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Discussion > Is Maths the 'Be All and End All' of Science?

Media Hoar has this right.

I would add a very simple point:
Science involves logic and reason.
Logic and reason can be described mathematically but that does not mean that mathematics is necessary for logic and reason to be used.

Therefore you cannot have science without mathematics being there - same as you can't play billiards without mathematics being there. But you can practise the scientific method without using mathematics.

Science cannot cannot jump to an unsubstantiated claim without declaring it is doing so. But it can create logical arguments with no recourse to mathematics. Indeed, in biology "Just-So" stories are the bedrock of the field. And in places where observations are rare enough as to be statistically insignificant, stories are necessary to create a verbal model of the world that can be tested.

50 years ago (before computers were commonplace) this thread would have been inconceivable. Not just because it held on the internet. Rather because the difference between logic and mathematics was self-evident before number-crunching became easy.

Mar 4, 2016 at 11:17 AM | Registered CommenterM Courtney

Far from being interesting, this vanity thread of Dung's is descending into farce, and as usual it is centred around semantics and the difference in meanings of words. Words which are loose and interchangeable in everyday usage, have specific meanings in Science which are not up for discussion.

You may, of course, do rudimentary "science" without mathematics. Science (small s) is observing, coming up with a model, and testing the model out to see if it actually describes nature. The models you come up with can be described as "science" (literally 'knowledge') You have learned something extra about the world.

Technology is then using that model to make things. This is not science, it is making things, though it sometimes involves the use of science.

A Palaeolithic man observes that when he uses a longer club than his friend he manages to kill more animals than him. Observation is the first step in science, but it is not science itself.

He may decide to call small clubs "twigs" and large clubs "thumpers". This is useful taxonomy, but it is also not science.

No science has been done yet.

The Paleo man becomes interested if other lengths of clubs improve or detract from the killing ability. This is the first stage of science. An observation had led to the crystallisation of a theory - that the lengths of club can change killing ability. Note, this is different from merely observing that they do. A theory has been formulated - that club length may be related to killing ability.

The scientific method has begun - He has a model or the world which he deduced from observation.

He might go on to test the ideas by assembling various lengths of club, and then observing which lengths provide the greatest killing yield. Perhaps there is an advantage up until a certain length, when the club becomes too unwieldy to use. Perhaps he observes that the clubs which have a heavy head work better than ones which are uniform thickness, perhaps this sets him off on another question about the shape of the club, not just the length.

The scientific quest has begun.

Now this Paleo man does not have a single ounce of mathematical training, it hasn't been invented yet.
So was his model a mathematical model? Did his science involve mathematics?

Of course it did.

1. He observed that larger clubs kill more. Numbers, trends, rates, frequencies, correlation.
2. He assembled a number of lengths to test. Intervals, sample sizes, test ranges.
3. He observed the killing rates of each one. Numbers, trends, rates, frequencies.
4. He compared the rates of each one. Comparison, estimation.

All that without a calculator.

This is yet another example of where lay people (Dung in particular, and latterly Media Hoar) take a word like 'mathematics' and have a very narrow view of what it means. Perhaps they equate tit to the rather dull algebra and calculus they perhaps skirmished with in their school education. Too much chalk dust and droning teachers. We had pages and pages of discussion about what "warming" means in physics, and he still didn't get it at the end. Semantics and linguistics are fun, but they have no bearing on scientific questions.

Maths is all around us. Every time you judge the speed in your car while cornering, or work out if you'll make it to the lights on time, you are doing mathematics and physics. Every time you throw another handful of rice in the risotto. Every time you work out if you have enough time to get the bathroom painted before Christmas. All day every day your brain is doing physics and mathematics without a single line of algebra.

Obviously you can do simple science without the formal mathematical education that a university gives you, because everybody can use maths without realising it. But when science pushes to the frontiers, it becomes highly mathematical in nature, and it is essential to understand it. Highly advanced physics gives us particles which can only be described mathematically, they have no substance we can relate to, which is why they resort to giving them friendly names like "up" "down" "strange" etc.

Science (big S) is impossible without formal mathematics.

Dung can show me the OED to his heart's content, that is compiled by linguists, not scientists. Nullius in verba.
Media Hoar can construct as many arguments about scientific elitism as he likes. It's still true.

Now carry on.

