1/2²

[DTLarca]

Is it immediately clear that

1/2/2 = 1/2²

[frank]

Is it immediately clear that

1/2/2 = 1/2²

Indeed.

1/4 = 0.25

[DTLarca]

Indeed.

1/4 = 0.25

If I were to explain why it is that so many techs and students have a problem working out how we get from m/s/s to m/s² or 1/2/2 to 1/2² how might I start explaining this?

[frank]

Why do you feel the need to explain it?

[DTLarca]

1/2 divided by 2 is the same as 1/2 divided by 2/1 as in 1/2/2/1

We then multiply the top and bottom by a special case of the number one being 1/2/1/2 which cancels out to 1/2²

But why do some people have a proble with this - what are they missing?

[DTLarca]

Why do you feel the need to explain it?

Because I'm looking to spend an equal amount of time explaining ratios as the principles of physics because they are almost the same thing any way

[frank]

Anything divided by 1 remains as is.

245/1 = 245

1/2/1/2 = 1/2/2 = 0.25

[DTLarca]

Anything divided by 1 remains as is.

245/1 = 245

Most (all folks I know) get that far...

1/2/1/2 = 1/2/2 = 0.25

But now even you have made a mistake, see how fuzzy this stuff actually is - it's difficulties are deceivingly more than we intuitively imagine

[mad fridgie]

Most younger techs have been tought maths in a slightly different way to pherhaps how we were taught
"BODMAS"
(1/2)/2

[DTLarca]

Most younger techs have been tought maths in a slightly different way to pherhaps how we were taught
"BODMAS"
(1/2)/2

BODMAS is British - the Americans do not use it in their schools. I wonder if they are actually doing the better thing?

[monkey spanners]

Is it immediately clear that

1/2/2 = 1/2²

No, but i have dyslexia so

I can struggle adding up 24 and 5 for example if i am tired.

Often i find it because i don't understand the question that i struggle to answer.

Jon

[mad fridgie]

1/2+3 =????

[Brian_UK]

I thought that ratios were signed with a colon ':' as in 2:1 etc. or is that the wrong math now-a-days?

[DTLarca]

No, but i have dyslexia so

I can struggle adding up 24 and 5 for example if i am tired.

Often i find it because i don't understand the question that i struggle to answer.

Jon

What does 1/2 mean to you?

[DTLarca]

1/2+3 =????

This has to be 3.5

[mad fridgie]

This has to be 3.5

could it not be 0.2?
(1/2)+3= 3.5
1/(2+3) = 0.2

[DTLarca]

I thought that ratios were signed with a colon ':' as in 2:1 etc. or is that the wrong math now-a-days?

I = V/R

The current through given resistance depends on the ratio of V : R

[DTLarca]

could it not be 0.2?

It depends on the conventions you, and those using the system with you, agree upon.

You and I could agree that 2+3 without any gaps is the same as (2 + 3) in which case 1/2+3 would be 0.2 and 1/2 + 3 would be 3.5

[monkey spanners]

What does 1/2 mean to you?

I'd say thats a half. I think i'm more verbal that written in my thinking. Thats why these things like tests and exams give me trouble. Or i'm just stupid Who knows?

If i was being flippant i would say that '1/2' is empty of any inherent meaning, it only means what you think it does because that is what you have learnt and you haven't seen anything since that learning to make you question that knowledge.

I don't mind my dyslexia, in many ways its a blessing. I am quite good at 3D stuff so bending pipes to fit is easy for me, and if i can get a picture of them in my mind i find systems easy to fault find.

Jon

[Magoo]

I use an RPN calculator, that saves a lot of greif.
I went to school to eat lunch then learnt more after that, by choice.
If I knew then what I knew now, that situation would be totally different, but I cannot change time. Bugger

[desA]

e^(pi*i) + 1 = 0

Why? What significance?

[mad fridgie]

Why? What significance?

? lost me

[lawrence1]

Don't know what they're on but i wouldn't mind some.

[lawrence1]

Ahhh now i see it's Franks Harvest Pale,,,,,,must be good.

