## Monday, September 14, 2009

### 12. Why does mathematics work?

As a stepping stone to the more general question about knowledge, we can have a look at one of the most magical things in the world: the number. Where does it come from? How does it work.

When I want a new floor in my bathroom I measure the floor. The floor is 360 cm x 360 cm. The tiles I like are 30 x 30cm. That means that I need 12 x 12 tiles equals 144 tiles. And the miracle is that when I buy 144 tiles they fit in exactly. Not a sinle tile left over.

And the most amzing thing of all is that when I get into any situation where 12 x 12 applies I just need 144 items to do the job.

You could object: what is so special about that. 12 x 12 = 144 is just an ordinary tautological statement, telling you nothing new, like the statement "a stallion is a male horse" doenst tell you anything new.

So, that my arithmetic operation predicted that I would need 144 tiles in not so shocking, like telling me that a stallion is a male horse isnt that revealing at all, unless you didnt know the meaning of the word.

It is just a convention or linguistic rule that 12 x 12 can be exchanged for 144 or "stallion" can be equally exchanged by "male horse". Mathematics is thus just a body of human conventions.

Conventionalism, as this point of view is called, arises in so many different forms that one can say little of substance about it as a general matter.

However, a distinctive thesis shared by most conventionalist theories is that there exist alternative conventions that are in some sense equally good.

Maybe there are two types of truth? Truth by our own making, like conventions, and factual truth. suppose I say "All stallions have ears.". That is something quite different. To establish the truth of that statement we have to go out and do research.

But is the truth of 12 x 12 = 144 merely based on a convention? If so, then it is thinkable that some aliens have conventions that lead to 12 x 12 = 150. That can be possible.. But when they gonna buy tiles for their floor, they always have 6 tiles left over.

So mathematics is not just human conventions only? Some philosophers indeed claim that our knowledge of mathematics is A PIORI, which means that for knowing mathematical truth you dont need sensory experiences. You alread know the truth of a mathemaatical statement before that.

The characteristics of mathematics which have led to the conclusion that mathematics is a priori are its abstract character and accompanying enormous generality and its great exactitude and certainty, which, indeed, have traditionally been considered absolute.

This A PRIORI interpretation means that all mathemathical truth and knowledge is just the product of our brains. We dont need a real world to do mathematics. But where does that A PRIOI knowledge come from?

Isnt is amazing that we then appear to be born with this knowledge? And isnt it more amazing that our empirical world appears to be quantifiable? Mathematics and reality is an amazing combination, which works.

And we still dont know what a number itself refers to. I mean we can apply it to objects to count them, but the number itself, for instance 2. What does it refer to? Does 2 exists? Plato believed so.

Besides these philosophical questions it is exciting to read about the origin of numbers. Mankind invented the number like it invented the wheel. People of tribes in the Amazone still cant count. They count ONE (me), TWO(and you), MANY....

Just one final remark on the origins of our mathematical thinking. What does a shepherd, who cant count, to keep track of the number of sheep he has?

He takes a stick or a bone and every time a sheep enters the stable he makes a notch in the wood or bone. And the other day, when the sheeps enter the stable again one by one, his finger slides from notch to notch.

When there are notches left when all sheep have entered he knows that he is missing some sheep. Such bones with notches have been found in prehistoric findings. So, maybe that is how our mathematics started.

The Discussion

[13:25] herman Bergson: So much on the magic of the number
[13:25] herman Bergson: If you have questions or remarks feel free...
[13:26] Alarice Beaumont: in egypt one finds hyroclives in the stones as inventory or selling parts
[13:26] herman Bergson: I agree it is not such a controversal subject...only fascinating to me
[13:26] Paula Dix: i can understand base 10 because of fingers. But why 24 hours??
[13:26] Laura Lyne: hieroglyphs :)
[13:26] Gemma Cleanslate: stars
[13:27] herman Bergson: Yes..and 60 minutes
[13:27] Paula Dix: lol exact!
[13:27] Gemma Cleanslate: all to do with stars
[13:27] Paula Dix: how??
[13:27] Alarice Beaumont: thx :-)
[13:27] Abraxas Nagy: and earth's rotation
[13:27] Karybdis Carnell: curious, well if it was 12, I would automatically think zodiac signs
[13:27] Rosie Hexicola: 365 days, + 1 day every 4 years
[13:27] herman Bergson: Has it something to do with the 360 degrees arc
[13:27] Gemma Cleanslate: yes
[13:28] Frederick Hansome: Mathmatics in itself is an absolute, always present and unwavering, consistent. Man's understanding of it had to be discovered and we are still trying to understand its implications.
[13:28] Paula Dix: ive seen on discovery there were 13 signs, but one was dropped

