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10k? 100k? A million?
I am not talking about calculating with numbers, but rather the point where numbers stop being comprehensible, or “no longer mean anything”.
Try visualizing exactly 10000 apples in your mind.
You're quite optimistic. I recall from old Psych classes that visualization breaks down even before double digits, so the 5-9 range. Don't have any references at hand so I might be misremembering it, but now I'm curious too and will see if I can find anything in my notes.
As an average, I usually see the number 7 bandied around. After that we start “chunking” where each group becomes its own conceptual object.
This is why phone numbers without the area code have 7 digits in North America.
That's not quite the same thing - the 7 digit phone number has more to do with short-term memory capacity than visual perception. Miller's Law of short-term memory is we can store 7 +/- 2 items at a time, depending how complex they are.
https://en.m.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two
Oh, I was way off, then.
7 sounds about right. When I see a number of stuff in front of me I can quickly grasp how many there are up to about 7. 8 already becomes two fours. 9 is 3x3 or 4+5 depending on how the objects are clustered.
Though I think I can estimate up to about a thousand. Usually by comparing to stuff I have already seen in that ballpark.
I got about 50000k but I'm in local politics
Interesting. I thought you could split numbers into "bundles" (1 bundle of 5 apples, 10 bundles of those, for example).
Edit: Or imagine 5 and then start doubling over and over.
Yes, but then you’re not comprehending all the numbers. There’s no difference between imagining 5 googolplex and 5 dragons.
Visualization and symbolics are not the only way we comprehend numbers. My mind has the ability to recognize astonishingly broad temporal intervals with remarkable accuracy. I can express the interval using numbers. Does that mean I am able to fully comprehend a number like in "90 minutes?"
I am able to remember sets of things, and distinguish all of the members of that set, up to very large numbers. It would not be unusual for a teacher to be able to call to mind every one of a couple hundred students currently attending their school. If I can manage a set of a particular size in my mind (whether or not I can visualize all the members of that set simultaneously) do I not have some comprehension of that number? What if every student is assigned an integer from a contiguous series, and I can remember each student's id number?
Some people cannot visualize at all. Do they fail to comprehend every number?
Yes I believe there’s an over-emphasis on the visual here. There’s a low limit on how many distinct objects we can perceive visually at once but that’s not entirely the same as what numbers we can grasp and comprehend.
There's also conflation with the number of "chunks" we can hold in mind at a time, which is often estimated at about seven things. But that doesn't mean we don't comprehend what eight is.
Numbers are DEEP. You can't just know things about a number, you have to discover them empirically, experimentally. Every number has essentially infinite properties and you can't know everything about a number, but you get a familiarity with them. Still, even the simplest numbers have the capacity to surprise in the right context.
Try visualizing exactly 10000 apples in your mind.
Impossible. The first apple inside my head would have killed me already.
I can visualize 1 apple im my mouth.
I can visualize 2 apples im my mouth, but with some struggle.
I cannot visualize 10 or 100 or 10,000 apples im my mouth.
So my answer is 2. Every human can grasp that number. Above 2, not everybody can.
I am bordering on aphantasia, i can't visualize an apple at all, just as an abstract drawing.
I can visualize numbers and graphs, for example 1-6 are easy with the symbols of a dice, 7 like six with a dot in the middle, 8 two rows of fours and 9 as a three by threw grid.
The thing is, I never visualize things literally, it's always abstract symbols - and understanding "more" requires better symbols.
Decimal system is also just a symbol, I can easily keep numbers in my mind up to six or seven digits.
Bigger, I have a bit of trouble with the scientific notation - I don't have concepts for numbers beyond 10^9, even these rather are a thousand million for me, conceptually. And speaking English right now doesn't help, as I'm from a big ladder country while the US is small ladder: 1 Billion (German) = 1000 billion (US).
"Hardcoded" numbers in the brain go to 4 or 5 or so, everything else is abstractions. piled on abstractions and how used you are to handling these.
In computers you deal with bytes, kilobytes, megabytes, gigabytes, terabytes. I visualize the difference between 1kb and 1Tb, as I have experienced each of these stages. (My first computer had 1kb, the second one 64.... it was growing exponentially for years)
"One.... Two.... Umm ... Many ... One many... Two many.... Many many..."
We are all Detritus lol
"Lots"
I don't think grasping and visualizing are the same. I am sure you can grasp the concept of 3. Like 3 cars waiting on a light, or 3 slices of pizza.
If the limit was visualizing, the answer would be zero, since some folks can't visualize at all.
Always a pleasure when people explain my texts to me. Even more so when I was deliberately unprecise, or not so serious at all 😉
Comprehension is a weird thing to define.
Like I know what 100 billion is. I can define it, I can say what's less or more than it. Is that comprehension?
You could take three counters and throw them on a table in front of me and I could intuitively tell you there are 3 counters without individually counting each one. If you threw 20 counters on the table I would have to count all of them individually before I could tell you how many there are. Is that comprehension?
In my opinion any number that could be uniquely described counts as being comprehended by a human. For example I think people can grasp the concept of pi despite not being able to really grasp the infinite nature of it. So any number large enough where you couldn't uniquely describe it to a person. Which is a pretty useless definition if we're being honest.
Have you ever been to a beach? Can't you visualize the 100s of millions of specks of sand?
Anything over a couple million probably. People can comprehend the largest amount with money (instead of apples for example). The fact that most people don’t realize how big of a difference a billion is to a million shows that the average person can really comprehend only up to maybe 7 or 8 digits.
infinity is both capable of being conceptualized and larger than any other number, so there's my answer
That's not how the human brain typically works. We summarize, categorize, lump etc so the concept of numbers is understood.
Such a question is entirely and completely subjective in answer.
I am not looking for an exact answer, but rather peoples opinions ("what do you think...").
You may as well be asking people their favorite color.