As I mentioned a few days back, I sent the following via email to some friends, as well as to ask.metafilter:

According to Leibniz, a theory must be simpler than the data it explains. In other words (for the nerds amongst us), understanding equals compression.

I challenge you to help me understand this via a thought-experiment:

Let’s take two experiences we are all familiar with: Pleasure and Pain.

Explain the difference between these two experiences.

There is (of course) no “correct” answer; however, I ask that you attempt to use as few words as possible to explain your answer.

I sent this email for many reason; the question itself being initially irrelevant.

Mainly, I wanted to see if the net, specifically email, could be used to spark wonder. I also wanted to gain further understanding of Leibniz theories where they apply to the work of Turing, Chaitin, the Omega constant, and elegance in computer programming. (I won’t get into that right now.)

The comments I received fell into the following camps:

• Perception
• Relativity
• Example
• Linguistics
• Links

There were also a signification number of responses that called my question into question.

In some cases I’ve combined similar comments to avoid repeats. Comments were also edited (in certain cases) for spelling, grammar, and length.

Perception

Pain is generally an aversive stimuli, pleasure a reinforcing one. Of course if you ask an S&M aficionado they’d likely disagree. Short answer, the difference is perception.

Pleasure - all things desired and the feelings gained from them.
Pain - all things undesired and the feelings gained from them.

Pleasure - positive emotional response (to some stimuli)
Pain - negative emotional response (to some stimuli)

Pleasure - the result of a stimulus that causes the brain to want to re-enforce the input.
Pain - the result of a stimulus that causes the brain to want to diminish the input.

Pleasure rewards, pain punishes.

Pleasure and pain are the neurocognitive functions that have evolved in the brain to reward or punish behaviors that are likely to increase or decrease an animal’s procreative success. Pleasure is the reward, and pain the punishment, and that’s the only objective difference.

Relativity

Pleasure is the opposite of Pain.

Pain and pleasure are relative. To fully understand & appreciate either, we have to experience both.

It’s entirely possible that the whole distinction is fictitious, that there are no poles or unmixed feelings, but a continuity, pleasure tinged with pain and vice versa.

Example

Pleasure is a beer, pain is the hangover.

Pleasure = icecream
Pain = burning it off on the elliptical trainer.

Pleasure and pain can be both good and bad. Pleasure can be joyful, a flower, or it could get you in trouble, Bill Clinton. Pain can hurt and that is usually negative, but it can also teach. Once bitten twice shy. fire=danger. No pain no gain.

Linguistics

Pain: Ow!
Pleasure: Oh!

Only difference I can see is in the spelling; pleasure (P-L-E-A-S-U-R-E) vs. pain (P.A.I.N).

Links

You might be interested in the “Define blah in 10 words or less” [google.com] series that 37 Signals run(s) at their blog.

Usual-stories on the Tree of Life

Questioning the Question

A theory doesn’t just rehash data; it elucidates a pattern in it.

Simpler doesn’t necessarily mean smaller.

I’d say asking for the difference between pleasure and pain is much like asking for the difference between red and blue. They’re primitives. No definitions are possible; hence, the differences cannot be articulated.

Pleasure and pain both are shorthand for (compressions of) complex chemical, biological environmental feedback loops. The terms already represent compressions of more complex realities.

Pain and pleasure are already conceptually simple, so it isn’t possible to simplify them further.

A theory is a tool, it’s not something that’s meant to explain things or provide a basis for philosophy. A tool is something that increases your abilities. If the theory is more complicated than the data, you are better off just using the data.

In your thought experiment, you defined a question, but not the data, so we have no way of determining if any proposed theory is more complicated or not.

Why do you assume that words, specifically the English language, is the appropriate medium for stating this particular theory? Why not use numbers or paintings or, better yet, why not come here and let me slap you and then offer you some chocolate. (Actually, I won’t share my chocolate with you. It’s mine!)

Your “understanding equals compression” is a bad simplification of Leibniz’s thought. Leibniz’s desire to break everything down into the simplest possible terms was a metaphysical attempt (to prove God’s existence) not a true scientific theory of understanding. One of these things is most definitely not like the other.

I wouldnt go too far with the compression analogy. A theory is just a mental model in which we can make simplifications in order to make progress. In most cases, this means losing data. Moral rules such as “Do unto others..” are still around because they provide decent approximations to the otherwise unfathomable complexity and dynamics of relationships. But they are not a “compression” of morality.

Rules and theories are good but don’t put too much faith in them - just as much as you need to. Einstein, of course, said it best: “everything should be made as simple as possible, but not simpler.”

I disagree with your premise. The main value of theories is to help us link and organize other data and theories into a corpus, which can then be conveniently “walked” both from the specfic to the general (induction), and from the general to the specific (deduction). There is no point in developing an infinity of disconnected theories over an infinity of data sets, if the theories don’t build into something still greater and more abstract; that greater thing being human knowledge.

Conclusion

I was overwhelmed by the number of responses, the variety of views presented, and the constructive criticism.

Thanks to the criticism, I now see that my choice of highly personal and polarized terms wasn’t the best tool to explore the relationship between data and theory. However, in terms of sparking wonder, the experiment was a success.

We must all remember that although science is often presented as fact, it remains an ever-changing man-made model; one which is open to, and thrives on, questioning and debate.

Learn to Question.
Question to Learn.

And on that note: Does time, as a dimension, actually exist?