Reply to: The fascination of Maths thread

[OwlHoot]

I think the structure of the sentence would suggest 'they' are CERN. As 'they' have spent the money I think 'they' are fairly confident whatever they are looking for will be found.

That seems to be a very specific answer, now who are the 'significant minority'?

Among many others, the guys (including Nobel Prize winners) who chose the "No they Won't" option here.

(You'll see that informal survey was done ten years ago; but I think it's fair to say that opinions haven't changed much if at all since.)

edit: There's an interesting blog article here that illustrates the basic point that nobody is sure what will be found, if anything. Oh and the author estimates the probability of finding supersymmetry at 0.1 %

[threaded]

Bollox. This is the continuum hypothesis. There is no PROOF that there is such a set and, more importantly - there is no proof of the contrary. There may or may not be such a set. But it is impossible to prove it. Go read Gödel. And don't post again until you've understood.

If CH is true then all sorts of interesting and useful stuff comes out. But, otoh, one implication is that you can, using normal transformations without stretching, transform one sphere into two.

Actually, I quite like the idea that it is neither true or false.

Which is what I thought this thread was about...

[OwlHoot]

... Please provide an example of mathematics being based upon observation. (As opposed to being a tool to analyse the results of observation.)

Bagpuss is right. A lot of modern maths is conjectural, based on observation.

I could give a dozen examples, and I will if anyone asks; but as it's almost bed time I'll content myself with citing the Birch Swinnerton-Dyer conjecture. This was formulated in the 1960s and hasn't been proved, except in special cases, to the present day. (There's a million dollar reward awaiting the first proof, as it's one of the Clay Millennium prizes!).

Also, much of the Langlands program, also devised in the 1970s based on numeric evidence, is still conjectural, as is much of Motivic cohomology which is a kind of "big daddy" of cohomology theories conjectured by the great Alexander Grothendieck

It's childishly ignorant and naive to think of maths as all done and dusted, or that experiment has no place. For every new result established, a dozen new questions spring up in its place, and theories which were barely known even thirty years ago have now sprouted into vast specialities in their own right.

[TimberWolf]

The relationship between science and observation does not mean mathematics is based upon observation.

Please provide an example of mathematics being based upon observation. (As opposed to being a tool to analyse the results of observation.)

How about the axioms of mathematics?

[Bagpuss]

:
In what branch of statistics is observation done that has become a basis of mathematics?

The Design of Experiments.

and..At least one statistical distribution was based on observation.

[minestrone]

Please provide an example of mathematics being based upon observation. (As opposed to being a tool to analyse the results of observation.)

That makes no sense at all.

[BrowneIssue]

Maths can be based on observation for example epidemiology and branches of statistics. Maths quite often is a big part of science.

Epidemiology is biology (transmission and control of disease), not mathematics. Mathematics can be used as a tool in assisting fiddling with the numbers when trying to determine what has happened / may happen but you are not doing mathematics by counting infections. Observation gathers the data for the science of epidemiology; not provide the foundations of mathematics.

In what branch of statistics is observation done that has become a basis of mathematics?

Yes, maths is part of science: as a tool for processing numbers. The relationship between science and observation does not mean mathematics is based upon observation.

Please provide an example of mathematics being based upon observation. (As opposed to being a tool to analyse the results of observation.)

[NotAllThere]

There is no set whose cardinality is strictly between that of the integers and that of the real numbers.

Bollox. This is the continuum hypothesis. There is no PROOF that there is such a set and, more importantly - there is no proof of the contrary. There may or may not be such a set. But it is impossible to prove it. Go read Gödel. And don't post again until you've understood.

If CH is true then all sorts of interesting and useful stuff comes out. But, otoh, one implication is that you can, using normal transformations without stretching, transform one sphere into two.

[Bagpuss]

Science is based upon observation, not logic. Hence mathematics, based upon logic, does indeed come under philosophy: it is in our heads and we make up the rules.

Maths can be based on observation for example epidemiology and branches of statistics. Maths quite often is a big part of science.

[minestrone]

The 'significant minority' should = 'most scientists reckon'.

Scientific method says (very poorly put):

1. Question - what are particles made of?
2. Theorise - to make the particle models work, there must be a Higgs Wotnot
3. Predict - if a Thingy particle is hit with one zigablatt of energy, a Higgs Wotnot might be produced, thereby proving they exist.
4. Test - build a particle cannon and blatt Thingy particles with Doobrie particles loaded with one zigablatt's worth of momentum and see if any Higgs Wotnots run away from the scene.

So the scientists that believe in Higgs Wotnots have to do a test to see if they are produced. The scientists that disagree, also want the test done.

Ergo, CERN must be constructed for both the confident scientists and the doubtful scientists ... and the confident scientists should be exhibiting the same behaviour as the doubtful ones.

