Math Is Fun Forum

Thanks, Kerim F.

Thanks, Kerim F

“For instance, not every scientific question has an answer.”

Could it be that every (valid) scientific question DOES have an answer; it’s just that the answer, in some cases, may be beyond our reach, or beyond our understanding even if it was presented to us?

“What could be the mechanism/process that lets a body detect (or be detected by) another nearby body in space? We simply see its fruit (result) only, their force of attraction. This unknown mechanism forms a certain field (which could be called gravity for example) in the region in which the two bodies exist.”

Why do you say the mechanism is unknown? Don’t physicists tell us that the mechanism is gravity, a force (or the curvature of spacetime)?

Thanks, Bob.

“When an artist paints a picture it consists of layers of coloured paints on canvas. The paint is distinct from the canvas but you could say the paint occupies the canvas. The canvas is the place where the paint 'sits' (cannot think of a better word here).”

Regards the one dimensional surface-of-a-region-of-the-earth weather map maybe a better analogy would be a special kind of artist who, instead of adding layers of paint to the canvas, treated it in some way (heated it?) in order to affect the colour of it, the way you have the ground beneath our feet (the canvas) and the Sun etc changing the temperature of that ‘canvas’. I hope that doesn’t sound pedantic; I’m just making the distinction between a thing that’s ALTERED and a thing that has ANOTHER THING LAYERED ON TOP OF IT.

“The fields you have described are abstract concepts.”

Why abstract? If they are indeed regions of space, with certain properties? From the article; “This has led physicists to consider electromagnetic fields to be a physical entity...”

Physical entity? Or abstract concept?

“You cannot touch the temperature values; nor can you have an isolated quantum of wind. But it's useful to think of a set of measurements superimposed on the space itself. It's the set of measurements that makes up the field.”

Ah, so you meant that the set of measurements, the numbers, symbols, etc, are the abstract concept?
But do they ‘make up the field’? Or do the merely describe it, represent it? Isn’t the field itself the region, with the particular properties?

“Imagine that by some magic you could lift all the paint off the canvas so it existed separate from the canvas.  That makes two objects.  It's harder to imagine the same happening to the temperatures, but let's try. Somewhere in hyperspace is a set of temperatures that can be mapped back onto the surface of the Earth.”

Interesting. But as I said above I’m thinking that a ‘heat treated’ canvas might be a better analogy. Although, having said that, I’m now wondering if somethin is actually added to the actual field (the region of space)? Is it filled with OTHER THINGS (particles or whatever)? For example when we create an electric field around a rubber balloon by rubbing it on our hair. What happens to that region of space around the balloon? Prior to the experiment it consisted of molecules of air (nitrogen, oxygen, etc), and whatever else (?). What happens to those molecules?

“It's not a concrete thing so it's harder to visualise but, if you are going to study advanced physics you'd better get used to it because I think it will happen a lot.”

I do get that a lot of this is going to be UNUSUAL, to say the least, and maybe, at times, beyond normal language. But I’m wondering if it could be helpful to push it that way as far as we can take it, if you know what I mean.

Thanks, Bob.

“An example of a scalar field is a weather map, with the surface temperature described by assigning a number to each point on the map.” Wikipedia.

The surface of what? (I’m asking rhetorically; as you said, this is a new area for you).

Because of the Oxford definition of ‘region’, and several other websites etc giving ‘region’ as the definition, I was thinking in terms of 3d space. ‘Surface’ does imply 3d, yeah?

So, the surface of..?

When we see a weather map on the telly we’re looking at regions, yeah? ‘Today it will be 10 degrees C in Liverpool.’ ‘Tomorrow it will be 6 degrees C in Blairgowrie.’ Not; 'Today it will be 10 degrees on the SURFACE of the region of Liverpool.'

Interestingly the article goes on to describe a wind as a 1 dimensional vector field.

Google AI Overview;

Rubbing causes electrons to transfer because it increases the amount of contact between atoms of different materials, which allows electrons to move from one material to another:
•Electron affinity
The material with a greater affinity for electrons receives them, while the material with a lesser affinity provides them. For example, when a rubber balloon is rubbed on a wool sweater, electrons move from the wool to the balloon.
•Static electricity
The electrostatic charge that builds up on a material's surface is called static electricity. When two surfaces are rubbed together, one surface gains a positive charge and the other gains an equal negative charge.
•Polarization
Electrons can also move within a neutral object due to the electric field of a nearby charged object. This can happen without the two objects making direct contact.
Static electricity can be used in many activities, such as photocopying, printing, and paint spraying.

Thanks, Bob.

Glad you mentioned the tree experiment. Good timing. I've crossed it off today's to-do-list

Thanks, Bob.

Logarithms are on my to-try-list, but further down the line. Looking forward to them.

I did try out 10^0.3010 and got ≈ 2

Then I tried 10^6-0.3010 and got ≈ 500,000

Q. Should that 6-0.3010 be in brackets?

Thanks, Bob.

So,
Q What’s the speed of the boarder WRT the train?
A Bring train to rest (apply -30m/s).
Same to boarder (5m/s-30m/s)
Boarder; -25m/s WRT train

Q What’s the speed of the train WRT the boarder?
A Bring boarder to rest (apply -5m/s)
Same to train (30m/s-5m/s)
Train; 25m/s WRT boarder

Q What’s the speed of the boarder WRT to me?
A No need to bring me to rest as I’m already at rest. Don’t apply anything
Boarder 5m/s WRT me

Q What’s the speed of the train WRT to me?
A As above
Train; 30m/s WRT me

*

The idea of moving at a negative speed is a curious one to a physics novice like me. Is this a helpful way of beginning to grasp it;

The train is travelling at 30m/s
The boarder, WRT train, is travelling at -25m/s
Assuming they start at the same point, after 1 second the boarder will be 25m behind the train
After 2 seconds the boarder will be 50m behind
Which seems to fit with him travelling at -25m/s (WRT train)

D=ST
D=-25m/s(2s)
D=-50m