Poll

I have this (No or little visualisation in my 'minds eye'

I have it and work in Tech or Science or Finance
I have it and work in Creative Stuff
I have it and work in Government/Military
I have it and work in a high street shop/place of work
I have it and work somewhere else
I don't have it and like cheese
I don't have it and don't like cheese

Author Topic: aphantasia  (Read 2871 times)

Offline Andy @ Allerton!

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aphantasia
« on: February 18, 2023, 11:50:33 pm »
I heard about this a few years back - when I close my eyes I see the inside of my eye lids.

When I imagine I'm on a beach I see blackness

When I try and remember my mum or grandad I see absolutely nothing (She was in a dream - been a few years since I have seen her and it was wonderful- then I realised my wife - and I asked her - could see her mum everytime she closed her eyes :(  )


So... Been reading up and I work in IT. When I get a new concept that people struggle with or a really complex idea, I just get it straight away and was confused how others couldn't. Turns out they couldn't 'see it' when I asked them - new ideas needed to be visualised. Because I can't do this, a new idea is just a new idea - I don't have to translate it into anything. It's an idea that's in my mind - just there that I can address any way I want.

I did more reading and a lot of people that have this work in IT or in places where you can imagine stuff without needing the bollocks of visualisation. Just wondered how many people on RAWK have it :)
Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

Offline Andy @ Allerton!

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Re: aphantasia
« Reply #1 on: February 19, 2023, 12:02:16 am »
As an example. I've been interested in infinty and have been watching a few series on it and the mathematics behind it.

When you say people saying 'I can't imagine it' - I don't believe that for one second.

I think they are saying 'I can't visualise it' because they are trying to imagine it like being on a beach or in a car or in a funfair. You can't visualise infinity - that would be mad.

I can imagine it quite easily because it's an abstract concept. My brain doesn't have to turn this into something I can 'see' - so the idea is easily absorbed. I can imagine infinity or various infinities.

For that - pick an easy example.

Infinity is infinate right?

Nah.

Odd numbers - infinite.

Even numbers - infinite.

Odd Numbers + Even Numbers - infinate - but bigger than that first set. Yeah I think so. And I can imagine that. Could I visualise that? Nah.
Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

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Re: aphantasia
« Reply #2 on: February 19, 2023, 01:18:08 am »
A Fantasia.

This is my upload of the second album by the 80s New Wave band Fantasia that doesn't otherwise exist on the internet. No idea what Andy's banging on about but give this a listen whilst you work it out:

<a href="https://www.youtube.com/v/3Iu4grDopzU" target="_blank" rel="noopener noreferrer" class="bbc_link bbc_flash_disabled new_win">https://www.youtube.com/v/3Iu4grDopzU</a>
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Re: aphantasia
« Reply #3 on: February 19, 2023, 01:44:56 am »


Infinity is infinate right?

Nah.

Odd numbers - infinite.

Even numbers - infinite.

Odd Numbers + Even Numbers - infinate - but bigger than that first set. Yeah I think so. And I can imagine that. Could I visualise that? Nah.


Get chanting this Sanksrit Shloka mate.

Om
Purna-m Adah
Purna-m Idam
Purnat Purna-m Udacyate
Purna-Shya
Purna-m Adaya
Purna-m Eva-Shisyate
Om

Translation.

This is whole ( perfect , infinite and Bajcetic )
That is whole ( perfect , infinite and Bajcetic )
And if you take the whole(  perfect , infinite and Bajcetic ) away
Then only Bajcetic remains.

Om Shanti.

He who sees himself in all beings and all beings in himself loses all fear.

- The Upanishads.

The heart knows the way. Run in that direction

- Rumi

You are held . You are loved . You are seen  - Some wise fella .

Offline BarryCrocker

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Re: aphantasia
« Reply #4 on: February 19, 2023, 05:33:01 am »
Get chanting this Sanksrit Shloka mate.

Om
Purna-m Adah
Purna-m Idam
Purnat Purna-m Udacyate
Purna-Shya
Purna-m Adaya
Purna-m Eva-Shisyate
Om


Or:

Smooth my floatin' like a butterfly
Notes set afloat, sung like a lullaby
Brace yourself as the beat hits ya
Dip trip, flip Fantasia
And all the world is football shaped, It's just for me to kick in space. And I can see, hear, smell, touch, taste.

