Mathematician Georg Cantor

Personal project illustration showing a portrait of mathematician Georg Cantor, together with a color variation of the diagonal argument that he used to prove that the set of real numbers is uncountable.
Not fully satisfied with it, but I at least managed to make something. Critics are welcome.

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I think you need to be a mathematician yourself to fully appreciate this. :slight_smile:

What is that thing on the right? Some sort of infinity symbol?

Really cool image anyway!

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That’s a Alpeh-One symbol.

From a pure graphical point of view, I like it.

After, my knowledge in mathematics are too poor to appreciate and being able to judge if your representation make sense or not (consider that a non mathematician just can’t understand even what the Aleph-1 represent :sweat_smile:)

Note: it took me time to see the portrait, but now it’s ok.
In fact the portrait is difficult to see in full size mode, need to look picture in small size to see it - that’s my personal perception, don’t know for other it’s the same

Grum999

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Hehe yeah, I didn’t give any explanation, so for sure you need to know about it already to understand. But I’m glad you find it looks cool :slight_smile:

As Grumm999 said, the symbol is Aleph-one, and you’re quite right that is represents some sort of infinity symbol. Roughly speaking, under some hypothesis, Aleph-one is the name given to the type of infinity corresponding to the number of elements contained in the number line (that is all the traditional numbers: 0.15, -2.468, 9.0047865… etc. In Maths this is called the set of real numbers).

Ok let’s go for the explanation, in case someone is interested. I’m happy to make a digital painting of whatever they want, to anyone who will read it till the end :laughing:


What Cantor showed is that such type of infinity is “uncountable”, that is, it is impossible to come up with some list that would enumerate all the numbers in the number line. In contrast, the whole numbers are “countable”, since I can easily come up with a list that would enumerate them all. Here is such a list: 0, 1, 2, 3, 4, etc. (another one would be, say 0,5,1,10,2,15,3,20,4,25,6,30…)

In my illustration, you see rows made of light green and light red squares.
For example, the first row shows squares of colour green, red, red, green, red, red, green, green etc.
If you add the second, third, fourth row, you start to have a list of such arrangement of green and red squares. The curve at the bottom that goes into the portrait is supposed to imply that the list goes on and on till infinity.

Now on top of this list, you see another arrangement of green and red darker squares, that goes diagonally. The colour of the squares of this arrangement are chosen by flipping the colour of the square below. So the 1st dark square is red, because below it, the 1st square of the 1st row is green, the 2nd dark square is red, because the 2nd square of the second row is green, then we have three green squares because the squares below are red, etc.

This construction ensures that the dark arrangement of green and red squares is different from each of the arrangement in the list, since there is always at least one square whose colour has been flipped… so we can be sure that such arrangement will not be on such list, whatever the list is… that is we proved that the arrangement of green and red squares are uncountable. Hooray :partying_face:

Now if you replace the green squares by 1s, the red squares by 0s, and you imagine a decimal point in front of each row, the list becomes a list of numbers.
First number is .1001001100…
Second number is .1110100…
etc.

The diagonal arrangement also becomes a number (.001110110…), and by construction, this number will never be on our list. So the decimal numbers made of 0s and 1s (and so of course the real numbers since they include all numbers) are uncountable! Hence the illustration is showing Cantor’s proof, but using colours instead of 0s and 1s.

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Cool! :slight_smile:

Well I didn’t know either until I became aware of this part of Mathematics, so I’m not surprised at all :smile:

Oh thanks for this feedback. Useful to know. Because yeah, we always tend to feel that everything is obviously clear in our drawings, but that’s cause we know what’s in it and where to look at.
… that’s why we need the feedback of other people! :wink:

Reading those words is like standing on the ground and looking at clouds in the sky… they’re both beyond my grasp. :slight_smile:

I think that’s a feature. Reminds me of an installation I saw once. Small squares hung in nearly invisible threads from the ceiling. At first glance they didn’t depict anything at all. Until you walked around and saw them from the exact right angle, then they became pixels in an image.

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