 Thales, Annexmender, and Annexmenes are all taking a common approach when trying to answer their respective questions. Now, Pythagoras is doing something of like what they're doing, but he's also doing something really different. How is it that Pythagoras is doing something like Thales, Annexmen, and Annexmenes, but it's also doing something really different? So Thales, Annexmender, and Annexmenes are all trying to answer the question, what does it mean to exist? And they all do so by trying to find some kind of commonality, something that all existing things have in common. Thales thought it was water, Annexmen thought it was boundless, Annexmen thought it was air. Pythagoras is also trying to find a commonality for all of these things. That much he's doing, and in that much he's doing the same thing as Thales, Annexmender, and Annexmenes by trying to answer the question, what does it mean to exist? By trying to find a commonality. Well, all four are looking for a commonality, trying to answer the question, what does it mean to exist by finding what all of these things have in common. This much Pythagoras is doing like Thales, Annexmender, and Annexmenes, but he's doing something importantly different. Thales thinks we can explain or answer what it means to exist by saying all of these have water in common. Annexmender by all of it has boundless. Annexmenes by saying all of it has air. All three of those guys are going to try to answer the question, what does it mean to exist by answering a different question, a second question, and the second question that they're trying to answer is, of what is it composed? We ask Annexmender, what does it mean to exist? He says, I'll answer that question by answering the question of what's it composed of is water. Annexmender says it's composed of boundless. Annexmender says it's composed of air. Pythagoras is not doing composition. He's doing something else. Now, he says, I'll tell you what it means to exist by answering a different question, a second question, and the answer to that question is not composition, or that second question is not composition. That second question is form. Pythagoras makes a crucial distinction, both in his reasoning and his conclusion. What's the crucial distinction? The crucial distinction Pythagoras introduces is the distinction between form and matter. Form and matter. Matter you are very familiar with. Matter you can see, matter you can touch, matter you can taste. It answers the question of what is a thing composed? So, matter is not something you have difficulty spotting, or even really comprehending as something that exists. Form is different. Form is not of what a thing is composed. We ask of what a thing is composed and we're going to give different kinds of matter. Form is what the thing is. Form is a definition, an essence, an abstract. So, for instance, we have this trail here. What's the matter of the trail? Well, we've got wooden beams. We've got a lot of dirt, leaves, twigs, some rocks. There's going to be at least some kind of metal stakes involved, I forget what they're called. You have to hold the wooden beams into place and that holds the dirt and the rock and sand, if there's sand in there, that holds all that into place. That's the matter of the trail. That's what composes the trail. What it is, is a trail. There's a difference between wood, metal pegs or metal beams, dirt, twigs, so on. There's a difference between that and trail. So, for starters, not everything wooden composes a trail. Sometimes they compose houses, sometimes decks, boats, so on and so forth. Matter can be used in different sorts of forms. So, not all matter is the same form. What Pythagoras is getting at here, there's more to what the trail is than simply what composes it. So, he'd look at dailies and say there's more to what the trail is than water. There's more to what the trail is than boundless. There's more to what the trail is than air. What that thing is, that's more to it is its form. You can think of the definition of a trail, the essence of a trail, the meaning of what it means to be a trail. Not every trail is composed of this. Sometimes it's just rock, sometimes it's flattened grass, all kinds of ways that you can make a trail. So, you have matter, what composes the thing, on one hand, and form on the other, what it is, what's composed. Matter is what composes, form is what is composed. Now, we will likely try to think of different definitions of trail and that's fine. But for Pythagoras, the only form that counts is its number. Form is a number. You never seen numbers. You never seen two. You've seen symbols representing two. Okay. But two itself, it's not composed itself, right? It's not something you can hold in your hand. What this trail is, is this number, the number of steps that go out this way, the length of the trail, the degree of the curves, all these numbers, the width of the trail, all these numbers go into what it means to be this trail. So, the distinction Pythagoras