[DTLarca]

Why? What significance?

Euler's identity?

They say beauty?

But that's is a radical change of topic from how fractions work to how transcendental constants interplay.

[DTLarca]

I'd say thats a half.

If i was being flippant i would say that '1/2' is empty of any inherent meaning, it only means what you think it does because that is what you have learnt and you haven't seen anything since that learning to make you question that knowledge.

Would you agree that it means something like "If I have part of a whole I can tell roughly how much of the whole my part is if I cut the rest of the whole into pieces equal in size to the part I have"?

The "/" means "per" so I have 1 per 2 as in I have 1 of the 2 or 1 for every 2. If there are just 2 of them then I have half of them but if there are an unknown or variable amount of them then I will be entitled to a ratio of 1 for every 2. Whether it is a fraction or a ratio is is the same thing. Physics formula are ratios but they become fractions once the amounts are known.

[DTLarca]

It's important to understand how we work with fractions if we want to talk of physical principles in terms of ratios...

What does this reduce to...

1/2/1/2/1/2

As in, for instance, when we have

kg m²/s²/N/m/s²/K

[nevgee]

Euler's identity?

They say beauty?

But that's is a radical change of topic from how fractions work to how transcendental constants interplay.

Apparently a 1:2 ratio is symbolically beautiful, and so a "golden ratio" may exist.

[nevgee]

Would you agree that it means something like "If I have part of a whole CAKE I can tell roughly how much of the whole CAKE my part is if I cut the rest of the whole CAKE into pieces equal in size to the part I have"?

The "/" means "per" so I have 1 per 2 as in I have 1 of the 2 or 1 for every 2. If there are just 2 of them then I have half of them but if there are an unknown or variable amount of them then I will be entitled to a ratio of 1 for every 2. Whether it is a fraction or a ratio is is the same thing. Physics formula are ratios but they become fractions once the amounts are known.

?????? Having read that I now think I'm dislexic also.

I think there is a fundamental error here. You've taken a simple concept, ie a fraction 1/2 and made it into an extremely complicated structure by your own method of description. I really don't think the fraction has any need to be extorted in such a way. Poor fraction.

simply 1/2 = one whole divided by 2 or did I miss a lesson? Maybe I need some Harvest Pale?

[desA]

Euler's identity?

They say beauty?

But that's is a radical change of topic from how fractions work to how transcendental constants interplay.

The topic goes a lot, lot deeper than Euler & pure beauty.

The diatribe on the continued fractions is rather esoteric & beautiful. It proves nothing & will lead to confusion. Better to retain only a numerator & denominator, with various combinations strung in series products - as per dimensional analysis theory.

It is easy to appear incredibly smart at others' expense, but this can be counter-productive in the long-run. If you really want to take on a challenge, try explanations of how the various RHVAC circuits work - & develop solid design rules for these. We can then all chip in along the way & this group effort can teach us all something.

[DTLarca]

The topic goes a lot, lot deeper than Euler & pure beauty.

The diatribe on the continued fractions is rather esoteric & beautiful. It proves nothing & will lead to confusion. Better to retain only a numerator & denominator, with various combinations strung in series products - as per dimensional analysis theory.

It is easy to appear incredibly smart at others' expense, but this can be counter-productive in the long-run. If you really want to take on a challenge, try explanations of how the various RHVAC circuits work - & develop solid design rules for these. We can then all chip in along the way & this group effort can teach us all something.

I'm trying to take that which appears esoteric or appears as meant to be esoteric and rather make it common place.

Consider this example... Specific heat capacity

kJ/kg/k

Why does it reduce to kJ/kg.K and not KJ.K/kg ??

I have answers to this question - I brought it up a few times with my HND students at Bath College. I thought it so important that I even invited the college's math lecturer in to the class on one occasion to discuss the matter with us. After that occasion the question wasn't fully answered but I am now happy that I have thought enough about it to be able to explain the difference to myself.

[cool runings]

I'm trying to take that which appears esoteric or appears as meant to be esoteric and rather make it common place.

snip

After that occasion the question wasn't fully answered but I am now happy that I have thought enough about it to be able to explain the difference to myself.

