# The puzzlement of a maths illiterate

• March 7th, 2014, 05:37 AM
Dissily Mordentroge
The puzzlement of a maths illiterate
First off my perspective. I have never had any facility for maths, in fact I've been clinically diagnosed as suffering the mathematical equivalent of dyslexia, discalcula.
I'm able to handle philosophic abstractions with ease until something like the notation used in linguistic analysis rears it's ugly head. Which leads me to my question.
I notice, especially when physicists and cosmologists discuss maths, many are attracted to what they term a particular theorie's "mathematic elegance".
Putting aside for now their frequent assertion simple formulae will be a necessary and sufficient explanation of 'a theory of everything' can anyone please explain( to a moron
such as myself) how a formula can be 'elegant'. More significantly how and why could one be ugly?
• March 7th, 2014, 05:43 AM
Dywyddyr
• March 7th, 2014, 05:45 AM
Strange
Like any aesthetic judgement, I don't think there is an easy way to characterise this. (And I am not mathematician, anyway.) But I guess it relates to things like simplicity and how well a simple bit of maths can explain something complicated.

For example, the flocking behaviour of birds can be described with just three (I think) simple relationships. From this, something as fantastically complex and beautiful as the murmuration of starlings can be modelled.

A simple one that I really like is the explanation for why objects of different mass fall at the same speed: the force of gravity depends on mass, so heavier objects have more force acting on them. But it takes more force to accelerate a heavy object. These cancel out so the acceleration is always the same. So I guess symmetries come into it as well.

But of course, simplicity is relative. The equations of General Relativity could be described as simple and elegant - but you would need several years of post-graduate study to appreciate that.

However, it is not clear that a theory of everything will be simple. Or even possible...
• March 7th, 2014, 05:46 AM
Dissily Mordentroge
A great deal of what?

Russell tells us "yet sublimely pure, and capable of a stern perfection such as only the greatest art can show."
I begin to grasp what he's attempting to say as such a description hints at something like
Bach's supreme musical genius. However, that leads me to wonder if I could exlain to the tone deaf why I find beauty in Bach's compositions when I can't even explain it to myself.
Maybe I'm mathematically deaf and asking for an explanation of the beauty of maths is as irrational as the tone deaf man asking "Please explain why you think that noise of Bach's beautiful"
• March 7th, 2014, 05:49 AM
Dywyddyr
Quote:

Originally Posted by Dissily Mordentroge
A great deal of what?

Let me rephrase: a large part of the judgement is based on concision and concinnity.
• March 7th, 2014, 04:06 PM
MagiMaster
Quote:

Originally Posted by Strange
But I guess it relates to things like simplicity and how well a simple bit of maths can explain something complicated.

As a mathematician, I think this about sums it up. But the inverse is also true, though to a much lesser degree. (That is, when something seemingly simple turns out to be much harder to model than expected.)
• March 7th, 2014, 04:56 PM
Dywyddyr
The Joy of Numeracy

S = u t + ½ a t2
has a joyous concinnity,
‘less you’re mentally impaired

v2 = u2 + 2 a s
is of sufficient elegance,
to pull you through any mess

ei pi + 1 = 0
the man who discovered that
must be some sort of hero
http://www.thescienceforum.com/art-c...tml#post399512

On the other hand: I regularly use
wv2 = kd3(t/d)n

While useful it always strikes me as somewhat clunky.

• March 7th, 2014, 05:55 PM
Dissily Mordentroge
Quote:

Originally Posted by MagiMaster
Quote:

Originally Posted by Strange
But I guess it relates to things like simplicity and how well a simple bit of maths can explain something complicated.

As a mathematician, I think this about sums it up. But the inverse is also true, though to a much lesser degree. (That is, when something seemingly simple turns out to be much harder to model than expected.)

I'm happy to be corrected in this so here goes - - - - is it not possible in working from a desire to see elegant and beautiful equations explain matters scientists may not see the forest for the trees? Let me explain as best I can in non mathematical language ( I have not other) with an example. Experiments at facilities such as at C.E.R.N. produce staggering numbers of events, so many with each collision in fact only a small fraction can be measured or observed.
As I understand it, the modus operandi in such situations is to design software and detection hardware specifically to search for results that will 'prove' a pre determined ( elegant?) theory. Could this not be a case of designing a self-fulfilling prophecy?
I'm not here attempting to denegrate scientific method as such as, only a particular perspective I find puzzling.
• March 7th, 2014, 05:57 PM
Dissily Mordentroge
Quote:

Originally Posted by Dywyddyr
The Joy of Numeracy

S = u t + ½ a t2
has a joyous concinnity,
‘less you’re mentally impaired

Obviously I am !
• March 7th, 2014, 06:27 PM
Dywyddyr
Quote:

Originally Posted by Dissily Mordentroge
As I understand it, the modus operandi in such situations is to design software and detection hardware specifically to search for results that will 'prove' a pre determined ( elegant?) theory.