[13:28] herman Bergson: Yes Frederick....we do mathematical discoveries
[13:28] herman Bergson: However it is not that absolute
[13:28] Karybdis Carnell: well I'm not sure how absolute math is. Those tribes in amazon seem to be able to count 1,2,few,lots,lots andlots
[13:29] Karybdis Carnell: They don't differentiate 3 colours from 4
[13:29] Laura Lyne: That's hardly math
[13:29] Laura Lyne: just rudimentary counting
[13:29] Frederick Hansome: it seems comforting, in some ways, to know that there is at least one constant in the universe
[13:29] herman Bergson: You could say that Frederick..
[13:30] Frederick Hansome: yes, I just did. :)
[13:30] Paula Dix: lol
[13:30] Laura Lyne: it becomes math when it can predict something not already known
[13:30] herman Bergson: But Math insth that complete...think of the incompleteness Theorem of Gödel for instance
[13:30] Rosie Hexicola: so counting is not math?
[13:30] herman Bergson: And wasnt it Fermat that showed something that cant be proven in math
[13:30] Paula Dix: whats that?
[13:31] Laura Lyne: I wouldn't say it is, no. Counting is a prerequisite for math, of course.
[13:31] herman Bergson: There are a number of paradoxes in mathematical theory
[13:31] Frederick Hansome: our understanding and ability to describe math is and probably never will be complete. But "math" is a unified whole
[13:32] herman Bergson: Well....Mathematics is a general concept refering to a number of things
[13:32] herman Bergson: Arithmetics is a part of it
[13:32] herman Bergson: Another enveavour was to reduce mathematics to Logic..
[13:32] Rosie Hexicola: and counting is a very simple form of arithmetics
[13:33] herman Bergson: Frege and Russell made it their project
[13:33] : Abraxas Nagy raises hand
[13:33] : Abraxas Nagy raises hand
[13:33] Paula Dix: so mathematics and logic are in the end the same thing??
[13:33] herman Bergson: to show that all mathematical statements can be deduced from logic
[13:33] Myriam Brianna: a project that lead to Gödel's theorem
[13:33] herman Bergson: Abraxas?
[13:33] herman Bergson: Yes Myriam...:-)
[13:33] Myriam Brianna: *led of course
[13:33] Abraxas Nagy: i have no idea how my hand got up there
[13:34] Myriam Brianna smirks
[13:34] Abraxas Nagy: sorry
[13:34] herman Bergson: np Abraxas..:-)
[13:34] Gemma Cleanslate: lol you hit the right keys
[13:34] Myriam Brianna: I sometimes have no idea how I get from one place to another, so no problem there ^.-
[13:34] Abraxas Nagy: obviously
[13:34] Gemma Cleanslate: directions on the wall
[13:34] herman Bergson: Dont fumble around on your keyboard during class ^_^
[13:34] Object: Alarice Beaumont, thank you for your vote !
[13:34] Gemma Cleanslate: lololol
[13:34] Paula Dix: lol
[13:34] Laura Lyne: The fact that computers can do math demonstrates very well that all math can be broken down into a series of logical (boolean) operations
[13:35] Laura Lyne: Yes/No steps
[13:35] herman Bergson: Is that really so Laura..?
[13:35] Laura Lyne: It seems to be
[13:35] Karybdis Carnell: well computers will get into infinite loops trying to do series expansions
[13:36] herman Bergson: Yes, but is the working of a computer a deductive process???
[13:36] herman Bergson: I dont think so
[13:36] Laura Lyne: No, deduction infers sentience :)
[13:37] Laura Lyne: Computers in infinite loops are simple doing math that doesn't have an absolute end result
[13:37] herman Bergson: I am not sure about that...
[13:38] herman Bergson: pushing 0000 and 111 around is something else than the program Logicism had...to deduce math from the basic rules of logic
[13:38] herman Bergson: I think you give to much credit to the computer Laura...
[13:39] Laura Lyne: Logic in computers and logic in people aren't the same
[13:39] Laura Lyne: we don't have to go boolean to be logical :)
[13:39] herman Bergson: It should be the same in my oppinion
[13:40] Myriam Brianna: there ain't two skies, Logic is Logic. But computers use different approaches (necessarily) when it comes to mathematical operations
[13:40] Laura Lyne: but maybe our brains do without our being aware of it
[13:40] Frederick Hansome: Laura, do you think that there will ever be a computer that can think?
[13:40] Laura Lyne: Yes
[13:40] Myriam Brianna: there is one, already. Billions of them, in fact
