earth that has now become a counterfactual upon their arrival on our Earth.
If the traveller were to then assert A, while on our Earth, they would be asserting something inconsistent with the situation on our Earth. If they were to act as in the fairy blood example -- do something to test the truth of not-A, while believing in A and arguing that the results will show A -- their actions would also be judged on our Earth to be incompatible with the internal logic of the situation on our Earth.
That's what I meant by "internally consistent" within the counterfactual world. It does NOT mean taking into account the "internal mental state" of the practitioner at all. It just means respecting the internal logic of the counterfactual world itself.
(=_=) (Jun 18 2020 at 06:55):John Baez said:
I've heard it, but almost nobody uses it.
This was brought up by Amar as something he was told, so apparently there exists at least one person who uses it.
Another little-used classification is "theoretical mathematician", proposed by Jaffe and Quinn as a way to distinguish rigorous mathematics from the kind of work Witten and others do, using physics to come up with new mathematical ideas. Their paper was met with an outpouring of scorn from Michael Atiyah, Benoit Mandelbrot, René Thom and others - quite amusing to read.
Thanks for reminding me of that. There is some historical value to reading these documents, and I see that some of the remarks in those letters are relevant to this discussion.
(=_=) (Jun 18 2020 at 07:16):I particularly liked the letter of Karen Uhlenbeck, who echoes what I think of the original "closed/open world" interpretation:
My main criticism of the [Jaffe-Quinn] article is that it draws broad conclusions from too narrow a perspective.
In particular, her criticism of the term "theoretical mathematics" also strikes at the heart of the preceding discussion:
I have serious objections of another sort to the idea of creating a discipline called "theoretical mathematics". Setting aside the semantics, in the broader context of its description, "theoretical mathematics" already exists. It is called "applied mathematics", a much bigger field than pure mathematics. Applied mathematics is done mostly outside departments of mathematics and draws in far more resources and many broad scientific interests. Only the combined elitism of very pure mathematics and high-energy fundamental physics would claim that its own brand of speculative and applicable mathematical structure should have a special name.
(=_=) (Jun 18 2020 at 07:19):And a nice quote from Uhlenbeck for the edification of [Mod] Morgan Rogers:
[P]ure mathematicians might well spend even more time building intellectual bridges to the rest of the scientific world. Jaffe and Quinn imply that it would help to collect a toll for crossing one of few well-built bridges. They have, however, done a great service by describing it in detail as worthy of tariff.
(=_=) (Jun 18 2020 at 07:33):I think I'd like to get back to tackling the question that [Mod] Morgan Rogers posed for us in naming this topic.
(=_=) (Jun 18 2020 at 07:33):What are Maths and Science?
(=_=) (Jun 18 2020 at 07:37):So John Baez tweeted about this blog post that briefly discusses what Eric Drexler thinks is the difference between "scientific inquiry" and "engineering design", as he wrote in Radical Abundance. I think this is helpful for answering the question of this topic.
@sarah_zrf @_julesh_ Eric Drexler has written eloquently about how science is adjoint to engineering: https://fs.blog/2013/07/the-difference-between-science-and-engineering/ He just needs a bit more category theory. https://twitter.com/johncarlosbaez/status/1273342937322029056/photo/1
- John Carlos Baez (@johncarlosbaez)
(=_=) (Jun 18 2020 at 07:39):Here's the diagram in John's tweet, which I will have occasion to refer to in the following.
(=_=) (Jun 18 2020 at 07:48):While this is a nice diagram, I'm skeptical of unidirectional flowcharts, because they tend to hide the presence of feedback and iterative actions. An example of a flawed unidirectional flowchart having an adverse effect is the idea that software development should follow the waterfall model, which was given a formal description by Winston W Royce in 1970 (ironically enough, to exemplify a flawed, non-working model of software development). I think this diagram by Drexler is similarly flawed, and he does acknowledge this in the text excerpted in the blog.
(=_=) (Jun 18 2020 at 07:58):A similar flaw exists in the usual distinction between mathematics and science. In Drexler's diagram, mathematics would take the place of "engineering design": mathematics is supposed to proceed by deduction from theory ("abstract model") to consequences ("useful product"), while science is supposed to proceed by induction from systems to theory.
(=_=) (Jun 18 2020 at 07:58):In reality, of course, the information flow in both maths and science is iterative and bidirectional.
In scientific inquiry, studying systems leads to theories by which we design new experiments to elicit more information about the objects of study and thus more theoretical development.
In mathematical inquiry, different lines of research can sometimes converge when someone observes (by "induction", i.e. postulating new hypotheses from the available results) that a more generalised structure or a system of axioms can subsume current results. Negative theorems can also send us to the drawing board to re-think the definitions of the mathematical objects we're working with.
