Kevin's Watch

wayfriend wrote:If 2 ^ x is multiplying 2 by itself x times, and x is 1, ...

What is the answer when you multiply 2 by itself 1 time? The answer is 4.

2^1 is not 4.
2^1 = 2

X^1 does not mean you multiply X by itself 1 time.

I am not saying you're wrong - describing powers that way is technically incorrect.

I am saying it is conventionally described that way, and that people largely understand what is meant when it is described that way.
Therefore, I don't fault chatGPT for relying on the convention.

There is probably a more technically correct way of defining it, but I bet it is so technically correct that no one understands it easily.

Yeah, WF's link is wrong. The exponent isn't the number of times the base is multiplied by itself. If 2 to the power of 3 is "2 x 2 x 2" then the base is being multiplied by itself twice, not three times. There are only two multiplication symbols here, so the act of multiplying is done twice, not three times. We could also write it as: (2 x 2) x 2. This shows that "2" is being multiplied by itself twice, since (2 x 2) is done twice, ". . . x 2." And then those results are added together.

So if 2 to the power of 3 has only two multiplication signs, 2 to the power 2 would have only one multiplication sign, and then 2 to the power of 1 would have no multiplication signs. Nothing is being multiplied (which is not to say that 0 is being multiplied).

It's a very bizarre mathematical function. Hard to define. No wonder chatGPT had trouble.

wayfriend wrote:I am not saying you're wrong - describing powers that way is technically incorrect.

I am saying it is conventionally described that way, and that people largely understand what is meant when it is described that way.
Therefore, I don't fault chatGPT for relying on the convention.

There is probably a more technically correct way of defining it, but I bet it is so technically correct that no one understands it easily.

This is fine for exponents greater than 1. But it cannot be described this way, technically or conventionally, with an exponent of 1. If someone does not know anything about exponents, or only understands how to do it with an exponent greater than 1, if you tell them "it means multiplying X by itself 1 time", unless X=1, they are going to get the wrong answer. Even though they will have done what they were told to do.

The more accurate definition would be "X^Y is 1 multiplied by X Y times."

2^2 is "1 x 2 x 2".
2^1 is "1 x 2".
2^0 is "1".

However, even this definition fails for fractional exponents and negative exponents.

That definitely makes it less ambiguous!

I think humans' understanding of consciousness is way too self preferential. It's not called the hard problem for nothing. Our common understanding is more like, "I can't define art, but I know it when we see it." We don't know what makes us conscious (we can say "the brain" but that first leads us to say we're not really talking about consciousness but brains and second to ask how brains create consciousness and why), but we're absolutely certain we can say what makes other things not conscious, like we're really doing anything than othering something that appears similar. Us:not us:: conscious: not conscious. Which is obvious enough that it doesn't need a debate, and I'm not sure being us is the prize we think it is to the rest of the not us universe.

But to use your example, Av, you don't know Armstrong landed on the moon, either. Even if you would have been alive, it still would have to have been related to you, would still have to arrive to you from a source you trusted enough to disregard other information. And the first time you actually heard it, it probably meant nothing to you. It took a lifetime of associations for you to build the perception of Armstrong on the moon being a fact in this present moment. It's a mental model that you have high confidence in, not an actual experience of the event (and even then we can start getting into Descartes territory).

Question for those who've used it.

Is this generative AI, in that it is capable of generating new content, and secondly how good is it (if it can do it at all) at text to graphic generation (ie you describe the image you imagine/want in words and it produces the picture)?

I guess this second question is related to the first in so far as production of the picture would be in effect generating new content.

AI leaders (and Elon Musk) urge all labs to press pause on powerful AI wrote:
“This pause should be public and verifiable, and include all key actors. If such a pause cannot be enacted quickly, governments should step in and institute a moratorium.”

These are people who know AI. And they’re warning that society is not ready for the increasingly advanced systems that labs are racing to deploy.

The cynics!