Offline liverbloke

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Re: aphantasia
« Reply #5 on: February 19, 2023, 08:05:16 am »
reading up on it i found a few things interesting -

aphantasiacs can still 'visually' dream - though this form of recall is involuntary

in can be linked with autism and a weakness in social skills generally

and that it can be seen, by some, as a precursor to dementia - kin el

but no, i am a creative person and have worked within that industry (as well as in IT) and don't suffer thankfully
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Offline KillieRed

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Re: aphantasia
« Reply #6 on: February 19, 2023, 09:35:07 am »
Richard Herring says he has this.
The best way to scare a Tory is to read and get rich” - Idles.

Offline Andy @ Allerton!

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Re: aphantasia
« Reply #7 on: February 19, 2023, 09:54:25 am »
reading up on it i found a few things interesting -

aphantasiacs can still 'visually' dream - though this form of recall is involuntary

in can be linked with autism and a weakness in social skills generally

and that it can be seen, by some, as a precursor to dementia - kin el

but no, i am a creative person and have worked within that industry (as well as in IT) and don't suffer thankfully

Yeah when I dream, the dreams have colour, lots of detail and sound. I tend to dream every night.

Although I haven't been practisiing lately, I could direct dreams - something you need to keep up with and anyone can do it - I can alter and choose what to dream about.

I wouldn't say you 'suffer' I just thought that when hypnotists said 'Can you see yourself on a beach' - I thought they were taking the piss.

I don't know how people leave the house if you can imagine all the best times in your life :D


The good news is that I can't really be hypnotised as it all starts with 'visualise this..'   arf..
Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

Offline Andy @ Allerton!

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Re: aphantasia
« Reply #8 on: February 19, 2023, 10:04:56 am »
Get chanting this Sanksrit Shloka mate.

Om
Purna-m Adah
Purna-m Idam
Purnat Purna-m Udacyate
Purna-Shya
Purna-m Adaya
Purna-m Eva-Shisyate
Om

Translation.

This is whole ( perfect , infinite and Bajcetic )
That is whole ( perfect , infinite and Bajcetic )
And if you take the whole(  perfect , infinite and Bajcetic ) away
Then only Bajcetic remains.

Om Shanti.



I don't need to. I guess other people need to do that to think differently though?
Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

Offline AndyInVA

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Re: aphantasia
« Reply #9 on: February 19, 2023, 10:26:05 am »
Richard Herring says he has this.

My daughter said her school friend has this. They were imagining an apple and one of them just couldn’t.

Offline KillieRed

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Re: aphantasia
« Reply #10 on: February 19, 2023, 10:43:15 am »
Yeah he said similar. He knows what it is, just can’t visualise one in his head. At least he’d make a good ghostbuster.
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Re: aphantasia
« Reply #11 on: February 19, 2023, 12:29:43 pm »
My daughter said her school friend has this. They were imagining an apple and one of them just couldn’t.

That sounds absolutely bonkers  ;D
So bloody what? If you watch football to be absolutely miserable then go watch cricket.

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Re: aphantasia
« Reply #12 on: February 19, 2023, 12:43:37 pm »
Andy did I moider your head about this on Friday? I deffo was talking about it later in the night with our group when we left the beer fest!

I have this. I only found out the other week when that "imagine an apple" thing was going around on Twitter. I don't see anything. I know based on having seen an apple what one looks like, but if you ask me to imagine one and visaulise it in my head, I can't do it. I was absolutely incredulous that people actually *see* an apple. Genuinely didn't even realise that was a thing for the majority of the population until a week or two ago. I'm 36. ;D

I very, very rarely dream / remember my dreams, and I spoke to someone else who also has it and thinks it's related.
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Offline Andy @ Allerton!

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Re: aphantasia
« Reply #13 on: February 19, 2023, 12:44:25 pm »
That sounds absolutely bonkers  ;D

In what way? I know what an apple is. I can imagine it and can even imagine eating one, but visually there isn't anything there, but I can imagine it.

Just the idea you can close your eyes and see an apple seems bonkers to me.
Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

Offline FlashGordon

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Re: aphantasia
« Reply #14 on: February 19, 2023, 12:46:13 pm »
I'm not saying it in a disparaging way, it just seems mad to me that people can't see an apple when they close their eyes.

