# People looking for proof to come from any research in science will be sadly disappointed

As an astrophysicist, I live and breathe science. Much of what I read and hear is couched in the language of science which to outsiders can seem little more than jargon and gibberish. But one word is rarely spoken or printed in science and that word is "proof". In fact, science has little to do with "proving" anything.

These words may have caused a worried expression to creep across your face, especially as the media continually tells us that science proves things, serious things with potential consequences, such as turmeric can apparently replace 14 drugs, and more frivolous things like science has proved that mozzarella is the optimal cheese for pizza.

Surely science has proved these, and many other things. Not so!

The way of the mathematician

Mathematicians prove things, and this means something quite specific. Mathematicians lay out a particular set of ground rules, known as axioms, and determine which statements are true within the framework.

One of best known of these is the ancient geometry of Euclid. With only a handful of rules that define a perfect, flat space, countless children over the last few millenia have sweated to prove Pythagoras's relation for right-angled triangles, or that a straight line will cross a circle at most at two locations, or a myriad of other statements that are true within Euclid's rules.

Whereas the world of Euclid is perfect, defined by its straight lines and circles, the universe we inhabit is not. Geometrical figures drawn with paper and pencil are only an approximation of the world of Euclid where statements of truth are absolute.

Over the last few centuries we've come to realise that geometry is more complicated than Euclid's, with mathematical greats such as Gauss, Lobachevsky and Riemann giving us the geometry of curved and warped surfaces.

In this non-Euclidean geometry, we have a new set of axioms and ground-rules, and a new set of statements of absolute truth we can prove.

These rules are extremely useful for navigating around this (almost-)round planet. One of Einstein's (many) great achievements was to show that curving and warping spacetime itself could explain gravity.

Yet, the mathematical world of non-Euclidean geometry is pure and perfect, and so only an approximation to our messy world.

Just what is science?

But there is mathematics in science, you cry. I just lectured on magnetic fields, line integrals and vector calculus, and I am sure my students would readily agree that there is plenty of maths in science.

And the approach is same as other mathematics: define the axioms, examine the consequences.

Einstein's famous E=mc2, drawn from the postulates of how the laws of electromagnetism are seen by differing observers, his special theory of relativity, is a prime example of this.

But such are only a part of the story of science.

The important bit, the bit that defines science, is whether such mathematical laws are an accurate description of the universe we see around us.

To do this we must collect data, through observations and experiments of natural phenomena, and then compare them to the mathematical predictions and laws. The word central to this endeavour is "evidence".

The scientific detective

The mathematical side is pure and clean, whereas the observations and experiments are limited by technologies and uncertainties. Comparing the two is wrapped up in the mathematical fields of statistics and inference.

Many, but not all, rely on a particular approach to this known as Bayesian reasoning to incorporate observational and experimental evidence into what we know and to update our belief in a particular description of the universe.

Here, belief means how confident you are in a particular model being an accurate description of nature, based upon what you know. Think of it a little like the betting odds on a particular outcome.

Our description of gravity appears to be pretty good, so it might be odds-on favourite that an apple will fall from a branch to the ground.

But I have less confidence that electrons are tiny loops of rotating and gyrating string that is proposed by super-string theory, and it might be a thousand to one long-shot that it will provide accurate descriptions of future phenomena.

So, science is like an ongoing courtroom drama, with a continual stream of evidence being presented to the jury. But there is no single suspect and new suspects regularly wheeled in. In light of the growing evidence, the jury is constantly updating its view of who is responsible for the data.

But no verdict of absolute guilt or innocence is ever returned, as evidence is continually gathered and more suspects are paraded in front of the court. All the jury can do is decide that one suspect is more guilty than another.

What has science proved?

In the mathematical sense, despite all the years of researching the way the universe works, has proved nothing.

Every theoretical model is a good description of the universe around us, at least within some range of scales that it is useful.

But exploring into new territories reveals deficiencies that lower our belief in whether a particular description continues to accurately represent our experiments, while our belief in alternatives can grown.

Will we ultimately know the truth and hold the laws that truly govern the workings of the cosmos within our hands?

While our degree of belief in some mathematical models may get stronger and stronger, without an infinite amount of testing, how can we ever be sure they are reality?

I think it is best to leave the last word to one of the greatest physicists, Richard Feynman, on what being a scientist is all about:

I have approximate answers and possible beliefs in different degrees of certainty about different things, but I'm not absolutely sure of anything.

This story is published courtesy of The Conversation (under Creative Commons-Attribution/No derivatives).

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## User comments

Sep 24, 2014
Yet, among other things, no attempt is made by "scientists" to dissuade the "news" from declaring absolute certainty in each announcement. Even supposedly scrupulous sites like PhysOrg, for example, hold off on opining that "scientists" have absolutely and utterly decided an issue or derived an unquestionable fact. And with all this parsimony of certainty, so called "scientists" still declare absolutely and unequivocally that God is not present even though they never examined the claim and even though they insist it can't be examined "because it's a negative".
And, incidentally, Einstein did not equate energy with mass. His formula only established a zero point for "relativistic mass". In the same way, the formula for the parabolic path of a tossed object implies that it continues falling even after it reaches the ground.

Sep 25, 2014
A very nice article! But (you knew there was a but:) Lewis description is partial. If bayesian inference was all we have it would be opinion (the betting part) and learning (the bayesian update part).

However, nature is regular (laws) and we have a method specialized to take advantage of that: testing. It is a statistical approximate method, but it allows us to accept good data and theories beyond reasonable doubt, or else compete methods to reject bad data and theories beyond reasonable doubt.

@julianpenrod: Trolling science isn't useful (like science is).

Yes, there are data and theories that are robust:

"The Laws Underlying The Physics of Everyday Life Are Completely Understood"

[ http://blogs.disc...MWPl_sfY ]

Sep 25, 2014
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Sep 25, 2014
But surely, there must be something about which the science is settled – climate; the accidental beginning and evolution of the universe, life and consciousness; multiverses; the death of god– something.

Sep 25, 2014
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Sep 25, 2014
A very nice article!

Agreed. I fear some will jump to the conclusion, though, that therefore no law can be said to be better than any other law (or better than a description that says "stuff happens randomly")

An excursion into etymology might help here: Science (from lat. scientia) is the search for knowledge - not proof. Knowledge is that which allows us to apply gathered information to make predictions. The better the prediction the greater the knowledge. Knowledge does not have to be perfect.
And it is easily arguable that perfect knowledge - omniscience - is impossible to attain as long as the thing that 'knows' is not also the entirety of the universe itself*

*which in turn would, bizarrely, be ultimate solipsism - and hence no certain knowledge at all.

Sep 25, 2014
Sorry, sarcasm is wasted on the humorless.

Sep 28, 2014
The most critical thing, is the erasure of the word 'law' in the world of physics and science.

The word must be dropped as it is about punishment of people for social and cultural misconduct.

The word law should never be connected to the postulates and theories of science.

Sep 28, 2014
All is heuristic.
Even science.
http://www.me.ute...ory.html

Sep 28, 2014
I do not want the science proof. It is good enough for me if you explain what you are saying in the way I can understand it. If enough smart peoples say the same thing that makes sense then that's all the proof I need until somebody has the better idea that makes more sense.

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