[13:40] Arlo Weir agrees
[13:40] Frederick Hansome: as well as an human?
[13:40] Paula Dix: i also would like to see just one logic :)
[13:40] Laura Lyne: Better, most likely
[13:40] Karybdis Carnell: our brains use boolean logic at the most basic level. Neuron on or off
[13:40] herman Bergson: I dont agree...:-)
[13:41] herman Bergson: Yes Karybdis :-)
[13:41] herman Bergson: Computers cant think..:-)
[13:41] Myriam Brianna: not yet
[13:41] Frederick Hansome: maybe we need to define what it is to "think"
[13:41] Laura Lyne: They can't right now, but why do you think they never will?
[13:41] Karybdis Carnell: silicon ones can't at least. I think I have a pretty good biological one in my head
[13:42] Myriam Brianna: yes, me too, Karybdis
[13:42] Paula Dix: ive seen an expert say that computer thinking level today is the same as lizzards
[13:42] herman Bergson: The Utilitarians thought that happiness was quantifyable..:-)
[13:42] Gemma Cleanslate: yes
[13:42] Frederick Hansome: 'puters can't think outside the box, humans can
[13:42] Myriam Brianna: thus the billions of bio-computers in the world, already conscious and thinking
[13:42] Laura Lyne: Computers ARE the box :)
[13:42] herman Bergson: Firs tof all whne we want to define thinking, we have to take into account the whole humanpersonality
[13:43] herman Bergson: a thought is not just a declarative or descriptive content....it is much more
[13:43] Frederick Hansome: oh oh...computers are conscious??? I don't think so
[13:43] Myriam Brianna: an emergent phenomen, no more real than a marble you "feel" between a large number of letters. But real enough.
[13:43] herman Bergson: No....computers are not conscious...:-)
[13:44] Karybdis Carnell: no silicon computer has demonstrated conscience to my knowledge yet
[13:44] Arlo Weir: yet
[13:44] Myriam Brianna: I am a computer, and I am conscious :x
[13:44] Laura Lyne: Consciousness itself is an emergent phenomenon.
[13:44] Myriam Brianna: yes.
[13:44] Paula Dix: welll our computers are so limited still
[13:44] herman Bergson: Reread the lecturess in Can my computer thing at http://thephilosophyclass.blogspot.com
[13:44] Karybdis Carnell: err conscious thought not conscience
[13:44] Gemma Cleanslate: yes we had a long discussion on this
[13:44] Paula Dix: yes we had this discussion earlier :)))
[13:45] Myriam Brianna: so there's no contradiction between the digital on-off state of our neurons and the epiphenomenal level of our conscious thinking
[13:45] Laura Lyne agrees
[13:45] herman Bergson: yes...so reread it to brush up your memory :-)
[13:45] Paula Dix: thats if our neurons dont work with fuzzy logic or something else :))
[13:45] Myriam Brianna: Fuzzy Logic is Logic
[13:45] Laura Lyne: Just as there is no contradiction between the simple fractal formula and the epiphenomenon of the pretty picture it can produce
[13:46] Paula Dix: (I mean non-binary system)
[13:46] Myriam Brianna: yes
[13:46] herman Bergson: Well at least I can advise you to look into the history of the number for instance...
[13:47] Karybdis Carnell: hmm. Back on the subject of, numbers, I suppose Plato would have approved of alternate universes. IF math can describe them, they are real
[13:47] herman Bergson: Teh basic philosopjhicla issue here is ..is math derived from empirical experience or is it innate, a priori
[13:47] oola Neruda: i believe it comes from experience
[13:47] Laura Lyne: It was always there. We just had to discover it.
[13:48] herman Bergson: I think the origins of math ly in the interaction between human needs and its environment...
[13:48] Myriam Brianna nods
[13:48] herman Bergson: however, that still doesnt explain why the mind was capable of quantification of reality
[13:48] Karybdis Carnell: I imagine mathematical experience is a product of the ways our brains work, at least to a degree
[13:48] Arlo Weir: math coms from greed
[13:49] Gemma Cleanslate: hmmmmm
[13:49] oola Neruda: i think this asks the question... did we create math or was it something that came with the earth... a bit like... if the tree falls in the forest and nobody hears it does it fall
[13:49] Paula Dix: Herman how the idea of "imperfection" like on Goddel would be in this? It can be natural on an a priori math??
[13:49] Gemma Cleanslate: greed??