Is this with everything or just certain things?
So bloody what? If you watch football to be absolutely miserable then go watch cricket.

Offline Andy @ Allerton!

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Re: aphantasia
« Reply #15 on: February 19, 2023, 12:49:36 pm »
I'm not saying it in a disparaging way, it just seems mad to me that people can't see an apple when they close their eyes.

Is this with everything or just certain things?

No I can't see anything mate. It doesn't seem weird to me because I've always never been able to see anything.

As I said, I used to watch shows on TV and actual stage shows and a hypnotist would say "Imagine you're on a beach... can you see the sea and see the beach" and then people would say 'Yeah. I can..'

I honestly thought they were taking the piss. It was only when I watched Spacecamp on Netflix that a character mentioned it and I asked my wife 'Can you see things you imagine - like they are there' and she said yes - she said she can see scenes that happened in the past and replay them.

I always wondered why I was so crap at recognising people I'd met and terrible at names and remembered things poorly, it's because I know the events and remember the experiences, but have zero picture/video recall of them.
Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

Offline FlashGordon

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Re: aphantasia
« Reply #16 on: February 19, 2023, 12:52:38 pm »
No I can't see anything mate. It doesn't seem weird to me because I've always never been able to see anything.

As I said, I used to watch shows on TV and actual stage shows and a hypnotist would say "Imagine you're on a beach... can you see the sea and see the beach" and then people would say 'Yeah. I can..'

I honestly thought they were taking the piss. It was only when I watched Spacecamp on Netflix that a character mentioned it and I asked my wife 'Can you see things you imagine - like they are there' and she said yes - she said she can see scenes that happened in the past and replay them.

I always wondered why I was so crap at recognising people I'd met and terrible at names and remembered things poorly, it's because I know the events and remember the experiences, but have zero picture/video recall of them.

I suppose the reason it seems so weird to me is because I can see things instantly and pretty vividly. Funnily enough though, I can't picture in my head construction plans or drawings before they are completed for some reason.
So bloody what? If you watch football to be absolutely miserable then go watch cricket.

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Re: aphantasia
« Reply #17 on: February 19, 2023, 12:53:41 pm »
I can’t picture what a room will look like with colour schemes and furniture and the like, but I can visualise 3D objects and rotate them …
So a bit yes, a bit no
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Re: aphantasia
« Reply #18 on: February 19, 2023, 12:57:44 pm »
I suppose the reason it seems so weird to me is because I can see things instantly and pretty vividly. Funnily enough though, I can't picture in my head construction plans or drawings before they are completed for some reason.

If you get a complex theory or connection description, can you instantly picture it?

I can't but if I have something explained, I can't see it, but I know how everything connects to everything else and all the complexities. It just kind of stays in my head - not as a picture though - as an idea.

So complex ideas of how stuff works - in work - just are there and I know what it all does.
Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

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Re: aphantasia
« Reply #19 on: February 19, 2023, 12:58:28 pm »
I can’t picture what a room will look like with colour schemes and furniture and the like, but I can visualise 3D objects and rotate them …
So a bit yes, a bit no

Wow. That's amazing mate. I can't understand how you leave the house. I'd be in all day just doing that if I could. Must be incredible.
Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

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Re: aphantasia
« Reply #20 on: February 19, 2023, 12:59:35 pm »
If you get a complex theory or connection description, can you instantly picture it?

I can't but if I have something explained, I can't see it, but I know how everything connects to everything else and all the complexities. It just kind of stays in my head - not as a picture though - as an idea.

So complex ideas of how stuff works - in work - just are there and I know what it all does.

If I had a general understanding of the subject then yes I would be able to. Construction just seems to be a black spot for me visually  ;D
So bloody what? If you watch football to be absolutely miserable then go watch cricket.

Offline TepidT2O

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Re: aphantasia
« Reply #21 on: February 19, 2023, 01:02:33 pm »
Wow. That's amazing mate. I can't understand how you leave the house. I'd be in all day just doing that if I could. Must be incredible.
It’s just molecules mostly… ;D

Then again, I can’t see those magic eye 3D things as I have one eye much more dominant than the other… also have poor depth perception …
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Re: aphantasia
« Reply #22 on: February 19, 2023, 01:08:30 pm »
It’s just molecules mostly… ;D

Then again, I can’t see those magic eye 3D things as I have one eye much more dominant than the other… also have poor depth perception …

You have to relax and unfocus and not rush it.