Mar 4, 2016 at 11:22 AM | Unregistered CommenterTheBigYinJames

OK so the OED is not up to the job of translating words in common usage into words needed to communicate with BYJ. Can sir please point me at the appropriate reference?

Mar 4, 2016 at 12:19 PM | Registered CommenterDung

So if Linnaeus' great work on taxonomy were not science then most of what Darwin did on his voyage was not the work of a scientist but that of a tourist-collector.

Mar 4, 2016 at 12:35 PM | Unregistered CommenterRaff

TBYJ, for a thread you don't consider interesting you are certainly making the effort, as that was quite a long post.

I quite enjoyed, inter alia, Media Hoar's description of the aTTP types.

Mar 4, 2016 at 12:49 PM | Unregistered Commentermichael hart

Raff, I'm not saying you can't use the results of Taxonomy to do science, but the Taxonomy itself isn't science. Naming and classifying things are essential pre-cursors to science, but they are just setting the naming conventions. Conventions that will be used in the doing of the science.

When Darwin collected and named species, that was not science. The science was in taking those findings and constructing theories concerning the entities he classified, the relationships, the possible ways they evolved. The thinking, constructing and publishing of his paper happened long after the Beagle voyages, and that was the science.

Sometimes Taxonomy and Science do not agree. What looks on the outside to belong to one genus after careful examination by science using techniques which do not rely on subjective classification, turn out to belong somewhere else.

The Taxonomy is not science, it's a labelling exercise. Essential but not science.

Mar 4, 2016 at 1:18 PM | Unregistered CommenterTheBigYinJames

Science is not just observation; perhaps the most important part of science is the explanation of the observation; the best way to explain most of what is being or has been observed is by mathematics. However, labelling the explanation is not science, thus, while taxonomy might be scientific, it is not science. The invention of the wheel was not science; it was technology. It possibly came about when a large rock was seen rolling down a hill, or when Caveman Ug began to push the rock he was moving over a log that was in the way; as he started to push the rock over the log, it began to roll, and he realise that he was moving the rock with less effort than before; all he needed was another log, and he could more easily push the rock all the way to its destination. It is possible that rollers like these were used a long time before someone had the bright idea of just using shorter lengths of the log, perhaps one on each corner of the rock, thus making wheels. There is one excellent example of this (from the Orkneys, I think), where the means of transport was on spherical rollers. A large number of stone spheres, about 4 inches in diameter, have been found, all perfectly spherical, all exactly the same size, many elaborately patterned. It was not known what these were for, until someone linked them with another mystery – lengths of wood with grooves cut along them. The stone spheres fitted neatly into these grooves; anything placed on them will roll along very nicely, thank you; line the lengths of wood up and you have a track. But all this is not science; it is technology. The science was in the calculation of the sphere sizes, in determining the optimum size, in assessing the rock to use, the methods to create the spheres, and the amount that would be required – all of which involves mathematics. Science is involved with studying this ancient form of transportation, and might be involved in the labelling and conclusions, but these labels and conclusions, while scientific, are not science. Science is, basically, useless. It is like one of those spherical rocks, sitting on a shelf – pretty to look at, interesting to study, but does absolutely nothing on its own. To use it, you need to know how to use it. Setting science to work is technology; science-based – yes; scientific – yes; but not science. To repeat myself: science alone is, basically, useless.

Mathematics was in use long, long before it became a means of communication; long before tally-sticks, before language, and even before humans; almost all animal life subconsciously (or instinctively, if you prefer) uses mathematics to some degree or other. We are constantly using maths on the subconscious level, assessing distances, angles and masses – when throwing a rock, we subconsciously analyse the weight of the rock, its shape, texture and probable wind-resistance; we judge the distance for it to be thrown, any effect the wind might have, and then calculate the various levers involved in the actual throwing. We may not think of this as maths, but it is. Caveman Ug applied some science to the act of throwing, and, utilising rudimentary maths, realised that he could extend the range by extending the arm – and the throwing stick was created (most probably before the wheel).

While scientific training is about understanding the often complex mathematics involved, it is primarily about teaching patience, observation, rejection of preconceptions, of constantly questioning assumptions, of rigorous testing of the conclusions and accepting that another viewpoint might be required to discover any inherent flaws and, finally, accepting that there is a high chance that you could well be wrong. Every one of those points requires mathematics; few, if any, of these essential points are being used in Climate “Science”.

