The Symposium

Mozibur Ullah

2:12 AM

Hi there david, are you there?

David H

Yep. And welcome to the chat feature! A member as active as you are would be a welcome addition here.

Mozibur Ullah

How does one invite people to a chat session? I tried the chat link at the top of the page - but he room was empty.

I thought there would be some feature to invite people along?

Where are you based? Over the pond?

David H

I don't how to invite people to chat directly other than by copying & pasting the URL like I did.

Over the pond? I don't understand the question

Mozibur Ullah

Ok, I'll remember that tip next time!

I mean the USA - the atlantic being the pond. British humour.

David H

Ah, I'll file that away. Yes indeed, 'Murica as we call it here

Mozibur Ullah

2:22 AM

I try to use the stack as a way of helping me learn phhilosophy - which is one reason why I've been active on it.

What sparked your interest in philosophy?

Are you studying it?

David H

Not formally, no. I'm a physics student, and for all practical purposes a math student as well..

Mozibur Ullah

Ah, I thought as much from that comment.

You prefer the maths to the physics?

David H

and I minored in history of science in undergrad. My hobbyist interest in philosophy just naturally grew over time as I acquired more and more questions that weren't answered in my physics work

Mozibur Ullah

I find that the one tends to confuse the other somewhat.

There so much technique to learn in physics/maths that other good questions kinda get pushed aside a bit.

David H

Well yes and no

Mozibur Ullah

2:29 AM

Do you get involved in actual grungy experiments?

Or are they all done on computers these days:)

David H

Hehe, that HAS been the common stereotype hasn

't it?

Mozibur Ullah

Yup, sure is.

David H

I'm a grad student, so there's really no avoiding SOME experimental work

Mozibur Ullah

How does that work?

Do you get to choose what to work on?

David H

For the most part

Mozibur Ullah

2:32 AM

There can't b as much choice as there is in actual theoretical work.

Which area are you working in?

David H

Usually, the decision of where to go to grad school though is based mostly on who you wanna work under and in what field you'd like to study

Mozibur Ullah

Rather than what big experiment you want to work on?

Grad school is tough I hear in the states. Do they still make you take exams during the process?

David H

My focus is on magnetohydrodynamics

Mozibur Ullah

I'm not even sure what that is!

magnetism in plasma?

or liquid metals?

David H

It's exactly what it sounds like of course! fluid dynamics with magnetic fields

Plasmas being the principle object of study

Mozibur Ullah

2:36 AM

yes, but i was trying to imagine swirling water with magnets...

ok, got it.

David H

well plasmas are fluids of electrical charges, so they react to a magnetic field. unlike say, air

Mozibur Ullah

like in the sun.

David H

exactly.

Mozibur Ullah

don't they produce them in fusion reactors too?

David H

that's actually the principal commercial interest in the field

Mozibur Ullah

2:39 AM

I thought fusion as commerical enterprise was still a distant prospect, is that changing now?

David H

My focus is actually more towards understanding the Earth's core

Mozibur Ullah

I imagine that is one very viscous liquid!

David H

as a viable of source of energy? no that's not really changing I suppose

Before I forget, here's a link I wanted to make sure I showed you (on the topic of your questions earlier)

Mozibur Ullah

sure.

David H

A Party Space for Philosophy.SE! Both philosophy and mundane c...

er no

Theory of conjoint measurement

The theory of conjoint measurement (also known as conjoint measurement or additive conjoint measurement) is a general, formal theory of continuous quantity. It was independently discovered by the French economist Gérard Debreu (1960) and by the American mathematical psychologist R. Duncan Luce and statistician John Tukey . The theory concerns the situation where at least two natural attributes, A and X, non-interactively relate to a third attribute, P. It is not required that A, X or P are known to be quantities. Via specific relations between the levels of P, it can be established that P,...

Mozibur Ullah

2:45 AM

it looks interesting.

David H

and unfortunately highly overlooked

Mozibur Ullah

I'm not quite sure what they mean by 'non-interactively relate'

David H

an axiomatic theory of measurement is long overdue

Mozibur Ullah

I never knew there wa a field called mathematical psychology! it figures, though

Its intriguing that Dana Scott is involved - as he's a highly rated mathematician. computer science mainly from what I understand.