[13:49] Gemma Cleanslate: I think it was necessity
[13:49] Myriam Brianna: we've evolved in this cosmos, none else. We have to interact with it, and it follows certain rules
[13:49] Arlo Weir: yes we trade stuff. i give you a sheep and you give me 2 pigs. so its not fair you want more sheep. etc..
[13:49] Frederick Hansome: IF math can describe them, it soes not prove that they exist, only that it cannot be provern that they do not exist; that they are possible
[13:49] Laura Lyne: We couldn't just dream up a math with completely random rules, and expect it to do anything useful
[13:49] Rosie Hexicola: hmm interesting arlo
[13:49] Gemma Cleanslate: but that is not greed
[13:49] Gemma Cleanslate: lol
[13:50] oola Neruda: there is a book called... is God a mathetician
[13:50] Karybdis Carnell: Or brains in order to memorize a concept must create a schema of it, and store that. So ideas come in descrete numbers; the basis of math
[13:50] Paula Dix: yes, makes sense our mind works in the same system as the place where it evolved :)
[13:50] oola Neruda: written by an astrophysicist
[13:51] herman Bergson: These are all plausible observations, but just observation...not explanations
[13:51] Karybdis Carnell: If our brain could create fully fluid ideas without storing them one at a time, perhaps there wouldn't be math
[13:51] Laura Lyne: Or would there.... only with no human users?
[13:51] herman Bergson: Again we can see how we are imprisoned in our sytem of thinking...we cant trascend it
[13:52] Myriam Brianna: we can, but there's no speaking about transcendence ;)
[13:52] Laura Lyne: Math is the way the universe works. For us, if was a matter of discovering it.
[13:52] herman Bergson: That is a realist view Laura..Plato would cheer too :-)
[13:52] oola Neruda: does math exist for dogs or spiders etc
[13:53] herman Bergson: sometimes it looks like that oola...
[13:53] Karybdis Carnell: That presumes that math can describe the universe fully. The jury still hasn't shown that one yet
[13:53] oola Neruda: if they cannot do math does it exist for them
[13:53] herman Bergson: the precision a spider makes its web for instance
[13:53] Paula Dix: i think yes
[13:53] Laura Lyne: Spider certainly do something that's quite mathematically intricate
[13:53] Gemma Cleanslate: yes
[13:53] herman Bergson: natur has wonderful mathematically perfect structures
[13:53] Laura Lyne: they may not be aware of it, but their brains do it
[13:54] Paula Dix: but then again there is this Goddel thing of imperfection... then nature, universe, is imperfect? accept things that dont fit perfectly??
[13:54] oola Neruda: again... if the tree falls in the forest and nobody hears it... did it fall
[13:54] herman Bergson: It is amazin gthat this pattern of a web is in the instinct/nervous system of the spider indeed
[13:54] Myriam Brianna: the Universe can't describe itself completely
[13:54] Gemma Cleanslate: lol how many times
[13:55] Laura Lyne: No, because the full description IS the universe
[13:55] Paula Dix: lol herman ive read spiders on LSD make perfect webs
[13:55] Gemma Cleanslate: OMG!!!
[13:55] Gemma Cleanslate: omg
[13:55] Myriam Brianna smirks - yes
[13:55] Gemma Cleanslate: lol
[13:55] herman Bergson: I'd like to see that Paula....a spider taking a trip
[13:55] Myriam Brianna: as a perfect map of Dublin _is_ Dublin. A model must be less than the thing it models
[13:55] Paula Dix: lol its on an old LIFE book my friend has here, about the mind
[13:55] Karybdis Carnell: On caffeine, they fail miserably at web making
[13:56] herman Bergson smiles
[13:56] Paula Dix: yes Kary, caffeine makes the web have more imprefections than usual
[13:56] Laura Lyne: Does the LSD actually affect them at all?
[13:56] herman Bergson: Good question...
[13:56] Paula Dix: lol it only mentioned the effect on webs :))
[13:56] Karybdis Carnell: I do wonder if we'll be able to create a full mathematical formalism of the universe. I suspect yes, but who knows
[13:57] Rosie Hexicola: perhaps I'm bad at math because i drink too much coke then :P
[13:57] Laura Lyne: I mean, maybe it's necessary to be self aware to get any effect from LSD
[13:57] Myriam Brianna: on a biochemical level, their nervous system. But there's no consciousness that could be aware of these changes to their cognition
