Linguistic thinker: I reach conclusions by feel, pretty much jumping to them, and then sniffing out the "warp trail" from that jump and putting that into words. It doesn't feel like inventing post facto rationalizations, but rather retracing the reasoning that happened in the background. And I do need to do that step - the conclusion doesn't seem "stable" unless I trace it back like this.
Words are also based on the same intuition, you just verbalize it and restrict yourself to what you have words for instead of all concepts and thoughts.
For example I do math entirely without any words in my process, and I easily got a master in math that way, barely had to study. No problem, you just translate it at the end. Limiting myself to words just makes it harder to think freely.
That just sounds so different to how I solve math problems. I was naturally good at maths, but it was always from monologue kind of bruteforcing different solutions until one of them seemed to work. I guess it might be a reason also why I find LLMs really exciting since I feel like if I can do it, LLM should be able to do it. I don't feel like I am doing anything special.
I always had problem with trusting my intuition or gut so I was worse in a lot of other real life things however. But math seemed abstract and solvable by words and brute force.
I wish things just magically came to me, but I think I always have to go through things with my inner monologue.
Like if I was to do multiplication in my head e.g. with same numbers, for example 62 x 62. I would have to go through it as a monologue.
I first remind myself of the strategy to do it, which is first I will do 60 x 60. Then it is 3600, then I add 2 x 60, 3720, and then there is 2 x 62 left, but I have to keep reminding myself occasionally what the last numbers were, that initial multiplication was 62 x 62, then I got 3720, and now I have to add 124... okay lets go 3820, 24 left, now 3844. Of course it is easier to remember as I am typing this, but in my head I have to keep reminding myself. And now I am not sure if I did a mistake so I go verify that on the calculator.
> I first remind myself of the strategy to do it, which is first I will do 60 x 60. Then it is 3600, then I add 2 x 60, 3720, and then there is 2 x 62 left, but I have to keep reminding myself occasionally what the last numbers were, that initial multiplication was 62 x 62, then I got 3720, and now I have to add 124... okay lets go 3820, 24 left, now 3844. Of course it is easier to remember as I am typing this, but in my head I have to keep reminding myself. And now I am not sure if I did a mistake so I go verify that on the calculator.
I do multiplication in my head similarly, just strip out the words, the numbers just flickers through and operations happens by themselves and I'm done in a second or two when I'm not rusty. Now that I'm rusty I do it more like (60x60=3600, 2x2=4, 60x2=120, 3600 + 4 + 120 + 120 = 3844), without doing any words, I just did that in my head right now and I am 100% sure not a single word, just the steps, I do sometimes verbalize the numbers so what I wrote in those parentheses is the most verbal my process for mathing that out gets.
Edit: Looking at that, I think it might be easier for someone to correct your thinking if you think in words, but thinking without words is way faster and way more creative since it removes the restriction of only thinking about concepts you have words for.
Edit2: I think your verbalization there is a ritual for the concepts to get to you. For me all I need to do is see 62x62 and imagine I want to solve it and all those thoughts flow to me automatically, basically a shortcut instead of having a large verbal ritual to piece together the concepts. I never did math verbally the way it is taught, so I am not sure how people think that way, to me this was always automatically this way.
If you can or ever were able to do this in 2 seconds that is unimaginable to me. Not in a doubting way, I just have no idea how I could do it in 2 seconds. It would take me 20 to 30s and at least. But most people wouldn't even try to multiply this top of their head.
Also this multiplying of two digit numbers I was never taught, I just came to a strategy that I explained with my thoughts. And I used to do these for fun as a kid. But I would only get faster than that if it was something I had memorized, but not numbers from scratch. And I had to constantly try to repeat numbers in my head that I had stored for addition down the road.
What is usually tougher top of my head and especially if I am tired at all, is something like 68 x 68. Then here first I have to decide whether I go from 60 x 60 or 70 x 70. Since it's that close to 70, I think 70 is more likely be easier. So I think okay 4900 - that's from memory right. Then I start to think what I have to take off from 4900 and what is 68 x 68 lacking compared to 70 x 70. So I will think that if I add 2 x 68, it will make it 68 x 70 and then I have 2 x 70 missing. So I need to deduct 140 and 136. So now at this point, this is much easier done in writing but here I frequently have to repeat numbers or redo some steps because I am not certain or I forget. But otherwise 4900 - 140, this comes easily instantly 4760 - maybe that's how it is for you with 62 x 62. And then now I take 100 off, it's 4660, and further 36 it would be 4624. Right now testing this in my head it took more than a minute because I wasn't sure whether I could just use the logic that I was thinking out of the box and I'm quite tired.
What if you were to have to do something more difficult e.g. 3 digits multiplication or 4?
Might sound weird but does the look of the operator matter? Say × vs x vs • vs *, I would assume it doesn't but I'm curious if there's a visual change, for lack of a better term.
> That is thinking slow for you?? How do you reach conclusions or how do you know the reasons why you reached the conclusion?
Are you thinking that using words during thinking helps with reaching conclusions and knowing why you reached the conclusion?
For me it's just there, the thoughts, the facts, the logic, the sequence, the connections, etc. Expressing all of that in words happens afterward (if it happens).
I don't even know how to think without words. I thought thinking literally means using words in sequence to problem solve. At least I used to think so. If someone says they are going to think about something I have always thought that they were going to focus on their inner monologue of sequence of words.