Are you offended when the media poke fun at your hobby?

Someone mentioned that he never watched TV. This is a mistake ! I find TV most useful when I have an upset tummy. After about 10 mins of watching the crap that,s on offer,I make a beeline to the toilet,to throw up.

Result ? no more tummy problems ! You should try it,cheaper than pills,and no side effects.

Maybe they do their best,if so,I,de hate to see their worst.! Much better to spend your time looking at your machines working away and even the sound is better !.

My maths master at school taught us how this worked. It relies on a seemingly plausible but wrong conclusion earlier in the calculation.

Despite working in an accountancy-based job and another electronics-based one, I have never needed to know anything more complex than square roots since leaving school. Yet, 20% of school leavers are functionally illiterate and innumerate despite 11 years of schooling! Check the reading age of popular newspapers, ask why so many bought Stephen Hawking's book yet have never read it, and why it is that anyone with an aptitude is regarded as a geek or a swot.

Geoff

I've read it at least twice so I think!!!!!! I now understand it.

Yes. Engineering degrees used to be a three year course but now they have been extended to four years. Amongst other reasons, to bring the students' knowledge of mathematics up to the required standard.

Russell

@SillyOldDuffer,

Proving that 1 + 1 = 2 is not that difficult at all.

Place 1 match in box #1 and place 1 match in box #2.

Now throw contents of both boxes on the table and count total.

You will (hopefully) find two matches.

For higher numbers you may run separate proving experiments or use concept of recurrence if you wish. Many thousands of years *before* Bertrand Russell was born peoples knew that 1+1=2.

Heck, even chimps, ravons and parrots can be trained in simple arithmetics. Parrots can handle numbers up to 20 if I remember well. They can also be trained not to add pears to apples. Lets hope that children leaving our schools will not lose this ability because they are (together with their teachers) on the best track to do so.

What Bertrand Russel did is that he expressed said proff in mathematically correct language, within the cannon. One way or the other it looks impressive.

Martin

Easily tested Chris. If it's only simple basic mental arithmetic can you share your full workings for:

a) LX ÷ IV
b) 0000000000101000 ÷ 00000000000000100
c) 0x28 ÷ 0x04

Rules:

• All steps to be explained
• No calculators
• No cheating by converting to or from decimal

Challenge for bright boys only:

LX ÷ III

Dave

Once you move beyond what you can do with multiplication tables and simple addition/subtraction, mental arithmetic is ALL about 'cheating!'

And you a Chemist Martin!

The experiment with two matches does not prove that 1 + 1 = 2. Although the evidence strongly fits the theory, it's not conclusive. It might not happen next time you try it. That's not as daft as is sounds, quantum mechanics suggests that matter is not absolute, only that its statistically improbable that you get other than two matches. Less contentious, repeat the same experiment using Rabbits or radioactive particles, and it fails to prove that 1 + 1 = 2.

For higher numbers you may ... use concept of recurrence if you wish. Not so. That's induction, not at all respectable in logic. Try this example. What numbers come next in the sequence starting: 1, 2, 3, 4, 5, 6, ...   There's no particular reason for it to be seven.

It may seem pedantic, but before it was mathematically proven people were only guessingt that 1 + 1 = 2 Loads of examples where our ancestors got it wrong. For most of time no-one believed in zero.

Dave

Edited By SillyOldDuffer on 29/10/2017 12:52:09

SOD's post above illustrates the difficulty the Romans had with advancing mathematics owing to their number system. We rely on the adoption of Arabic numerals and the recent invention of the concept of "0" for most of our numerical ability so 1+1 is a relatively new concept.
Most early civilisations and languages only had "1" and "lots" without even the concept of numbers just like (untrained) animals so no words to describe them. There was no need. Either you were on your own so you had a concept of being one or you were with your village so you had the concept of a crowd.
A recent Radio 4 program explained that a rat cannot understand or remember that the food is in the maze next to the red wall which is an abstract concept unlike the press this lever to release food which is a motor skill. Amazingly CHILDREN UNDER 6 HAVE THE SAME PROBLEM because they have not developed the language skill to describe internally abstract situations, This was backed up by study of deaf mutes who had not been taught any sign language so could not express thoughts internally when missing the external ability.

Where is this going? Hobbies often develop a set of unique words and expressions that make those who do not understand them feel alienated and excluded, From there it is an instinctive response to be defensive by throwing (thankfully verbal) rocks at the 'alien'.

@SillyOldDuffer,

Experimental evidence is an acid test of any theory and in Nature it is considered conclusive. You would have to wait far longer than Universe already exists (as per our believes) and convert all atoms within it into experimenters busy with nothing else than repeating experiment before any other result than 2 cropped up (it would entail exceedingly rare QM events before it have happened). So proposed method is sufficiently sound and not a guess at all.

Maths also relies on unprovable truths (axioms) which are nevertheless accepted without further debate.

So for example go and prove that only 1 straight line can be drawn by 2 points within Euclidean geometry.

Unprovable? yes

True? yes.

This does not imply that entire Euclidean geometry is just a guess. Why? Because we have plenty of evidence that it is realised in Nature.

And in theory is that possible for *other* geometries to exist? yes. Would they have some different sets of unprovable truths? yes. Are they realised in Nature? No, with possibility that at an extremely large scales comparable with size of Universe and larger some non-Euclidean factors crop up.