Media Hoar: please do not rely too much on the myth around Galileo and the Church; the Pope at the time did acknowledge that the Bible is not really about the physical universe, it is about the spiritual one. By all accounts, Galileo was a cantankerous old codger, who liked to rub folk up the wrong way, hence he managed to irk a few priests into enmity. Also, the world was never thought of as flat – Columbus knew it was round, as did the Romans and the Mesopotamians; the “flat Earth” idea seems to have originated in the Victorian era, possibly to highlight the progress they had made by belittling those preceding them – a practice still in common use, today.

Mar 4, 2016 at 1:47 PM | Registered CommenterRadical Rodent

Dang, TBYJ – your argument is so much better than mine! What is needed for my wax dolls to work is some toe-nail clippings or a lock of your hair; if you could e-mail one or both of those to me, I’ll make sure that you suffer!

Mar 4, 2016 at 1:58 PM | Registered CommenterRadical Rodent

BYJ your posts are so full of holes that you have created a target rich environment.
First of all the driving analogy:
Have you ever heard the term "seat of the pants"?
Have you heard the term "feedback"?
What do you think feedback through the steering wheel is?
What do you think feedback through the seat is, doing maths through your arse? (I am sure you can do this)
I repeat my question BYJ, where do the poor lay people like me go to find the real meaning of the mathematical terms ?
I note that on your repository thread you say that correct thinking leads to messy solutions and specifically that the migration problem is a complex one and that the solution will therefore be a messy one.
Well regardless of what the solution turns out to be, you would be quite stupid not to at least look for a simple solution before you try and analyse every aspect of the problem.
I believe I am right in saying that we elect the UK government (EU not withstanding) to serve the interests of the UK and its population. We do not elect a government to feed the world or save the planet or to give a home to all people who want to live here. All we need to do is refuse to allow migrants off the ferry (or EUROSTAR) and return them to the country they last came from. I think even you could figure out how to do that BYJ.
By the way the migrants are the bad guys :)

Mar 4, 2016 at 2:06 PM | Registered CommenterDung

BYJ your posts are so full of holes that you have created a target rich environment.

I'm sure there are a few small logical and grammatical slips in there, but the corpus of it looks whole to me. I don't see any holes that you would comprehend, anyway. The fact that you may not understand it, or that you disagree with it out of petulant rage is none of my concern.

What do you think feedback through the steering wheel is?

It's feedback. Picked up by the sensory receptors in your hands and arms, and relayed to the appropriate sensory processing areas of the brain (in the case of your arms, it would be the sensorimotor area).

What do you think feedback through the seat is, doing maths through your arse?

Absolutely, though it is your brain which is doing the maths - somewhere in between the magic of the sensorimotor processing area and the primary motor cortex, the maths is worked out and signals sent to the cerebellum to begin coordinating any motor response required. Your arse is just a sensory receptor, it's unable to drive by itself. Or do maths.

I repeat my question BYJ, where do the poor lay people like me go to find the real meaning of the mathematical terms ?

I would suggest any good university physics text book, e.g. Sears and Zemansky's University Physics.

System 1 kneejerk thinking and general ranting snipped.

Still haven't shown me those holes have you? And that's because there are no holes, and if there were holes, you aren't smart enough to find them. Dung, you rail against me all the time with your witless diatribes, but it's like swatting flies.

Mar 4, 2016 at 2:28 PM | Unregistered CommenterTheBigYinJames


Since I do not possess the book you reference, can you simply give me your 'scientific" definition of mathematics and technology :) ( do not forget to reference your definitions of course)
The holes in your arguments are the statement that your body is doing maths, defining maths would be a big help. I am sure you correctly identify the parts of the brain involved (well I will take it on trust anyway). You are basically saying that the only way to throw accurately is to do the maths and you believe the body works out ALL the variables needed.
My body knows the temperature and density of the air, the wind speed and direction, measures the distance to target (metric?) and works out mathematically the force needed to complete the throw. My body does not do maths, it works on trial and error which is why I miss a lot.

Mar 4, 2016 at 2:50 PM | Registered CommenterDung

Dung Beetle use of the principle of the wheel, predates Man's ability to define Pi.

The ability of a sailing boat to sail at upto +/-45 degrees towards the wind was worked out well before 1400AD, possibly by the Arabs, see Lateen Sail, but how this was possible wasn't understood scientifically until the 1920s, after aerodynamics were refined as a result of WW1.