Just don't think about anything and stop thinking about what you are trying to do and it'll pop out.

Once you get one then it gets easier each time.
Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

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Re: aphantasia
« Reply #23 on: February 19, 2023, 01:09:40 pm »
You have to relax and unfocus and not rush it.

Just don't think about anything and stop thinking about what you are trying to do and it'll pop out.

Once you get one then it gets easier each time.
No, I physically can’t do them ….I have a ‘lazy’ eye. 
“Happiness can be found in the darkest of times, if one only remembers to turn on the light.”
“Generosity always pays off. Generosity in your effort, in your work, in your kindness, in the way you look after people and take care of people. In the long run, if you are generous with a heart, and with humanity, it always pays off.”
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Re: aphantasia
« Reply #24 on: February 19, 2023, 01:11:45 pm »
Try this one.

Take off any glasses you might have. Try relaxing, cross your eyes. Relax. Move your head about. Relax. Stop thinking and just relax and look - don't stare.

Quote from: tubby on Today at 12:45:53 pm

They both went in high, that's factually correct, both tried to play the ball at height.  Doku with his foot, Mac Allister with his chest.

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Re: aphantasia
« Reply #25 on: February 19, 2023, 01:20:11 pm »
Andy, I can’t change my eyes!  They don’t do stereoscope well.
“Happiness can be found in the darkest of times, if one only remembers to turn on the light.”
“Generosity always pays off. Generosity in your effort, in your work, in your kindness, in the way you look after people and take care of people. In the long run, if you are generous with a heart, and with humanity, it always pays off.”
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Re: aphantasia
« Reply #26 on: February 19, 2023, 02:26:56 pm »
been thinking about this...

when i imagine my late nan i can see her but not as in something that appears in my vision but as an imagination of her wherever that takes place in my brain

when i dream i experience all images and scenes as if they are real - like a (very surreal) movie

but when i am addressing a problem within a circuit board (the components and if any are at fault) then i visualise the circuitry as a diagram - is that weird?
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Re: aphantasia
« Reply #27 on: February 19, 2023, 02:44:10 pm »
In what way? I know what an apple is. I can imagine it and can even imagine eating one, but visually there isn't anything there, but I can imagine it.

Just the idea you can close your eyes and see an apple seems bonkers to me.

I wonder if this is just semantics. I can "see" things, but its not "in front of my eyes". Its in my head. I mean, I can close my eyes and remember the game and see a little Nunez taking the ball, bouncing it off his chest and smashing it into the net. If you ask me, what which arm did he pull away, I can look at it and tell you. But its not playing out on the back of my eyelids. If I close my eyes, I see just a bit of afterglow or whatever from the lights before. I can see that at the same time as little Nunez, and I'm very aware of what is in my head and what is coming from my eyes.

Oh, and I'm perfectly fine imagining non-visual things. It's not an either/or thing.


I find it interesting though. Of the other senses, I can also "hear" things in my head, like sing a song, and I can also remember touch and smell, I think. But I can't do it with taste. If you ask me how strawberries taste, I'd probably say, a bit sweet, bit its purely a "learned" answer, because I know they're supposed to be sweet. I can't actually imagine the taste.
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Re: aphantasia
« Reply #28 on: February 19, 2023, 03:11:31 pm »
The Sorcerer's Apprentice is deservedly iconic, but my favourite part is the Night on Bald Mountain

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Re: aphantasia
« Reply #29 on: February 19, 2023, 03:36:11 pm »
Andy did I moider your head about this on Friday? I deffo was talking about it later in the night with our group when we left the beer fest!

I have this. I only found out the other week when that "imagine an apple" thing was going around on Twitter. I don't see anything. I know based on having seen an apple what one looks like, but if you ask me to imagine one and visaulise it in my head, I can't do it. I was absolutely incredulous that people actually *see* an apple. Genuinely didn't even realise that was a thing for the majority of the population until a week or two ago. I'm 36. ;D

I very, very rarely dream / remember my dreams, and I spoke to someone else who also has it and thinks it's related.