DT you ask questions but you have a mightier than thou attitude..
You come over as somone who has taken it upon himself to educate others around you.

But........................

But you do not educate you talk down and undermine others.

You are obviously very educated and extremely inteligent but you come
across as a condicending pr*ck who has had a humour bypass.

You have taken it upon youself to make us better but
you have not asked us if we want your help.

Some of us are not very well educated and when an academic starts showing
off at how inteligent he is, others just put you in the w*nker box.

I have been watching your posts on here since you joined and I have tried to weigh you up...

But I can't, I can't weigh you up, you preach and talk down to people, you never realy offer any
constructive advise, you just spout on about how good you are.

Some engineers on here could not add 2 and 2 together but I would trust them
with a set of spanners and gauges, you would try to belittle them, just to make you look better.

I'm in two minds regarding you.....

Your a w*nker and you need to be filed in the w*nker box

OR

You might have a lot of usefull information and you might be of help to a lot of
good engineers and teach them, if you would only get off your soap box and stop preaching to us.


Now if you are a troll and a wind up merchant you have just won and I have
lost because I bit and mouthed back at you.....

If your a pr*ck then you'll continue as you are.

If you are a decent bloke you'll pull your head out of your arse and offer constructive advise in a way that helps.


coolrunnings

.

[monkey spanners]

Would you agree that it means something like "If I have part of a whole I can tell roughly how much of the whole my part is if I cut the rest of the whole into pieces equal in size to the part I have"?

The "/" means "per" so I have 1 per 2 as in I have 1 of the 2 or 1 for every 2. If there are just 2 of them then I have half of them but if there are an unknown or variable amount of them then I will be entitled to a ratio of 1 for every 2. Whether it is a fraction or a ratio is is the same thing. Physics formula are ratios but they become fractions once the amounts are known.

I understand fractions and their use, its just that its like numbers are a foreign langauge that i don't know that well, so unlike normal talking where you don't have to think to comunicate, i have to really think sometimes just to do what others may regard as a simple calculation.

I think it was when prime numbers were being taught at school that things started to go wrong for me, we were taught that a prime number is only divisible by itself and 1, e.g. 7 is a prime number.
But to me and my litteral way of taking things 7 and 1 is 8, and i may be daft but i know 8 won't fit in 7....

Jon

[DTLarca]

Specific heat capacity

kJ/kg/K

Why does it reduce to kJ/kg.K and not KJ.K/kg

To go from kJ/kg/K to kJ/kg.K we could say that we did the following

kJ/kg/K/1 was multiplied top and bottom by a special case of 1 being 1/K/1/K (1/K goes into 1/K once).

But then that invokes the question why not...

kJ/1/kg/1/K/1 which when subjected to the same treatment gives us kJ.K/kg.

One way we can look at it is to say that specific heat capacity kJ/kg.K just means that if you had 1kg of the substance then its enthalpy content would increase so many kJ per K temperature rise but at the same time if your substance were to rise in temperature by 1K then the enthalpy rise would be so many kJ for every kg of the substance you had. In which case it doesn't really make sense to think of it as kJ per kg per K but rather from the very outset to think of it as kJ per both kg and K at the same time.

But then we might look around at other examples of the layout and say that always where we have three levels to a fraction we actually have a numerator in fraction form and a denominator implicitly in fraction form which just needs the "over 1" or "/1" to be added beneath it to make explicit that when the numerator is a fraction so too must the denominator before transposing the whole arrangement.

How though does this view stand in regard to acceleration which does seem quite clearly to be m/s/s or meters per second per second as in Velocity per Second. It doesn't seem right to start off from the outset with meters per second second. I feel that m/s² is different from kJ/kg.K and if it is then in what way is it different?

[DTLarca]

I understand fractions and their use, its just that its like numbers are a foreign langauge that i don't know that well, so unlike normal talking where you don't have to think to comunicate, i have to really think sometimes just to do what others may regard as a simple calculation.