Good grief no.
Experiments are run to see IF the predictions hold up.
"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong". Richard P. Feynman 1
Even the "wrong result" 2 from an experiment can lead to new insights.

Quote:

Could this not be a case of designing a self-fulfilling prophecy?
I'm not here attempting to denegrate scientific method as such as, only a particular perspective I find puzzling.
It's an accusation that has been levelled more than once, but the ones that do denigrate fail to understand that, while elegance in an equation is appreciated (and even lauded) it's not a requirement.
There may, however, be attempts to "untangle" a verified equation to reduce complexity/ ugliness, but that's not the same thing.

1 This is where many cranks fall down. They tend to be of the opinion that their "theory" is somehow "more correct" than observations simply because the "theory" is "simpler" or "less complicated".
2 Can't remember if I've said it on this forum or elsewhere but: I was always taught that there's no such thing as a "failed experiment" 3, 4 because experiments are run to see what happens.
3 Barring equipment failures/ incorrect procedures and the like.
4 Which is why I maintain to this day that Reading University has an anomaly in one building where gravity is only ~3.5 m/ sec 2. ;)
• March 7th, 2014, 06:33 PM
tk421
Quote:

Originally Posted by Dissily Mordentroge
I'm happy to be corrected in this so here goes - - - - is it not possible in working from a desire to see elegant and beautiful equations explain matters scientists may not see the forest for the trees? Let me explain as best I can in non mathematical language ( I have not other) with an example. Experiments at facilities such as at C.E.R.N. produce staggering numbers of events, so many with each collision in fact only a small fraction can be measured or observed.
As I understand it, the modus operandi in such situations is to design software and detection hardware specifically to search for results that will 'prove' a pre determined ( elegant?) theory. Could this not be a case of designing a self-fulfilling prophecy?
I'm not here attempting to denegrate scientific method as such as, only a particular perspective I find puzzling.

A common misconception among a lay audience is that science is about proving things. But proof, generally, is impossible. If I run an experiment and get a result that is consistent with theoretical expectations, I've not proven much. I certainly haven't proved the theory to be correct, for the next experiment could always yield a result that disconfirms the theory. And that's the proper way to view CERN's activities. If theory says that they should see some signature, but do not, then it's time to revise or discard the theory. If the experiment yields the expected result, then that bodes well for the theory, but hardly proves it. The more experiments you run, over a wide range of conditions, the less likely it is that the theory happens to explain everything just by chance. That's the best science can do, and that's all that science ever claims.
• March 7th, 2014, 07:21 PM
Dissily Mordentroge
Quote:

Originally Posted by Dywyddyr
Quote:

Originally Posted by Dissily Mordentroge
As I understand it, the modus operandi in such situations is to design software and detection hardware specifically to search for results that will 'prove' a pre determined ( elegant?) theory.

Good grief no.
Experiments are run to see IF the predictions hold up.
"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong". Richard P. Feynman 1
Even the "wrong result" 2 from an experiment can lead to new insights.

Quote:

Could this not be a case of designing a self-fulfilling prophecy?
I'm not here attempting to denegrate scientific method as such as, only a particular perspective I find puzzling.
It's an accusation that has been levelled more than once, but the ones that do denigrate fail to understand that, while elegance in an equation is appreciated (and even lauded) it's not a requirement.
There may, however, be attempts to "untangle" a verified equation to reduce complexity/ ugliness, but that's not the same thing.

1 This is where many cranks fall down. They tend to be of the opinion that their "theory" is somehow "more correct" than observations simply because the "theory" is "simpler" or "less complicated".
2 Can't remember if I've said it on this forum or elsewhere but: I was always taught that there's no such thing as a "failed experiment" 3, 4 because experiments are run to see what happens.
3 Barring equipment failures/ incorrect procedures and the like.
4 Which is why I maintain to this day that Reading University has an anomaly in one building where gravity is only ~3.5 m/ sec 2. ;)

Richard P. Feynman's quote is well worth repeating, especially in an age when so many want to push science into the background if it's claims are uncomfortable ( climate change) or it's methodologies unnerving to the superstitious. Yes, a theory may disagree with experimental results but limiting which results are to be observed could also prevent data being unearthed that could induce new thinking about other possible theories.
I do like your first point Dywyddyr;535434 but wonder what you're trying to say about Reading University. If I remember correctly there are slight gravitational anomalies at a number of locations on our planet. I can only guess the 'anomaly at Reading University' is a joke I don't get.
• March 7th, 2014, 07:21 PM
MagiMaster
Quote:

Originally Posted by Dissily Mordentroge
Quote:

Originally Posted by MagiMaster
Quote:

Originally Posted by Strange
But I guess it relates to things like simplicity and how well a simple bit of maths can explain something complicated.