introduces is the distinction between form and matter. Matter is what composes the thing. Form is what's composed. And for Pythagoras, all form is number. What this trail is, is its numbers. What these trees are, are their numbers. And what you are, are your numbers. So, Pythagoras makes a distinction between form and matter. Form is material. Kind of, you know, repeating myself here. The water, the rock, the dirt, the fibers, carbon, nitrogen, oxygen, right? This stuff is material. That composes the thing. And form is what's composed. I can feel and see and taste and touch the matter. I can't feel or see or taste or touch form. What this is, is a tree. But I can't see the form tree. I comprehend it, but I don't see it. I might see that tree, but not the form, right? Because I got that tree. I got that tree. I've got all kinds of trees behind me. These are all trees. They have the form tree. Pythagoras is going to say, yeah, yeah, yeah, tree, whatever. It's the numbers, right? So, I don't see the numbers. I don't see what, 25 feet tall, I'm estimating 25 feet tall. I can comprehend 25 feet tall, but I don't see it. I see green. I see brown. I see blues. That's, that's what I see. I don't see number. Matter is the concrete, the particular, the sensual, almost, right? At least some of it, right? Form is the abstract. It's the universal. It's what all these things have in common, but it's not any one of those particular things. So, why would Pythagoras make this distinction between form and matter? That's one question. Why would even make this distinction? And secondly, is he right or does form not exist? Well, got a bit of a river here. We'll have to return to this. Let me get to Heraclitus. But, you know, for now the question is, why did Pythagoras think that this commonality, what everything has is form? And why does he even think it exists? Well, you know, maybe just a four-stall, one, you know, one mistake here is not through observation. It's not through observation. He didn't observe number and neither do you. Nobody observes number. We comprehend number. So, I think about the length of this ivy. I comprehend the length of the ivy. I think about the number of leaves. I got one, two, three, four, five, six, seven, at least above my fingers, seven leaves above my fingers here. Okay. Do I see seven? No. I mean, I counted it out. For starters, what I see is green and very shades of green. I got some whites. I got some very pale green. I got some yellow green. Don't have too much blue green in here. That's what I see. That's so my eyes can detect his color. I can't detect number with my eyes. I can comprehend it, but I can't detect it. All right. So, he didn't make the distinction between form and matter because he could, you know, see it. He can't see it. Nobody can. So, why would he make this distinction? Well, I mean, he could at least start, you know, thinking that numbers are real because they were doing arithmetic. They were actually doing some pretty advanced mathematics in those days. You'd be surprised. And all these things obey the laws of mathematics. I mean, in addition, they obey the causal laws, but the causal laws are more restricted than the laws of mathematics. You can describe all these events happening around me in terms of mathematical equations, the rate of growth of the leaves, even this pattern that they have as they split off, right? You can write an algorithm that describes this pattern, had the leaves split off, the ratio, the distance between the leaves. You ever notice a really regular and depending upon the breed of plant you have, that ratio changes. So, these are some kind of oak, I guess. These are some kind of oak. Would you ever notice that the way that the leaves spread out on an oak is very different from like a fern? And yet the fern has its pattern and oak has a different pattern. I'm looking at the waves here. The way that they come into the shore, the force exerted by the waves, how much water moves down the river, all of this can be measured mathematically, all of it. So, it's not that Pythagoras saw form everywhere. He comprehended form everywhere. And that things don't disobey the laws of mathematics. There is nothing in existence, right? What Pythagoras noted is there's nothing in that existence that's both 1 and 3 and 19 and 48 things at once. Now, there's only one thing. Now, you start counting the parts of a thing, but then that's the parts. That's not the thing itself. There's all kinds of ways that these objects that nature around us, that we ourselves, follow the laws of mathematics. It's, you know, this is a big endeavor in any of the sciences is to try to figure out the patterns, the miracle patterns, of the existence of things. So, he didn't see form everywhere. He didn't see number everywhere. He comprehended number. And the more he looked, the more he comprehended, he realized all these things. Not only have numbers, but are measured by numbers, and their existence can just be plotted out. In terms of equations.