I think it was when prime numbers were being taught at school that things started to go wrong for me, we were taught that a prime number is only divisible by itself and 1, e.g. 7 is a prime number.
But to me and my litteral way of taking things 7 and 1 is 8, and i may be daft but i know 8 won't fit in 7....

Jon

I don't understand the relevance of prime numbers myself. I fell asleep just at the point where I read the words in your post above - now that I have woken up I hope to make a quick escape from any further consideration of them

I have limited mental capacity - so I spend most of my efforts eliminating what I think is not important - I tend only to discuss or get involved with discussions on stuff I know is very importantly relevant to what I do.

[nevgee]

I have limited mental capacity - so I spend most of my efforts eliminating what I think is not important - I tend only to discuss or get involved with discussions on stuff I know is very importantly relevant to what I do.

Everything has limits?

[DTLarca]

Where acceleration is m/s/s and so m/s/s/1 becoming m/s² after multiplying it by a special case of 1 being 1/s/1/s we can do the reverse for pressure as in N/m² which can become N/m/m as in Newton per meter per meter.

If the force (Newton) was created by 10kg of water which would be 10 x 9.81 = 98.1N was over an area of 1m x 2m then the pressure in Pascals or N/m² would be 98.1/(1x2) = 49N/m² (Pa).

We could just as easily have followed N/m/m as in 98.1/1/2 = 49Pa.

Here we can look at 98.1/1/2 as if it were (98.1/1) divided by 2 gives 49Pa or someone might say "No, I see 98 divided by 1/2 which is 196Pa".

The correct answer seems to always come about when we treat the top most fraction as a whole number and then the remaining lower value as the denominator and treat it, during superposition, as an implied fraction by adding and "over 1" to it.

[DTLarca]

Everything has limits?

And everything has a probability and the probabilities of all things must add up to one so something rather than nothing HAS to happen

[nevgee]

And everything has a probability and the probabilities of all things must add up to one so something rather than nothing HAS to happen

1 is the answer …….. and I thought it was 42!

[Quality]

I thought 3 was the magic number

[DTLarca]

1 is the answer …….. and I thought it was 42!

The answer probably is DA's 42 because the probability notion is nonsensical - it presents a paradox - the more things we can think of as possible the less likely they are if the sum of all probabilities can only equal 1 because how then can we think them possible.

[desA]

Consider this example... Specific heat capacity

kJ/kg/k

Why does it reduce to kJ/kg.K and not KJ.K/kg ??

The correct way to write this is

kJ.kg^-1.K^-1

or, kJ/(kg.K)

The first form is the scientific way, the second is an 'easier' way - both are mathematically correct. kJ/kg.K infers kJ/(kg.K), but is sloppy notation.

[DTLarca]

The correct way to write this is

kJ.kg^-1.K^-1

or, kJ/(kg.K)

The first form is the scientific way, the second is an 'easier' way - both are mathematically correct. kJ/kg.K infers kJ/(kg.K), but is sloppy notation.

Certainly, but that does not change the fact that, for example, acceleration is (m/s)/s as in rate of change of velocity and can be represented as m/s/s without being in any epistemic way wrong.

[nevgee]

And everything has a probability and the probabilities of all things must add up to one so something rather than nothing HAS to happen

With probability there will be uncertainty.

Is not the case that an uncertainty principle states by precise inequalities that physical properties, cannot be simultaneously known to arbitrarily high precision.

meaning that it is impossible to determine with any great degree of accuracy or certainty.

Can you then be certain it is One? Or should it be one and a little bit, or one and a little less?

[DTLarca]

With probability there will be uncertainty.

Is not the case that an uncertainty principle states by precise inequalities that physical properties, cannot be simultaneously known to arbitrarily high precision.

meaning that it is impossible to determine with any great degree of accuracy or certainty.

Can you then be certain it is One? Or should it be one and a little bit, or one and a little less?

In quantum theory Heisenberg's uncertainty principle applies to concepts such as trying to determine at the same time both the position and velocity of a sub atomic particle or at the same time the energy and the time.

It is like trying to know at the same time the tone of a musical note the current amplitude of the emitted sound - you cannot know both at the same time because a tone is a series of waves not a point moment of a wave.

