Physically - maybe 10,000. I might be overestimating.
Abstractly - maybe 10^20.
I was just thinking about how it's hard to truly understand large numbers. If you see a LOT of people, beyond a certain point it just boggles the mind. As for the abstract version, to me 10^70, 10^80, and so on all feel rather similar, even though the differences are astronomical.
> Physically - maybe 10,000.
Funny you should say that, as 10,000 in Chinese is identified with infinity as in "innumerability", similiar to the Greek "myriad". You will often find that number in ancient Chinese philosophical texts when such concepts as infinity are regarded.
As for abstract infinity - I don't think you can express it numerically as that always implies the notion of possibly topping it once more.
I know 10^24, actually a pretty everyday number (approximately the number of atoms in one mole), is utterly incomprehensible to me.
Having quite recently experienced the conversion from Finnish Marks to Euros, I know what a maze of special cases a person's (or at least my) perception of money is.
Anything up to maybe 30€ now works automatically, but beyond that I have progressively weaker intuitive perceptions. Having lived my first ~20 years with Marks, I have a pretty good grasp of how much 118 914.6 mk is. The equivalent 20 000€ is very cryptic though. I have never handled any sum even close to that in either currency.
My point is that I suspect that above a very low level (between <10 and <50) we could just as well not get it at all - and conversely, if only appropriately trained, we might well understand 10^23 and similar.
I think the difficulty is that we are naturally inclined to view objects individually, while numbers are represented in base 10. So when you see a small number, you can sort of invision that many objects. As the numbers get bigger, all you see is an extra 0 on the end. And when you get more numbers than you can envision individually...
In graphic design any time you repeat the same object more than 7 times it is considered innumerable (either a mass of objects or a texture). However that's just because people don't usually bother to count anything beyond that, it bores them.
I can't envision anything more than a million. If I look at a billion dots, I think "gee that's a lot, is it a million?"
I've seen a thousand people at the same time; so I can envision it. I tend to think of a million as a thousand thousands.
Also, the word "thousand" sounds really weird now.
http://www.kokogiak.com/megapenny/ this, interesting.
Dang nice link.
>>10
Imagine knocking over that stack of a quintillion pennies...
That's simple: Incomprehensible.
Remember that infinity is not a number. That in itself makes it difficult to grasp. Same with that magical function (and number at the same time) e....
Infinity is not a number, sure, but what on earth are you babbling on about e? It's a transcendental number, just like pi. It's not a "magical function" of any kind. Transcendetal numbers have a their own counterintuitive properties, but they are still numbers.
>>6 Thats because the (average) human mind can distinguish 7 objects without effort. Anything more requires concentration and is work for the brain.
This also means that if you hold a presentation or something, you shouldn't have more than 7 points on a single sheet because else your audience will be distracted by trying to grasp the mass of objects.
>>16
I've heard it can range from 5 to 9 though, depending on the person. As a programmer, the way I think of it is "The human mind is a register-starved machine." Heh.
>>17
I was also taught in my psych class that it's "7 +/- 2", a.k.a. 5 to 9. I believe most people tend to average at 7, however.
Really for the third staved member wagon there is little more than three of the initial proctors. "That third and most starved of the senses really originates in the most sacred of places, the bottom of our essence." Or so said mahatma Bhudda in his inaugural third annual pin the tail on the donkey, cunard, anchovy.
Furthermore a notion entertaining with great dignity any nuance in the conveyance of a minute-by-minute no holes barred, rate my little red wagon or the bank is gonna take our farm away pleases mr mayor.
Go play with your Markov chain somewhere else, OK?
> Remember that infinity is not a number.javascript:alert(isNaN(Infinity))
I think if I were to try and comprehend the idea of infinity the best way would be not to think about a really big number but to think about a singular; 1. Or a circle, figure of eight or whatever, the essential concept is the idea that infinity contains itself because there is no start or end; hence thinking of an infinate 1 which contains the entirety of its sum :S
I always considered infinity "too big to think about"
But, I'm a Computer Science major, who was always told that I was "good at math" since Elementary school.
For me, the concept of infinity is best represented in terms of another number, such as in writing domains or drawing number lines. Unlike the standard form of a domain, however, the number line simply starts at a point (let's say x > 0) and austerely points in the direction of positive infinity. There is no such actual number as infinity (though it IS used in math, and is definitely useful) because it is not part of the series (a number by definition is part of a series) of numbers ranging from one to infinity. The "number" infinity is more of an idea and a (very useful) tool than an actual number.
>>25
I agree.
A number is a value, wich means there is an end to it. PI is a number, and it has an ending.. somewhere. But if your calculator can produce a digit, it has a start value, and therefor an end value aswell.
I think of infinity as having no value, there simply is no end to it. I dont believe the universe is infinite, i cant explain why not tough XD
> A number is a value, wich means there is an end to it. PI is a number, and it has an ending.. somewhere.
Incorrect on both counts.
pi is infinitely long and never repeating. so if you calculate enough digits of pi in binary, you'll eventually get to a point where it contains the entire windows xp source code...
Infinity is a concept: to describe it i would say:
anything done infinite times randomly will bring non random result.
or, an infinite amount x divided infinite amount of times will result in nothing
>>29 just divided by zero