[13:57] Paula Dix: well if it changes how spiders do the webs, or they are aware or it works on non-aware beings
[13:58] herman Bergson: A full mathematical formalism of the universe...yes Karibdys...
[13:58] Laura Lyne: Oh, the trip webs are better than the regular ones?
[13:58] oola Neruda: the point i was aiming at is... does math exist outside of our mind
[13:58] herman Bergson: but it still doesnt answer the question why reality fits mathematics
[13:58] oola Neruda: math is conceptual
[13:58] Paula Dix: yes, they dont have "holes" like the usual ones, the pattern is complete
[13:58] Laura Lyne: Remarkable
[13:59] Laura Lyne: Math fits reality
[13:59] Gemma Cleanslate: see you all tuesday have to go now
[13:59] Karybdis Carnell: does it? the mathmatics of Gravity and of Quantum theory contradict each other. We assume it's because we're missing something
[13:59] herman Bergson: Ok Gemma....on Tuesday we'll have a look at knowledge in general
[13:59] Paula Dix: oola for me it looks like math is outside, yes, and our brains are made with it
[13:59] Laura Lyne: Yes, but they both work
[13:59] oola Neruda: the world has more than just mathmatical explainations... we could be having this discussion on color or other subjects that really are conceptual
[14:00] Laura Lyne: we are obviously missing an element to unify the two
[14:00] Paula Dix: Oh Kary perfect you said so, i always though that but was afraid it was me not getting it
[14:00] herman Bergson: Yes Laura....such a feeling I have too....something is missing in this picture, but what?
[14:00] Karybdis Carnell: Paula: if the two are put together, you get a divide by zero error. Computers would feel sympathetic
[14:00] Paula Dix: lol
[14:00] Frederick Hansome: The problem is our lack of knowledge, not that there is a contradiction in the two
[14:00] oola Neruda: math is a language to describe something we notice... was language here before we spoke
[14:01] oola Neruda: math is a tool
[14:01] herman Bergson: no
[14:01] Paula Dix: i see, then there is no imperfection on the whole (universe), but only on our concepts of it
[14:01] Laura Lyne: English doesn't have the power to predict anything. Math does.
[14:01] Laura Lyne: so it's not just another language
[14:01] CONNIE Eichel: sorry, got to run :)
[14:01] herman Bergson: If math is a language it should have meaning, refering to something, but it doesnt
[14:01] Paula Dix: bye Connie
[14:01] Myriam Brianna: it depends what you mean by imperfection, Paula *shrugs*
[14:02] Paula Dix: well, in this case, the Goddel thing
[14:02] oola Neruda: can you touch a math... you cannot touch english.... they are concepts not physical things
[14:02] Myriam Brianna: then it's a fundamental problem, to my guessing
[14:02] oola Neruda: a language that describes things
[14:02] herman Bergson: Math doesnt predict Laura
[14:02] Frederick Hansome: Before everyone leaves, there will be a discussion of "consciouisness" at Plato's Academy, 6 PM SLT on Sept 21
[14:03] Myriam Brianna: cool
[14:03] Laura Lyne: It doesn't?
[14:03] herman Bergson: Plato's Academy?Never heard of Frederick.....where is it?
[14:03] Paula Dix: thats interesting, then math describes only? its like painting with different brush??
[14:03] herman Bergson: Math produces tautologies...
[14:04] Laura Lyne: Plenty of later empirically tested things came about initially from mathematics only.
[14:04] herman Bergson: 12 x 12 doesnt predict that I need 144 tiles
[14:04] Laura Lyne: Hmm... I'd say it does
[14:04] oola Neruda: things have come about because we have language for communication
[14:04] Frederick Hansome: A new philosophical discussion groupp, led by Plato Greybeard
[14:04] herman Bergson: that is true....but these were all deductions....not new knowledge
[14:04] Arlo Weir: dont forget the grooves!~hihi
[14:04] Myriam Brianna: as in the case of logic: Mathematical operations explicate, - it was there, in the initial input
[14:05] Frederick Hansome gave you Plato's Academy, Mountains Forest (230, 61, 301) Academy lawn.
[14:05] Myriam Brianna: of course with your initial input you couldn't predict anything ;)
[14:05] Laura Lyne: Well, then prediction is perhaps the wrong word to use in anything in science
[14:05] Karybdis Carnell: well, math does lead to new knowledge. Answers found out in math have led to new theories of reality