Yeah I can't see a thing, but my dreams are really vivid and I seem to dream pretty much every day.

But yeah my mind was blown when I heard others could replay stuff from their lives and see loved ones and whatever.

Seemed incredible to me.
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Re: aphantasia
« Reply #30 on: February 19, 2023, 07:43:59 pm »
My brother has this, he can't visualise anything, he was telling me he can read a book and it's just words.

I can sit here and picture myself walking down a street in Tenerife looking at the sunset, or my lad trying to crawl on the AstroTurf at the hotel when he was 6 months old and the reaction of the people watching
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Re: aphantasia
« Reply #31 on: February 19, 2023, 08:12:47 pm »
Andy you can see things others can't....your Trent Alexander Arnold and I claim my £5.

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Re: aphantasia
« Reply #32 on: February 19, 2023, 10:06:00 pm »
As an example. I've been interested in infinty and have been watching a few series on it and the mathematics behind it.

When you say people saying 'I can't imagine it' - I don't believe that for one second.

I think they are saying 'I can't visualise it' because they are trying to imagine it like being on a beach or in a car or in a funfair. You can't visualise infinity - that would be mad.

I can imagine it quite easily because it's an abstract concept. My brain doesn't have to turn this into something I can 'see' - so the idea is easily absorbed. I can imagine infinity or various infinities.

For that - pick an easy example.

Infinity is infinate right?

Nah.

Odd numbers - infinite.

Even numbers - infinite.

Odd Numbers + Even Numbers - infinate - but bigger than that first set. Yeah I think so. And I can imagine that. Could I visualise that? Nah.

The set of odd integers is the same size of infinity as the set of even integers, and is the same size of infinity as the set of integers, it's not a bigger infinity.

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Re: aphantasia
« Reply #33 on: February 19, 2023, 10:11:17 pm »
The set of odd integers is the same size of infinity as the set of even integers, and is the same size of infinity as the set of integers, it's not a bigger infinity.

You'd need to take that up with Georg Cantor mate.

And you're wrong :)
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Re: aphantasia
« Reply #34 on: February 19, 2023, 10:27:36 pm »
You'd need to take that up with Georg Cantor mate.

And you're wrong :)

There is a bijection

f(x) = 2x

between the integers and the even integers. This means that the two sets have the same cardinality.

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Re: aphantasia
« Reply #35 on: February 19, 2023, 11:05:15 pm »
There is a bijection

f(x) = 2x

between the integers and the even integers. This means that the two sets have the same cardinality.

So you're saying Georg Cantor is wrong and there aren't infinite infinities?

Remarkable. I'd like to read your paper where you turn mathematics on its head :)

I'm not a mathematician, but I have read about this fella. Basically you take the stance that an infinite set contains every single number ever. Therefore any set that isn't that set is a subset of that set. Once you accept that any set that is a subset of the complete set then that means that there are infinite subsets. Therefore infinite infinities.

But if you think he's wrong fair enough
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Re: aphantasia
« Reply #36 on: February 19, 2023, 11:43:27 pm »
So you're saying Georg Cantor is wrong and there aren't infinite infinities?

Remarkable. I'd like to read your paper where you turn mathematics on its head :)

I'm not a mathematician, but I have read about this fella. Basically you take the stance that an infinite set contains every single number ever. Therefore any set that isn't that set is a subset of that set. Once you accept that any set that is a subset of the complete set then that means that there are infinite subsets. Therefore infinite infinities.

But if you think he's wrong fair enough

I am a mathematician. In fact I'm a mathematician with a masters degree from Cambridge. I didn't say anything about Cantor, it was you who brought him up. I'm not saying that Cantor is wrong. I'm saying that *you* are wrong. I appreciate that this may be because you're shitposting for a laugh, but in case you're serious you need to know that you're wrong and are exhibiting classic symptoms of the Dunning Kruger effect.

The size (mathematically we say Cardinality) of the set of integers is the same as the Cardinality of the set of even integers or the set of odd integers.
This is because you can pair up each integer with an even integer (a bijection) so the sets must therefore be the same size.