Science does not have opinions, only empirical evidence and theories.

When I set the question I knew the answer to be given would not be the point, I just wanted to see if someone would offer an explanation, to a maths grad on a maths thread, to a quantity on an unquantifiable term. The term 'significant minority' is completely useless and meaningless.

[BrowneIssue]

Who are "they"? Most physicists reckon supersymmetric particles and the Higgs exist. But there are a significant minority who don't.

I think the structure of the sentence would suggest 'they' are CERN. As 'they' have spent the money I think 'they' are fairly confident whatever they are looking for will be found.

That seems to be a very specific answer, now who are the 'significant minority'?

The 'significant minority' should = 'most scientists reckon'.

Scientific method says (very poorly put):

1. Question - what are particles made of?
2. Theorise - to make the particle models work, there must be a Higgs Wotnot
3. Predict - if a Thingy particle is hit with one zigablatt of energy, a Higgs Wotnot might be produced, thereby proving they exist.
4. Test - build a particle cannon and blatt Thingy particles with Doobrie particles loaded with one zigablatt's worth of momentum and see if any Higgs Wotnots run away from the scene.

So the scientists that believe in Higgs Wotnots have to do a test to see if they are produced. The scientists that disagree, also want the test done.

Ergo, CERN must be constructed for both the confident scientists and the doubtful scientists ... and the confident scientists should be exhibiting the same behaviour as the doubtful ones.

Science does not have opinions, only empirical evidence and theories.

[minestrone]

Who are "they"? Most physicists reckon supersymmetric particles and the Higgs exist. But there are a significant minority who don't.

I think the structure of the sentence would suggest 'they' are CERN. As 'they' have spent the money I think 'they' are fairly confident whatever they are looking for will be found.

That seems to be a very specific answer, now who are the 'significant minority'?

[OwlHoot]

.. Take CERN for example, they know the particles exist, they just want to see them. ..

Who are "they"? Most physicists reckon supersymmetric particles and the Higgs exist. But there are a significant minority who don't.

[minestrone]

"e: the Story of a Number" by Eli Maor is the story of how a handful of major players (and scores of only slightly lesser ones) dedicated their lives to a particular interest and made a name for themselves in the process.

Through dedication and devotion, they pushed forward an academic field a little further each time. In so doing, they made available tools that others could use in engineering, chemistry, physics, civil engineering, biology et al.

There is infighting, emotional blackmail, intrigue, family feuds, the fall and rise of civilisations, and all sorts of other good stuff in this book.

It also gives a bit of an insight into how and why cutting-edge trainspotter-type behaviour can be appealing to some people.

It is a story similar to "who invented the motor car?" to which the answer is "hundreds of people over a few centuries". Fortunes were made and lost, industrial empires built and lives devoted to the most intricate of tiny improvements that allowed huge leaps forward in progress. So it is with the number e but from an academic standpoint.

Although it does demonstrate and explain some horrible degree-level maths, it is not a maths text book. It is the story of great lives well spent and a demonstration of how incredibly hard it is to achieve eternal fame. With twists upon the way too - Pythagoras was famous for what, exactly? Are you sure that was actually Pythagoras...?

The book starts with Napier's Bones. Strangely, so did the "History of Data Processing" module of my Computer Studies course. Whereas as I made the decision to switch from a life in academia studying pure mathematics to industry doing applied computing, so this book carries on along that path of mathematics research and traces a four century long line that is not yet complete - and never will be. A line that began at least four millennia ago.

Whenever we fear for the collapse of society, the end of the world or whatever will become of us, here is a lifeline: the story of a number that has continued, unbroken. A spark of hope that humanity cannot be destroyed while there are those who study the past and wonder:

Where can I go from here?

I agree with what you are saying there, every gain is a bonus for society but maths for enjoyment is just a step too far for me. 6 years I was in uni for doing maths based subjects and I never found any total creativity, it was mainly based on proving a know fact or interpreting an existing axiom. Yee cannie change the laws of physics and all that. Take CERN for example, they know the particles exist, they just want to see them.

Software was a jump up for me because you make your own laws, I see OOP as the most creative thing we have ever made. It is a pure invention of the mind and not constrained by existing laws or boundaries. But still I would not spend my time outside work studying it for enjoyment.

I'm not saying people who derive enjoyment form maths are wrong but I just cannot see what joy there is in the subject.

Anyway for enjoyment I spend it it playing the drums, piano, obsessing over beach boys songs, running, going to the boozer and going to the football although that seems to be quite joyless these days.

[sasguru]

There is no set whose cardinality is strictly between that of the integers and that of the real numbers.

Your random googlings only serve to underline your absolute pretentiousness.

HTH