[14:06] Laura Lyne: Nevertheless, predict is commonly used
[14:06] herman Bergson: No..when you use induction you get to a theory....and deduce a hypothesis from the theory and test it...
[14:06] oola Neruda: because it is a useful tool... conceptual tool
[14:06] herman Bergson: falsification of the hypothesis shows that your inductive rreasoning from observable facts wasnt correct
[14:07] Laura Lyne: What if the hypothesis arises from math alone?
[14:07] herman Bergson: The hypthesis is a prediction
[14:07] herman Bergson: that can never happen...
[14:07] herman Bergson: only in combination with empircal data
[14:08] Laura Lyne: Empiricism comes into it once you want to test the hypothesis
[14:08] herman Bergson: a deduction in math is just a true amthematical proposition eventually
[14:08] oola Neruda: deductions and predictions are done by human minds... using a tool
[14:09] Arlo Weir jawns
[14:09] herman Bergson: Yes I agree Laura...but your started with an empirical theory at least
[14:09] Laura Lyne: Oh
[14:09] Laura Lyne: I see. You're saying that the *first* hypothesis can't come from math
[14:09] Laura Lyne: sure
[14:09] herman Bergson: For instance....
[14:10] herman Bergson: They observed that Uranus showed an erratic elliptical path....
[14:10] Arlo Weir: LOL
[14:10] Arlo Weir: URanus
[14:10] Arlo Weir: hihihi
[14:10] Laura Lyne: Shush
[14:10] herman Bergson: by calculation they predicted that this only could be if there was another mass nearby
[14:10] Laura Lyne: lol
[14:11] herman Bergson: lol
[14:11] herman Bergson: and so it was...Neptune was discovered.
[14:11] Arlo Weir: sorry beeing silly
[14:12] Paula Dix: silly is good :))
[14:12] herman Bergson: I should put you in the corner for that Arlo :-)
[14:12] Arlo Weir: hehe
[14:12] Rosie Hexicola: have him wear donkey ears
[14:12] Laura Lyne: In that case, a prediction was made using mathematics.
[14:12] herman Bergson: Yes Rosie!
[14:13] herman Bergson: Yes Laura....applied to reality
[14:13] Paula Dix: that makes me think math is a priori, since it is related to the reality and not our thinkings
[14:13] Paula Dix: no, the prediction came from analisys of math data
[14:13] Laura Lyne: Right
[14:13] herman Bergson: Their prediction came from the mathematical analysis of observed phenomena
[14:14] Karybdis Carnell: just patiently following and seeing how much of this I get
[14:14] Paula Dix: and then that become a tool to find new planets used all the time now
[14:14] Laura Lyne: Well, it was a case of "What would make Uranus behave like that?" and then using orbital mechanics math to fill in the blank, which is Neptune
[14:14] Karybdis Carnell: But I know what herman is saying I think
[14:14] Karybdis Carnell: The math itself didn't predict anything. It was only the application of it that predicted
[14:15] herman Bergson: Right Laura...
[14:15] Paula Dix: true laura, math just described uranus behaviour, didnt explain it
[14:15] herman Bergson: yes Karibdys...correct
[14:15] Laura Lyne: Ok then... it was a semantic issue then. I said "Math predicts", where you say "The use of math predicts"
[14:15] Paula Dix: so math is like the reality, its just there, we have to notice it
[14:15] Arlo Weir giggles
[14:15] Laura Lyne: that was what I meant, of course
[14:15] Laura Lyne: math itself doesn't do anything
[14:16] herman Bergson: And just that makes it so special....math as such is empty referentially
[14:16] Laura Lyne: Right :)
[14:16] herman Bergson: Or it refers to mathematical entities as somePlatonists claim
[14:17] Laura Lyne: In that sense, it's a bit like "Red" or "Blue". They don't make sense without an observer.
[14:17] herman Bergson: .
[14:18] herman Bergson looks at the clock
[14:18] herman Bergson: As we are controled by numbers...^_^
[14:18] Paula Dix: lol
[14:18] Arlo Weir is lost completely
[14:18] herman Bergson: I think it is time to thank you for your participation and dismiss class :-)
[14:19] Laura Lyne: It was a real braintwister :)
[14:19] Karybdis Carnell: thanks herman :)
[14:19] Paula Dix is convinced now that math is a natural thing
[14:19] herman Bergson: Next lecture will be on knowledge in general...
[14:19] Frederick Hansome: Thank you, herman. Good discussion
[14:19] herman Bergson: Thank you all :-)