The analogue-summing '3D' effect: what actually is it?

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Re: The analogue-summing '3D' effect: what actually is it?

Posted: Thu Jun 04, 2020 1:10 pm
Folderol wrote:Very interesting, what you say about patterns. When attempting to teach people a bit about understanding electronic drawings I always make a point of telling them they need to develop a mental image of what is going on in the various devices. It doesn't matter how 'correct' the image is, just that it gives them a reasonably accurate idea of what to expect coming out, knowing what is going in.

This is especially true of logic diagrams!

That's exactly what you gotta do with math. It's only a language to describe stuff, if you don't have an image, there's nothing to describe!

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Thu Jun 04, 2020 5:52 pm
That's where I struggled with calculus. First and second order differentials and intregrals were easy enough to picture, but as you got into the higher order stuff my mental models broke down - and then I was really just remembering tricks and techniques and not really, properly, understanding the maths.

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Thu Jun 04, 2020 7:17 pm
Makes sense, Drew - I do wonder if trying to picture it, in one form or another, is where it goes wrong for many people?
I know it's how a lot of teachers seem to approach it, and it can work with simple stuff so is certainly potentially useful, but you get to a point where trying to picture something very abstract/complex may perhaps actually serve as more of a distraction?
I think I'm quite lucky in that maths seems to exist in my head as a thing all of its own - the closest tangible thing to it is probably the physical sensation of texture rather than any sort of image. Alas I have no real idea how to translate "that theorem feels somewhat knobbly" into something that might help others understand it better :lol:

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Thu Jun 04, 2020 7:48 pm
Sounds like it's almost a kind of synesthesia to you. Does it taste kind of purple too? ;)

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Thu Jun 04, 2020 8:58 pm
Logarhythm wrote:Makes sense, Drew - I do wonder if trying to picture it, in one form or another, is where it goes wrong for many people?
I know it's how a lot of teachers seem to approach it, and it can work with simple stuff so is certainly potentially useful, but you get to a point where trying to picture something very abstract/complex may perhaps actually serve as more of a distraction?
I think I'm quite lucky in that maths seems to exist in my head as a thing all of its own - the closest tangible thing to it is probably the physical sensation of texture rather than any sort of image. Alas I have no real idea how to translate "that theorem feels somewhat knobbly" into something that might help others understand it better :lol:

Well it did work for Feynman! :D

But I guess people are different.

Also, the importance of repetition in math is often underestimated. You cannot learn to use a formalism until you're using it in anger. Then it will start to just "feel" right or wrong for the direction you want to take.

The challenge with school is that to sustain that level of repetition you need to be interested, otherwise is far too easy to just give up. Very similar to practice with a musical instrument.

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Thu Jun 04, 2020 10:44 pm
The inability of today’s yoof to do mental maths is shocking though
I have to admit that I'm not great at mental arithmetic, I'm not too bad at adding two low values together, but as the list gets longer (or the values get longer) I can't remember my subtotal up to that point, e.g. 10.3 + 2.5 = 12.8, but 10.42 + 2.96 + 11.8 will be a problem for me. I'm pretty good at multiplication tables up to 12 times but 13 times onwards forget it if you need a quick response.
I managed to get an O Level Maths, just, and did A level Physics where learned equations I found pretty straightforward but I started additional O level in Maths for one term and really struggled, mostly because it was all letters representing numbers.
when I visit my parents we watch Countdown together, my Dad, a retired accountant has no problem with the maths side whereas I do well at the words, Countdown conundrum and teatime teasers.
I put it down to different wiring in the brain and as for the 'yoof' they've only ever had calculators :lol:

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Fri Jun 05, 2020 2:24 am
CS70 wrote:...The challenge with school is that to sustain that level of repetition you need to be interested, otherwise is far too easy to just give up. Very similar to practice with a musical instrument.

Quite. One person with the inner drive of interest will spend years of their lives studying a subject, practising a sport or musical instrument, and eventually making it their lifetime occupation. Whereas someone else from the same set of parents, and brought up in the same household, and going to the same schools, will have little or none of the same interest. Yet in spite of that some continue to maintain our minds are just blank slates and any differences in interest or performance are purely or mostly due to differences in training.

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Fri Jun 05, 2020 8:56 am
CS70 wrote:Well it did work for Feynman! :D
Yeah, but that's not a great example as it's not like he accomplished much with it :bouncy:

Couldn't agree more on the repetition element though - whether you see maths as some sort of wiggly mental picture or believe that it tastes purple, it's exactly like learning an instrument - need to practice until it becomes so natural that you don't realise you're doing it.

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Fri Jun 05, 2020 10:20 am
Logarhythm wrote:
CS70 wrote:Well it did work for Feynman! :D
Yeah, but that's not a great example as it's not like he accomplished much with it :bouncy:

Couldn't agree more on the repetition element though - whether you see maths as some sort of wiggly mental picture or believe that it tastes purple, it's exactly like learning an instrument - need to practice until it becomes so natural that you don't realise you're doing it.

Haha no he just made up some little diagrams :D But honestly I don't know, I'm most definitely not a particle physicist, so maybe they're not really much relevant anymore?

Another interesting aspect (that appears in this thread, like it always does) is how people mix up mathematics with arithmetic and calculations - especially the ability to calculate mentally.

I surmise that everyone here who's using a DAW is doing mathematics but not necessarily arithmetic and while some mathematicians can be friends with numbers, not all are (if not, nobody would have thought of inventing computing machines.. :) )

Very often for me it gets down to a feeling that a certain quantity is or is not in the right ballpark, but if I have to find the precise value, it's pen and paper time! But of course, I've stopped going to my mental calculation gym long long time ago.. so maybe that's training as well, dunno.

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Fri Jun 05, 2020 1:47 pm
So if you don’t use it, you will lose it.
If so I better start finding some fun arithmetic games apps as I feel I’m losing it. I am grateful for going through school just as calculators were invented and not yet common to see. I was able to add up purchase totals in my head while waiting in the checkout line.
Several times I’ve noticed that checkout people would be absolutely lost if they didn’t have a cash register in front of them.
What stumped me was ‘ buy 4 for reduced sale price’ I could never figure out the cost of 3.
Rambling a bit here, sorry.
Last thought -
Cellphone calculator is absolutely brilliant for figuring out per gram cost etc in the supermarket to see if the sale price actually was a good deal compared to other regular prices. Think of the pennies I’ve saved that I can put to a new piece of gear. rubs hands with glee and snickers!

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Fri Jun 05, 2020 2:22 pm
ManFromGlass wrote:So if you don’t use it, you will lose it.
Yes, unfortunately so...

I found stacking shelves / working on a checkout particularly good for developing mental arithmetic speed. It was such a boring job that I'd calculate pointless things that were vaguely related to what I was doing just to stave off the despair. e.g. multiplying barcodes of things I'd put on the shelves, estimating how many individual baked beans I moved this month, how high a tower would I be able to create with the mince pies shifted over Christmas (alas my manager's sense of humour/curiosity didn't stretch to allowing experimental verification of this :D ), or calculating the total in each of the baskets of the people in waiting in the queue before they got to the till.

ManFromGlass wrote: rubs hands with glee and snickers!
Doesn't that make your hands too sticky to then use any gear? :D

Re: The analogue-summing '3D' effect: what actually is it?

Posted: Sat Jun 06, 2020 12:51 pm