(=_=) (Jun 18 2020 at 08:03):This suggests that we should model maths and science as "learning systems" or "learners", by analogy with Fong et al.'s Backprop as Functor. By an observation of Jules Hedges, these are also open games, so we may think of the practitioner of maths or science as being "Player 1" in a game with a certain "Player 2". Usually, "Player 2" is called the "environment", which is an analogy that works for science, but what is "Player 2" for maths then, without resorting to Platonism?
(=_=) (Jun 18 2020 at 08:15):Here's where I need to refer again to Drexler's diagram.
I've proposed earlier that maths can stand in for "engineering design" in the diagram, because of its emphasis on the deductive process. I should emphasise, once again, that one should not be misled by the diagram into thinking that the process is unidirectional.
Of course, maths does not have, as its goal, the direct creation of useful physical systems. What it does is produce useful theories in service of science. This means we should stack the "engineering design" (aka "maths") diagram on top of the "scientific inquiry" diagram. As a corollary, the "flow of information" arrow along the "scientific inquiry" side now points towards the direction of increasing abstraction.
(=_=) (Jun 18 2020 at 08:33):Going back to the game-semantic interpretation, we may now see that "Player 2" or the "environment" for maths turns out to be... the abstract model itself! In fact, you can stack more "maths" diagrams on top of the "abstract model" module of the original "maths" diagram, which corresponds to the further abstractions that would eventually lead to "pure" mathematics.
Incidentally, this is probably why Platonism seems to be intuitively true to mathematicians, even though it's not well-justified on philosophical grounds. Box's aphorism probably applies here.
(=_=) (Jun 18 2020 at 08:42):Back to the question of this topic: What are maths and science?
In terms of what I have discussed above, it's probably not too much of a shock to conclude that mathematics is a science. This echoes what Armand Borel wrote in his letter in response to Jaffe-Quinn's "theoretical mathematics":
I have often maintained, and even committed to paper on some occasions, the view that mathematics is a science, which, in analogy with physics, has an experimental and a theoretical side, but operates in an intellectual world of objects, concepts and tools. Roughly, the experimental side is the investigation of special cases, either because they are of interest in themselves or because one hopes to get a clue to general phenomena, and the theoretical side is the search of general theorems. In both, I expect proofs of course, and I reject categorically a division into two parts, one with proofs, the other without.
Jason Erbele (Jun 23 2020 at 07:14):I don't quite understand why doing a blood test on coca cola should not be considered science. Motivation, belief, and good faith of the experimenter don't seem to come into play at all (aside from the social aspect of science, where good faith is important in reporting the results).
Jason Erbele (Jun 23 2020 at 07:14):The act of performing the experiment, recording the results, and comparing against the expected results sounds to me like science, regardless of the experimenter's a priori beliefs. How often is history littered with scientific advances where an experiment was accidentally performed, where the best minds of the day "knew" it would be "stupid" to intentionally carry out the experiment?
Jason Erbele (Jun 23 2020 at 07:15):If the coca cola blood test gave an unexpected result, that would be the basis for further inquiry. If the coca cola blood test gave the expected result, that would support the prevailing theory. Either way, the application of the process – intentionally or not – would be an example of science.
(=_=) (Jun 23 2020 at 08:08):Jason Erbele said:
How often is history littered with scientific advances where an experiment was accidentally performed, where the best minds of the day "knew" it would be "stupid" to intentionally carry out the experiment?
Exactly, and we already know one example in our lifetime. The 2005 Nobel Prize in Physiology or Medicine was given to two Australian doctors, Barry Marshall and Robin Warren, for their work in discovering the role of the bacterium Helicobacter pylori in causing gastritis. This theory was dismissed by all the experts at the time -- everybody "knew" stress was the culprit -- until Barry Marshall ingested the bacteria himself and developed gastritis.
(=_=) (Jun 23 2020 at 12:36):Jason Erbele said:
I don't quite understand why doing a blood test on coca cola should not be considered science. Motivation, belief, and good faith of the experimenter don't seem to come into play at all (aside from the social aspect of science, where good faith is important in reporting the results).
Earlier, it was asserted that the difference between mathematics and science was:
I can do maths about a counterfactual world, I can do dance and paintings about a counterfactual world, but by definition I can't do science about a counterfactual world (unless it's really just maths).
This was what motivated the whole "doing a blood test on a fizzy drink" scenario. The argument was that, since the experimenter was "pretending" that a fizzy drink is "fairy blood", then it can't be science. Morgan and I made the same point as you did, and I also pointed out that the counterfactual world being considered is inconsistent.