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Re: aphantasia
« Reply #37 on: February 20, 2023, 01:05:07 am »
I am a mathematician. In fact I'm a mathematician with a masters degree from Cambridge. I didn't say anything about Cantor, it was you who brought him up. I'm not saying that Cantor is wrong. I'm saying that *you* are wrong. I appreciate that this may be because you're shitposting for a laugh, but in case you're serious you need to know that you're wrong and are exhibiting classic symptoms of the Dunning Kruger effect.

The size (mathematically we say Cardinality) of the set of integers is the same as the Cardinality of the set of even integers or the set of odd integers.
This is because you can pair up each integer with an even integer (a bijection) so the sets must therefore be the same size.

The sound like different things to me. I can see that odd numbers and even numbers pair up. But how can odd numbers + even numbers pair up with either odd numbers on their own or even numbers on their own?

The set of odd numbers + even numbers is even and odd numbers isn't it? You can pair up the odd numbers with the odd numbers and the same with even, but how to you pair up odd numbers on their own or even numbers on their own against a set of even and odd numbers? That doesn't seem to make any sense.

Not sure why you're even having this argument unless its so you can tell everyone that you've got a maths degree :D  But obviously you must be right if you have a degree in it. Just confirms my suspicion that maths is stupid :D
« Last Edit: February 20, 2023, 01:09:26 am by Andy @ Allerton! »
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Re: aphantasia
« Reply #38 on: February 20, 2023, 01:28:11 am »
The sound like different things to me. I can see that odd numbers and even numbers pair up. But how can odd numbers + even numbers pair up with either odd numbers on their own or even numbers on their own?

The set of odd numbers + even numbers is even and odd numbers isn't it? You can pair up the odd numbers with the odd numbers and the same with even, but how to you pair up odd numbers on their own or even numbers on their own against a set of even and odd numbers? That doesn't seem to make any sense.

Not sure why you're even having this argument unless its so you can tell everyone that you've got a maths degree :D
:D not trying to be boasty (sorry if it came over that way!) just laying my credentials on the table.

As long as you can pair up each number in (say) the integers with every number in the (say) even integers then the sets are the same size.

If I pair up 1 with 2, 2 with 4, 3 with 6 and so on off to infinity then I've got a bijection (it's 1 to 1 and on-to), that is, each element of the integers pairs up with a single element of the even integers and vice versa. If I have an element of one set there's exactly one matching element in the other set (and it works both ways). No elements in either set are missed. Therefore, the number of elements in each set is equal. I.e. the sets have the same Cardinality.

The mistake here would be to think that there are half as many integers in the even integers as the integers because you're leaving out every other one; that's a misunderstanding of what infinity is and how it works.

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Re: aphantasia
« Reply #39 on: February 20, 2023, 09:21:44 am »
:D not trying to be boasty (sorry if it came over that way!) just laying my credentials on the table.

As long as you can pair up each number in (say) the integers with every number in the (say) even integers then the sets are the same size.

If I pair up 1 with 2, 2 with 4, 3 with 6 and so on off to infinity then I've got a bijection (it's 1 to 1 and on-to), that is, each element of the integers pairs up with a single element of the even integers and vice versa. If I have an element of one set there's exactly one matching element in the other set (and it works both ways). No elements in either set are missed. Therefore, the number of elements in each set is equal. I.e. the sets have the same Cardinality.

The mistake here would be to think that there are half as many integers in the even integers as the integers because you're leaving out every other one; that's a misunderstanding of what infinity is and how it works.

Nice one thanks for posting that. I certainly stand corrected. I was reading up on it a bit last night, but although I accept that it's right, it seems pretty counter-intuitive. Probably why I haven't got a maths degree :)

So much of maths doesn't seem to make too much sense. Look at PI - it's only 1.34159... because we have ten fingers and went for the Arabic number system as far as I'm aware. Perhaps there is a point where all these mad and recursive numbers aren't as crazy. Maybe they only work in this 3d (or 4d) reality? Then you see the Universal constants. Why are they the values they are? I have read that they have to be that way for this reality to exist. Maybe we have the answers now or will work them out - these new quantum computers look pretty amazing and should give us a new way of viewing the world.. We might only get there if computers recursively program themselves out of the control of mere humans.

But I think I've gone off on a tangent now (As is my wont :D )
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