Comments on: Jellyfish Math

By: Weekend Roundup at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics

Sat, 23 Jan 2010 07:03:18 +0000

[...] math invented or discovered? We visited this ancient question here and [...]

By: jj

jj — Thu, 14 Jan 2010 22:03:58 +0000

Even the moon is not a discrete, countable object if you sense it at the quantum level; it has a wave function. How about quantum energy levels, though? Might they be discrete and countable?

By: Zach Cox

Zach Cox — Wed, 13 Jan 2010 12:40:55 +0000

The question: “Is mathematics discovered or invented?” is the same question as: “Does God exist or not.”. The human mind is constructed so as to come up with the two answers, “Yes” and “No”. When humans think deeper about such questions they come up with the third answer, “I do not know.”.

On even deeper thinking a better answer is: “I do not understand the question.”

I think an even better answer is: “I do not understand the question and we can show mathematically that you do not understand the question either.” Having Gödel and Tarski in the list would have helped with this answer.

The question then becomes: “Why do humans insist on asking question that they know they do not understand.”

If we think of consciousness as an emergent property of motile organisms that has the purpose of modeling its sensory inputs so it can predict the way that environment will evolve so it can then successful negotiate that environment in order to persist then and important attribute of that modeling engine is that it must not freeze up or grind to a halt on in input set.

This means that an organism so equipped when presented with a question that it does not understand naturally will come up with an answer. The more complex the organism the more complex the answer.

By: Real Numbers at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics

Wed, 13 Jan 2010 07:02:16 +0000

[...] Buy « Jellyfish Math [...]

By: dWj

dWj — Wed, 13 Jan 2010 05:17:09 +0000

dave, assuming there are no magnetic monopoles, where there’s a magnetic field, there must be moving charges (or changing electric field) to produce it. A stationary charge just produces electric fields. In many materials, there is plenty of “motion” in the relevant sense at the atomic level, so you can get magnetism that way; for the production of large magnetic fields, though, you generally move currents in a more macroscopic way.

By: dave

dave — Wed, 13 Jan 2010 03:34:03 +0000

im also in the ‘we create numbers’ camp. there may be two poles, but there is only one magnetic field. without some lodestone, even the existence of the field would be difficult to imagine.
on a side note, im under the (often mistaken) impression that a bodies magnetic field had to do with its composition and not its rotation. illuminate me on this?

By: John Faben

John Faben — Wed, 13 Jan 2010 00:00:34 +0000

I’m not entirely convinced its possible to do mathematical research without being convinced that the reality is ‘out there’ somewhere. You are doing research: there is only one possible answer to the question you’re asking, and that answer would be the same whether you had asked the question, someone else had asked the question or no-one had asked the question. As for the point that 1.

As for “”1+1=2″ is true, but so is “2+2 = 1″, modulo 3. You know that..”. I have almost literally no idea what the point of that sentence is. Are you suggesting that there is some other part of the universe in which the remainder you get when dividing 4 by 3 is different to 1? That it would be possible for an intelligent creature to ask itself “what is 2+2 congruent to modulo 3?” and come up with an answer other than one.

As for the historical examples. Obviously what is *known* about mathematics is a cultural issue. As Steven said, for most of the history of the universe nothing was *known* about mathematics, but 4 was still congruent to 1 modulo 3.

By: Revyloution

Revyloution — Tue, 12 Jan 2010 22:10:39 +0000

I fell into the ‘numbers are abstractions’ way back in 5th grade when we learned to calculate Pi. We can never know the exact value for Pi, and just use an approximation that gives an answer with the accuracy needed, whether its 3.14, or 3.141592353589793.

The same could be said of counting apples, or moons. If I have two apples, does that mean both apples are identical? If I mash up 10 sets of 2 apples, will all sets have the same mass? You can even use that type of thinking on subatomic particles. If you have 10 protons, not all of them will be exactly the same, but we can abstractly call them all ‘protons’ and count them up.

Once I took higher math in college, I became even more convinced that math was an abstraction that we overlay on reality. Calculating the minimum number of stars in the observable universe, we come up with three to seven times ten to the twenty second power. I seriously doubt that the number of stars would add up neatly to a figure with 22 zeros, and since stars are constantly being born and dying, we come up with an estimate to work with. And how different is an estimate from an abstraction?

By: Stephen

Stephen — Tue, 12 Jan 2010 21:59:07 +0000

I tend to agree with Ben, autogen, and Saber on this point. Numbers are mental constructs that we use to describe the world. In Atiyah’s example, these constructs don’t exist because the jellyfish haven’t created them. In this type of scenario, numbers may still exist, but only in the sense in which any potentially conceivable mental construct exists.

If in the future a more potent method of understanding the world is conceived that replaces the number system, what would that mean? In the 17th Century, a proponent of Phlogiston might have argued that Phlogiston always existed, but we now have a more advanced system of concepts.

In any case, Atiyah’s point was that counting is not clearly a primordial notion. At least in the excerpt provided, he wasn’t attempting to prove that numbers “exist” even if they are neither invented nor discovered. In fact, he clearly assumes that counting is a “notion.” It remains to be argued that numbers are not a notion, but are something else, and, if so, what.

By: Al V.

Al V. — Tue, 12 Jan 2010 20:03:31 +0000

Wow! I’m quite surprised how many people believe that numbers exist only in our heads. I am firmly in the camp that numbers, and all of mathematics, exist independently of us, and in fact independently of our universe, as described in Max Tegmark’s “Mathematical Universe”.