David H

Patrick Suppes is also highly regarded

Mozibur Ullah

2:50 AM

And I've heard of debreu somewhere too.

still I find it puzzling that they can start with an assumption that the quantities they are attempting to measure are not quantities.

perhaps they mean that the actual knowledge of how it is quantified is missing.

Dana scott worked in topology - so lots of experience with continuous functions there.

David H

Well think about Peano's axioms

Mozibur Ullah

and of course you can have a space with a topology.

and that doesn't have to be quantified with numbers.

David H

You don't start have to start knowing that you're dealing with the natural numbers. You just have to verify that the peano axioms hold and then you can use anything that follows from the axioms

Mozibur Ullah

sure, but people didn't come up with peanos axioms out of thin air. Peano was axiomitising arithmetic - something that hadn't been done before.

But I see what you mean.

David H

and the goal here is to axiomatize quantity and measurement

Mozibur Ullah

2:57 AM

Isn't that in how you decide to measure?

Like with a ruler?

Or a clock?

David H

I'm not sure what exactly you're asking there. Could you elaborate?

(I realize we're dealing with something that's very difficult to verbalize so this may take some patience)

Mozibur Ullah

I mean you still are making the choice of parameter to measure.

how do you axiomatise that?

also every theory I know of has assumptions built in.

The peano axioms for example is built around the model of numbers.

David H

ah I think I understand

Mozibur Ullah

you could instead make a choice of a set of models.

but that choice is already made.

David H

let's talk about length measurement from a fundamental perspective

Mozibur Ullah

3:03 AM

what happens when you come across something that your axiomatic theory wasn't built to work with

you then adapt it.

let me give you another example

David H

ok

Mozibur Ullah

the category of topological spaces can be used as a space of measure of cohesion and proximity

but it has an in-built assumption that there are points

this has not been usually thought of as a problem

but there are theories which now prefer not to have to make that choice

so you have generalised topological spaces called locales that don't have them - unless you put them in.

this isn't a new idea.

in the early days of topology, guys like whitehead were pushing merelogy

mereology as an alternative to topology as a theory of area

and regions

it didn't have points

but topology kinda won out

but do you see the point i'm making?

David H

I think so

the thing, having points usually doesn't present a problem

Mozibur Ullah

well, yes.

for most but not all purposes

the question you were asking was the fundamental & presumably philosphical question as to what it means to measure

in which case exceptional situations are the important ones to look at

David H

but exceptional to what?

Mozibur Ullah

3:10 AM

you know feynman path integral?

that although it works - it isn't mathematically well defined?

using the standard theory of measure?

David H

pointless topology generalizes topology with points, but we needed to axiomatize normal topology before generalizing was even an option

Mozibur Ullah

because there is no translation invariant measure on an infinite dimensional space

which is a property you would expect a measure to have

someone showed recently that if you dropped the requirement for points

you can get that property

thats the way it worked out historically.

David H

I'm familiar with measure theory, but I was unaware of that interesting result. that's neat

Mozibur Ullah

but like I said Whitehead and others were exploring other approaches - mereology

ultrafilters on a space give a topology

to be honest the problem isn'tin the topology

its in the set theory underneath it

but still - lets get back to this problem of measurement

Its a new result - I only saw it a few days ago somewhere

David H

I'd like to look into sometime. If you could save me the trouble of finding a link, that would be great

but yes, back on the topic of measurement.

Mozibur Ullah

3:17 AM

sure.

what confuse me about it being axiomatic - is that there are choices that are not determined.

if you measure the area of a table

you and I will get the same result

if you and I were to measure the psychological profile of someone

and we happen to disagree on methodology

as we look we do here

we're going to get different results.

David H

that's what axioms are for, in a way

axioms are an agreement on methodology

Mozibur Ullah

I think you're conflating two concepts.