As a mathematician, I think this about sums it up. But the inverse is also true, though to a much lesser degree. (That is, when something seemingly simple turns out to be much harder to model than expected.)

I'm happy to be corrected in this so here goes - - - - is it not possible in working from a desire to see elegant and beautiful equations explain matters scientists may not see the forest for the trees?

That was my answer as a mathematician, but as others have pointed out, in science it's the results that matter in the end. As for why math is important in that:
- On the one hand it isn't. Evolution is considered a pillar of modern science, but you never hear anyone talking about the equations behind it. That's because evolution is fundamentally qualitative instead of quantitative. You can probably use it to derive some testable equations for the probabilities of speciation events (or something like that), but the key points of evolution aren't really about numbers. But it's still predictive and testable. Evolution predicts that certain fossils should exist, and eventually we find exactly such fossils. It's such results that matter.
- On the other hand, for something like physics that is fundamentally about measurement and quantifiable data, math gives us the chance to express things in a succinct, universal language as well as having useful properties of its own (such as being able to rearrange F = ma to tell us that m = F/a or a = F/m). As soon as you measure two things and try to find the relation between them, you're using math whether you know it or not. Again though, it's the results that matter and we only still use F = ma (and any other equation) because it still works. We even still use Newtonian gravity because that still works as long as we accept its limits (low speed, moderate mass).

Also science isn't about proving things. It's about disproving things. We've disproven every other explanation we've been able to think of, but have failed (after many attempts) to disprove general relativity, quantum mechanics or evolution (among others). So we accept those things as our current best explanation until something better comes along.

Edit: BTW, about disproving things. The word crank gets used a lot on this forum. It basically refers to someone that continues to hold on to and defend something that has already been disproven. Many such theories were accepted or at least seriously considered at one time but have fallen by the wayside because we've found evidence that they don't work. But cranks won't accept such evidence and use a variety of tried and untrue tactics to convince themselves and others that (for example) the modern scientific establishment is attempting to cover up the true nature of the universe (for some reason).
• March 7th, 2014, 07:38 PM
Dywyddyr
Quote:

Originally Posted by Dissily Mordentroge
Richard P. Feynman's quote is well worth repeating

Given the respect in which Feynman is held AND the validity of the quote it's a "standard mantra".

Quote:

Yes, a theory may disagree with experimental results but limiting which results are to be observed could also prevent data being unearthed that could induce new thinking about other possible theories.
I think I see what you mean but: we have to look somewhere.
Experiments are predicated - to one extent or another - on the theories, and that means that we "look in a particular place" or in a "particular way".
This doesn't mean that other avenues aren't explored, but time, effort and funding can't be spread all over. Those considerations alone "dictate" that we look in the places/ ways that are considered most likely to produce results that apply to the problem at hand.
No examples spring to mind at the moment, but I do know they exist: different - non-"big news" - approaches have been known to yield results, as have seemingly unrelated avenues.
I'm not sure about "limiting which results are to be observed", because, as far as I'm aware, ALL data is kept and looked at (especially on the "big science" projects) it's just that the "obvious" results get checked first.
Plus, it may seem that this is not the case, but that's mainly due to the sheer volume of data produced with concomitant long periods of sorting through it identifying as precisely as possible what those results actually are and mean.

Quote:

I do like your first point Dywyddyr;535434 but wonder what you're trying to say about Reading University. If I remember correctly there are slight gravitational anomalies at a number of locations on our planet. I can only guess the 'anomaly at Reading University' is a joke I don't get.
In the case of Reading the value "I and my team" 1 obtained was roughly one third of the actual figure - far too large to be an actual gravitational anomaly.

1 Of course, my explanation was that everyone else in the team made the errors. And that's what my biography will unequivocally state.
• March 9th, 2014, 05:36 AM
Sealeaf
I'm good with geometry and poor with the rest of math, but an elegant geometric proof is one which makes its point clearly, unambiguosly and does it in the minimum number of steps.