Regarding arithmetic - if you are mathematician you must understand that arithmetics (and entire maths) cannot be *both* complete and consistent. This was conclusively proven by Kurt Goedel in mid 20 century.

So *there are* statements in arithmetic which are proven to be unprovable but nevertheless accepted as true. Call them undecidable, if you wish.

Martin

Regarding a late Post about proving that 1+1=2,I would not be so sure about that [if some of my results are anything to go by ] Some of my measurements and calculations have produced results which would call this into doubt.

Sometimes,I have managed to get 3+2=5 [or even 7 ] Dont ask me how,all I can say is it,s not easy !

I think some of it might be accounted for by reading a rule upside down,or perhaps by seeing two numbers rather than one [strong drink can have this effect]

Again,this is not easy,but someone has to do it !

Hi Martin,

Interesting mix of true and false in your post. The subject is a minefield.

True that experimental evidence is the acid test of any theory. False that experimental evidence is conclusive. Experiment can prove that a theory is wrong but never that a theory is right. There's always a possibility that  evidence will turn proving that any theory is faulty. It may be unlikely but it happens.

True that maths relies on unprovable axioms, false that they are accepted without further debate. One of the cornerstones of mathematics is proving that axioms really are unprovable and failing. Fermat's Last Theorem is a good example.

True that other than Euclidian geometries exist. False that they don't exist in nature.  You mention cosmology yourself.

I think it all rather reinforces the point I was trying to make which is 'there is no such thing as simple mental arithmetic' and 'don't believe you're smart just because you can do sums'. Nicholas Wheeler was spot on when he wrote 'Once you move beyond what you can do with multiplication tables and simple addition/subtraction, mental arithmetic is ALL about 'cheating!' Knowing a selection of maths cheats does not mean you are cleverer than someone who hasn't learned them.

An example that fits in with your excellent point about unproven axioms. What's 5 - 7? Simple mental arithmetic says the answer is -2. Hurrah, that's very useful. But it's a complete fake in that negatives do not exist in nature. You cannot have -2 apples, or -2 cars, or -2 children. That act of simple mental arithmetic with a minus sign means the brain has to accept an impossibility. I think it's one of the reasons maths is difficult: it jumps in and out of reality making the flow difficult to follow. Many maths basics aren't basic at all. Ask most of us to properly answer simple questions like 'What exactly is a number?' and we are liable to blow a gasket. That's why I have no problem with someone using a calculator to divide 40 by 4 - it's just another cheat, no different in kind from the others.

Dave

Edited By SillyOldDuffer on 29/10/2017 17:40:20

if one needs to prove that 1+1=2 perhaps one should have taken up another hobby/profession. Engineering is about applying the laws of science to the real world for the betterment of mankind, not the baffement of mankind!

Dave [Silly old duffer],

As you say,you can,t have -2 apples,but how can the average family have 2.3 children ? Makes me wonder !

Did you ever get the feeling that you,de be better off making swarf ?

I think I,ll bring the dogs out for a walk,before I go nuts with all this !!

You can have -2 cars after the showroom was robbed the night before.

Mike

@SillyOldDuffer,

Experimental evidence is conclusive in falsifying theory. Theories are models of reality, not reality itself.

Models are applicable within some ranges of conditions and less perfect ones are just special cases of those more widely applicable (eg Newtonian and Einsteinian physics).

Yes, non Euclidean geometries are there and applicable in GR for example, so I was wrong here. On the other hand, space in largest scales appears to be flat (Euclidean) base on up to date observations and gravitational curvatures are just local abnormalities.

I have heared that last Fermat theorem has been recently prooven after all but base on maths not available to Fermat himself. Did anyone undermine this proff?

Minus 2 apples means give away 2 and you will have zero (of course impossibility but yet a foundation of entire credit system).

A lot of terms (like word "number" mentioned by you) are some sort of natural truths, reasonably understood without further debate. For example word "life". What it really is?

There are many interesting proves in maths. Someone (Euler?) have proven that sum of all natural numbers is equal -1/12. This prove is not even difficult to understand and many interesting results are produced if it is accepted as true.

What about "renormalization"? Legitimate? Not? Illegitimate but we cannot produce many useful theories without it?

Finally I still do have troubles with peoples unable to divide 40 by 4 in memory. There is an overwhelming evidence that wealth is usually transfered from societies where such peoples are in abundance to societies where they are more rare. We are going to learn this simple truth a hard way.

Re. woman having 2.3 children... lets assume that she is living averagely 80 years (960 months) and pregnancy is 9 months long we can find out that at any given time she is 2.15625% pregnant.

Martin

Edited By Martin Dowing on 29/10/2017 18:48:45

Edited By Martin Dowing on 29/10/2017 18:55:09

Neither.

It's an axiom that defines what a straight line is in Euclidean geometry - 'the shortest distance between two points'.

So you don't 'prove' it in Euclidean geometry, it's part of defining what Euclidean geometry is

Neil

@ Neil,

In non Euclidean geometries it is also shortest distance but space itself is bent.

There must be geometries out there where many straight lines could be drawn through 2 points.

In closed bent spaces it is certainly possible.

Martin

I just view maths as a tool, I don't need to know how it works although I think knowing how things work lets you make better use of them.

Mike

And all of this debate followed the question "Are you offended when the media poke fun at your hobby."

Aren't our minds magical?