But when it comes to "probabilities" we define them ourselves - probabilities lie between 0 and 1 or in terms of induction between just above 0 and just below 1 but never 0 or 1. As in the proposition "The sun has risen everyday in all of known history therefore it will rise again tomorrow" is a probability which cannot be a perfect 1. And the probability that the sun will not rise tomorrow cannot be a perfect 0 - we just cannot be so certain.

[desA]

Certainly, but that does not change the fact that, for example, acceleration is (m/s)/s as in rate of change of velocity and can be represented as m/s/s without being in any epistemic way wrong.

In matters of this nature, less confusion is found if standard conventions are adhered to.

This is precisely the reason for writing kJ.kg^-1.K^-1.

[DTLarca]

In matters of this nature, less confusion is found if standard conventions are adhered to.

This is precisely the reason for writing kJ.kg^-1.K^-1.

Yes, I tend to agree - I am fluent with the index notation - it has its own questions that crop up every now and then like why is anything to the index 0 equal to 1. Because 2²/2² is also 2² x 2­­­-²­ = 2²-² = 2° = 1

But look at it from this point of view. Picture yourself standing in front of a white board explaining acceleration on a velocity/time graph (Vfinal = at) and you are explaining that where velocity is meters traveled per second (m/s) acceleration is meters per second PER SECOND and you place that on the board as m/s/s so that the students can see that you mean precisely meters per second PER SECOND.

How does it help them to understand it, when they are your typical level 3 student who hardly understands what 5² means let alone what 5-² or 5^½ means, if you throw it up on the board in index notation - how are they to get a feel for what we are talking about?

When I went to college for my tech cert we had to have at least matric math and science. In the UK most students are doing fridge only because they were poor at math and science, not because those were their favorite subjects (very odd but true) and this is what my quest is about.

[nevgee]

But look at it from this point of view. Picture yourself standing in front of a white board explaining acceleration on a velocity/time graph (Vfinal = at) and you are explaining that where velocity is meters traveled per second (m/s) acceleration is meters per second PER SECOND and you place that on the board as m/s/s so that the students can see that you mean precisely meters per second PER SECOND.

How does it help them to understand it, when they are your typical level 3 student who hardly understands what 5² means let alone what 5-² or 5^½ means, if you throw it up on the board in index notation - how are they to get a feel for what we are talking about?

I remember doing the motion equations at school .... we didn't know what was going on, it was given to us in formula and by experimentation and model work. I recall specifically that we would draw our results in graph form (x & y axis).

acceleration was noted as m/s2 not m/s/s .. pointless notation which can only confuse further.

During my eductational and working life I found that it is essential for an instructor to level themselves at their students intellect level, Then work up from there. Pre judging someone's knowledge skill and then writing them off as being "stupid" is not the way forward and doesn't come over as very professional iether. I'm sure a good educator worth his salt can find the way to impart their knowledge to a student in the form that the student will understand, without having to try and rewrite conventional standards.

[DTLarca]

acceleration was noted as m/s2 not m/s/s .. pointless notation which can only confuse further.

I have found the m/s² form is either taken for granted as representing acceleration but rarely something a student can put into words explaining what is happening when something accelerates or it is just plain not understood.

I find that when we set that aside and instead go to talking about how the meters traveled per second are increased by so many meters per second every second, as in m/s/s, then eye's start to light up. Then the question after that is usually "ah, okay, that makes sense now - so then how is that related to m/s² ?" and this is then when we get to the reason this thread was started.

[monkey spanners]

There are a few things i find are helpful in learning new things.

One is believing i need to learn it, that the new knowledge will be useful to me.
For it to go in, it needs to be demostrated so i understand it, and for me to practice it and then become proficient.
I then need to use it regularily to keep it fresh in my mind.

I wonder if a lot of engineers are practicaly natured, and would benefit from real world examples of how these formulas are useful.

I can see how it would be frustrating to have to teach students who lack even the basics, sometimes i get fed up repairing things or bored with installation work but i try to remind myself that without this work i would not be able to earn a living