I can agree that for example that there is a set of of axioms for a theory

but refuse to belive or agree with them

David H

Perhaps that does slightly conflate the two, but meant the relation as only implicit

Mozibur Ullah

still - lets decide we agree on an axiomatic framework - that is we agree on a methodology

and lets think about peanos axioms

suppose with peanos axioms you proved that 2+3=7

I wouldn't accept that answer, and simply say that the axioms aren't quite right

because we're already familiar with how numbers behave

that is the truth about numbers come about before the truth of the framework

David H

I don't agree

Mozibur Ullah

3:28 AM

How?

you mean what I said about peanos axioms?

David H

about numerical truths

mathematical truths are defined as those which follow from axiomatic truths

Mozibur Ullah

are you saying that this is how they have come about?

David H

Like Euclid's parallel postulate

it wasn't really a mathematical truth about parallel lines, but a physical truth

Mozibur Ullah

Do you at least agree that people were working with numbers in an intuitive way before peano came up with his axioms?

David H

surely

Mozibur Ullah

3:33 AM

so if Peano came to you and bragged about this new axiomatic system that hes put together for the natural numbers

and asked you whether you wanted to take it for a run

so you did, and following all the rules

you showed that 2+3=7

its a formal truth

since it was consistently deduced from the axioms

but don't you think Peano would be a bit embarrassed about his claim to axiomatising the natural numbers?

David H

I think you're missing my point

Mozibur Ullah

Which is?

You're talking about formal deductions in a formal system

I'm talking about axiomatising something

David H

my point is that numbers are formal objects, so they really don't have any existence to speak of without a formal system

Mozibur Ullah

so the babylonians were working with a formal system?

David H

oh heavens, no

Mozibur Ullah

3:39 AM

so, how is that consistent with what you just said?

My basic point is this - we have something in nature. we try to axiomatise its properties. we need to make sure that this axiomatisation works.

Its an intersting question why plane geometry was axiomatised 2000 years ago

David H

The Babylonians obtained their rules for adding and multiplying numbers by adding and multiplying rocks and assuming that the distinction between numbers and rocks didn't matter

Mozibur Ullah

but no-one bother with numbers until recently

well thats how I learnt to deal with numbers too.

if I remeber my childhood correctly

anyway lets track this back a bit

are you claiming that all things and conepts can be measured?

David H

That's because up until the recent(ish) discovery of things like non-Euclidean geometry, the assumption of a fairly direct correspondence between physical reality and mathematical reality was taken granted

Not at all!

Mozibur Ullah

ok, at least thats one thing we can agree with!

Cerberus

phew!

David H

3:46 AM

My lord, is that what you thought I thought?

Cerberus

I would expect a Kant-fan to mostly agree with Hume as well, but...

Mozibur Ullah

I did kind of.

Cerberus

So I'll assume your discussion was about a tiny little detail of a huge theory that you already agreed on.

Mozibur Ullah

to be honest, I'm not keen on the idea of quantitive measurements of human & subjective characteristics.

David H

You mean my comment on the page about measuring success?

Mozibur Ullah

3:48 AM

that too.

Cerberus

Measuring success, and not as a metaphor?

Mozibur Ullah

I think sometimes one can suppose that there is a measure without ever having any hope of knowing what it is

Cerberus

Sure, why not.

David H

There is a measure if there is a measuring device

Mozibur Ullah

yes, but it might not be measuring anything of any interest

Cerberus

3:51 AM

The problem with utilitarianism is partly that you can't quantify happiness, but also that you don't know the exact consequences of your actions.

Mozibur Ullah

yes, that what I was trying to get at with my blunt comment

Cerberus

I was just reading that newly posted question about the doctor and the abusive parents.

Mozibur Ullah

I passed on that - I didn't really want to think about abusive doctors

Cerberus

I didn't really want to think about quantifying the unquantifiable.

David H

and all I meant by my comment was if we had a success-ometer that we could point at a person, and if the numerical readings faithfully corresponded to actual states, then we could measure success

Mozibur Ullah

3:53 AM

I'd agree with that

Cerberus

The first thing you'd need would be goals.

No success without goals.

Mozibur Ullah

but the real meat of that is the faithful correspondance.

David H

might I suggest researching the history of the thermometer and temperature scales?

Mozibur Ullah

Anyway david, its been a real pleasure chatting with you - it looks like we had a healthy debate.