Infinity

[polymath257]

How many other people think that when equations produce the answer 'infinity' that they are not deep and profound but actually are simply nonsense and point to the fact that we have no idea what's going on.

For example, the singularity which has infinite mass and density is a product of our ignorance and simply cannot exist.

That depends on the situation. Sometimes it means we don't understand something. Other times it is the 'correct' answer and makes sense in context. Other times it is correct but doesn't 'exist'.

For example, when infinities happen in our calculation of the mass of an electron, we can be pretty sure we are missing something important going on.

But, when water melts, the specific heat goes to infinity. That is just a fancy way of saying that adding heat doesn't lead to an increase of temperature (it leads to more water melting).

Finally, in the Big Bang scenario, the infinities seem to go away when we do quantum gravity. But they also may still be around and signify that our assumptions about space, time, matter, and energy may have to be re-evaluated. In the original BB theory, the singularity means that we cannot even define t=0, let alone t<0. it only makes sense to talk about 'after the Big Bang'.

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How many other people think that when equations produce the answer 'infinity' that they are not deep and profound but actually are simply nonsense and point to the fact that we have no idea what's going on.

For example, the singularity which has infinite mass and density is a product of our ignorance and simply cannot exist.

In math, they can be useful, except for divergent series, that's a no go.

Actually, even that isn't so obvious. There are ways to get information out of divergent series that may, indeed, have physical import.

So, for example, using Cesaro summability, the series

1+(-1)+1+(-1)+1+(-1)+...

which diverges in the ordinary sense, actually converges to 1/2. The same is true for Abel summabillity.