The Greeks Romans and Eqyptians were all able to engineer solutions to problems, with some understanding of maths and science. The Normans helped reintroduce Europeans (not just England) to engineering.

The evolution of medieval Cathedral design, is either a triumph of engineering, or a triumph of trial and error, followed by learning and more trial and error. The reason many cathedrals took 100s of years to build was they kept falling down.

Climate science, on the other hand, is a tragedy caused by arriving at a conclusion first, and then using trial and error, and error, and error to prove it, failing, and resorting to computer adjustments instead.

I don't pretend to know how nuclear power or bombs work, but I accept the technology works with demonstrable results. Nobody can prove climate science works, and there is no demonstrable proof either.

Mar 4, 2016 at 3:21 PM | Unregistered Commentergolf charlie

My body does not do maths, it works on trial and error which is why I miss a lot.

You're not thinking this out properly.

What does it mean to try? What does it mean to err? If you think about this carefully you will see the maths.

When you try, what that means is your brain hasn't 'learned' the exact amount of strength to get the ball to the destination. So it uses visual information about the distance and conditions, sensory information about the weight and texture of the ball, and the history of other times something was thrown. It crunches the numbers on these, and comes up with a best guess at the strengths. The primary motor cortex instructs the cerebellum what it wants, and it gives it its best shot.

This is why when you 'try' to throw the ball, you're usually not a million miles away, even if you've never thrown a ball before. Your brain is good at doing the maths.

Now when you "err" the ball is lying on the ground someway short or too far, or off to the side or a combination. This visual information is fed into your brain. We have some actual measurements - how far it fell short compared with the goal, did it drift with the wind, was the throw too shallow, etc. These measurements are crunched and fed into the "try" that you did a moment before. The motor cortex now tells the cerebellum to do it a bit differently, a nudge here, a slight flick there, a bit farther back on the backswing...etc, and the ball gets closer... and we try again...

All those tweaks are mathematical calculations which are combined with the previous "tries" worked out before.

If you still don't believe this, then apart from throwing my hands up in the air (my own primary motor cortex expressing disbelief at the depressing sensory information), then you should consult any basic resource about brain function.

Even your replies to my posts are carefully calculated mathematical responses.

Mar 4, 2016 at 3:25 PM | Unregistered CommenterTheBigYinJames

"When you try, what that means is your brain hasn't 'learned' the exact amount of strength to get the ball to the destination. So it uses visual information about the distance and conditions, sensory information about the weight and texture of the ball, and the history of other times something was thrown.
No, it is your muscle(s) that are learning not your brain.

Mar 4, 2016 at 3:36 PM | Registered CommenterDung

No, it is your muscle(s) that are learning not your brain.

Muscles are lumps of jelly that jerk when appropriate electrical impulses are fed into them.
They do not learn.

In order to learn you have to have a way of sensing information, assimilating it, and storing it.
There are no structures in muscles for any of these functions.

Honestly Dung, you skewer yourself with every statement.

Mar 4, 2016 at 3:50 PM | Unregistered CommenterTheBigYinJames

Silence is just because I have switched off from the posts. I got what I needed. Nothing written really has any relevance to what I wrote or my thinking. Different universe.

Mar 4, 2016 at 4:09 PM | Unregistered CommenterMedia Hoar

Yin, my opinion is worth no more or less than yours. But if you hold a view of science that is so narrow as to exclude Linnaeus (and doubtless countless others who would traditionally be called scientists) then in my opinion it is worthless.

Mar 4, 2016 at 5:58 PM | Unregistered CommenterRaff

I didn't realise it had taken so long to find/remember what I was thinking about. Anyway it was something by Marcus du Sautoy I can't find it on iPlayer now. The only quote I can find is in The Guardian my bold.

The columnist wrote in the Guardian a few months ago that he considered mathematics to be a waste of time, that it was less useful than Latin and Greek and that it deserved no support from the public. For his part, du Sautoy was unamused. 'I presume he [Jenkins] did badly at the subject at school and has held a grudge against it ever since,' he said in an interview with The Observer last week. 'It simply isn't true, of course. Mathematics underpins all of science and the technology that runs our lives.'

You're right about having a two-faced view of the BBC. I do listen to quite a lot of the BBC, I don't read much on the website unless linked from here, I steer clear of stuff on climate/environment and "Any Questions?" but with all the BBC output there is an opportunity for even them to put out something worth listening to. I'm a bit of a quiz person and the dumbing down of Mastermind by Humphries drives me to distraction, even more than some of the other biased stuff that comes out of the organisation.

Re OED, my wife is a bit of linguist and reckons that Roget's Thesaurus was created by the son of a Swiss immigrant because most Latin based European languages have a very limited vocabulary whereas English takes words from every other language and happily makes up new ones every week has a huge vocabulary. I have no knowledge as to whether she is right or not but Roget's Thesaurus is a very useful tool.

Mar 4, 2016 at 6:17 PM | Unregistered CommenterSandyS

The one underpinning trait required for science to work is honesty.
Whether measurement, modeling or analyzing evidence, the maths don't matter so much if those doing the math are going to use the tools to fib.
Character counts.
Hide the decline, and all of that.

Mar 4, 2016 at 6:53 PM | Unregistered Commenterhunter

It depends on your definition of science. Was realising, as Gallileo did that falling objects moved with the same acceleration regardless of weight, science? Of course it was, as was Newton's realisation that this applied generally to all bodies with mass. Later people put this acceleration into a mathematical framework and Newton provided a pretty accurate mathematical relationship which explained the effects of gravity between two masses. I was always told that mathematics was the language of science, i.e. it explained the science, but does Darwin's theory of evolution need maths to explain it? Was the development of penicillin science? and did it need to be clothed in mathematics to be so?

As Lord Kelvin is purported to have said: "If you can't explain your theory to a barmaid, it probably isn't very good physics."

I'm off to start the Angels on the Head of a Pin thread.

Mar 5, 2016 at 7:05 AM | Unregistered Commentergeronimo


I do keep asking for authoritative definitions of ,science and technology from BYJ because he dismisses the OED but fails to give an alternative reference (apart from 'any good university physics text book, e.g. Sears and Zemansky's University Physics.')
Geronimo you quote Lord Kelvin above and I can quote Feynman who both basically agree that if you can not explain complex theories in simple terms then you do not understand your subject.

Mar 5, 2016 at 9:17 AM | Registered CommenterDung

Sears and Zemansky's University Physics. that's had a long life! It was a 20 year old book when I had my copy. I see the cover has been modernised as well as (hopefully) the content.

Technocrats are often unable to express things in a way that ordinary mortals find understandable. It's not their fault they can't put themselves in the other persons position, we all have different skills. I think Rutherford was over optimistic in that respect.

Mar 5, 2016 at 11:07 AM | Unregistered CommenterSandyS


You may be right although I am not convinced and not sure if I am a mere mortal let alone an imbecile as BYJ playfully likes to call me ^.^ I think it is incumbent upon those who have a skill to at least be polite and reasonable to those who have different or lesser skills (unless he is a genius in which case I would forgive him).
So you too are an atomic physicist and part time brain surgeon then Mr S? hehe

Mar 5, 2016 at 11:55 AM | Registered CommenterDung

Well, as the late unfortunate Professor Joad used to say "It all depends what you mean by...." (maths, science, and so on). Within certain limits, you are entitled (like Humpty Dumpty) to use words to mean what you want them to mean. Your readers then have to try to understand what you intend to say. Words do not have an absolute meaning, regardless of context. However, if you want to be understood, you have to take into account what your readers will understand by the words you use. This means conforming to (what you think is) general usage: or if not, producing your own crystal-clear definitions.

So, if you wish, you are entitled to understand science as being entirely based on mathematics. If you do so, then (possibly) you will be entitled to say that taxonomy is not a science. You'd better have a special definition of mathematics, though. If you quote Lord Kelvin, it can sound as if mathematics was solely concerned with counting. That must be wrong. Symmetry - sets - groups - topology - these are all forms of mathematics. Taxonomy (I suppose - I'm not a taxonomist) is about observing similarities and differences among groups of organisms, and classifying them on this basis. This can lead to inferences about how they evolved. If taxonomy is not a science, what about chemistry? That started as a random collection of facts, which have since been classified and explained (to a steadily increasing degree) by theories of atomic structure. It may not have started as a science, but it's certainly a science now. Is meteorology a science? Or what about....?

Mar 5, 2016 at 1:50 PM | Unregistered Commenterosseo


You remind me of Ernest Rutherford, who said

"All science is either physics or stamp collecting."

Mar 5, 2016 at 1:52 PM | Unregistered CommenterEntropic man