By ruined day I was more talking about spurious signals in your electronics (leading to unpredictable behavior) and ionization of your chemical explosive detonators (both of which may lead to premature detonation). I don't know if these issues have been solved and I can't cite a source other than that I've overheard several other physics types disucussing it and that it fits reasonably well with what I know (although checking the decay products/energies, it's not as bad as I recalled...maybe the issue had to do with protactinium and thorium impurities?).
The result was that it was not something you'd want to make a bomb you would keep out of.
If, on the other hand, there were some person/group with the technical ability to build said bomb and the ability to steal the uranium who wanted to detonate it immediately, then I would think there would be plenty of other things to worry about (such as said person sabotaging one of the archaic positive feedback reactors still in service).
I'd classify myself as much a science nerd as computer nerd (if not more). And I know plenty of physicists who you could at a stretch call nuclear (mostly more along the lines of quantum) who read it frequently.
Also I was under the impression getting 233 from a thorium reactor was rather old news, and the gamma emissions would ruin your day if you actually tried to build a bomb with it.
I suppose my post was somewhat poorly worded.
To expand/try again somewhat, uhm
First a few things that aren't maths, or that maths is not.
For one, it does not generate entirely new axioms/rules. The results often seem novel, but they are directly implied by the axioms -- a small set of things simply taken to be obvious New mathematics comes from greater insight into previous assumptions, elimination of redundant assumptions, or examination of assumptions that noone previously bothered with taking as true/false.
Another thing that maths isn't when done correctly is ambiguous. It should mean only one thing to anyone with the correct context. Two sufficiently capable mathematicians given equivalent axioms should come up with equivalent answers given the same question.
There is mathematics for dealing with vagueness and uncertainty; do not confuse this with ambiguity. Errors due to approximations can be quantified, and all sets of lower/upper bounds on answers should overlap even if different people are making different approximations. Some equations also cannot be solved (or approximated with known error) given our current knowledge.
There is also the whole field of applied mathematics (scientists, most statisticians, mathematicians who actually interact with real data etc do this) ambiguity is sometimes/often found here for various reasons (practicality, ambiguity of knowledge of what is being modelled etc) -- like anything dealing with the real world.
In short, properties of something that's maths:
The important/defining properties aren't altered by representation. Ie. it could be expressed in C++, Finnish, traditional Mathematics notation, some beads on a string, by sufficiently well defined interpretive dance, specially shaped toy blocks, or in a brain and still serve the same function.
It is not inductive (scientific/philosophical definition of inductive, not mathematical) in nature.
It is unambiguous, or is the direct application of something unambiguous.
I agree with your comment; although I don't see how what you said is relevant to what I said. GP was claiming that Maths was a product of logic (product of a way of reasoning), in response I claimed that logic was a subset of maths (ie. maths is a way of reasoning, one that encompasses the way of reasoing GP claimed maths was a product of).
Continuing with your line of discussion. There is some discussion of alternate logic in quantum physics. Usually largely in the realm of science philosophy/interpretation, but the notion of 'the particle is here (or the cat is alive if you prefer)' can be thought of as neither completely true nor completely false in some interpretations -- ie. that the superposition represents neither your confidence in your measure or reality, nor the probable end result of some unknown event(s), but that the truth of the particle being at point a is at 2/3 of the way from false to true, and the truth of the particle being at point b is 1/3 of the way from being false to true.
There are other non-traditional logics (a simple one is a three valued true, false, unknown) which see application as well as less used (in science/engineering at least) paraconsistent logics which are often studied in philosophy.
If the injectors can handle both oil and water, and you have a pressure release valve in your hot oil reservoir, I see no reason why partial mixing would be a problem.
You would get a build up of grease and such, but engines do that anyway.
Recognising, identifying and using patterns is mathematics. By collecting things which demonstrate the fibbonaci sequence together your Kenyan kid is doing mathematics even if he is not very good at formally structuring his thoughts using the conventions form academia.
Ambiguous communication (ie. communcation can mean more than one of the available things that aren't degenerate in the current circumstances) is merely bad communication.
Approximations, qualitative analysis and context dependant communication (one of the reasons you can't input into a CAS using traditional notation or just using the same LaTeX as you would for presentation) are common in mathematics. If you don't believe me, go study chaos for a few years. There are plenty of other examples (such as statistics given in the rather hard to follow anon post above).
You don't often see the exact words you mentioned, or communication that depends that heavily on intuition and state of the recipient because it is (usually) too ambiguous to be useful.
Again, if you ask anyone that practices the art, they will be more inclined to say that mathematics is the process of organising, identifying, structuring etc. patterns than the current set of conventions and results we have. Communicating a precise thought unambiguously is important for this; this is why we use the languages/notations/etc that we do.
Then what do you refer to the study of, and manipulation of logical systems including non-tradition (ie. meta-consistent logic). It is sometimes done by those who identify as philosophers, but I think you'll find that the majority of such work is done by people who identify as mathematicians and call it mathematics.
Math (according to anyone I know who has studied it deeply at least) is the thought process. The models and tools which are then applied to the real world are more often referred to as results
To my mind this belies a misunderstanding of what mathematics is.
It does not depend on any one representation, or encoding. It encompasses any (non-ambiguous) expression of rules and relationships between things (be they real, ideals based on reality, or entirely fictional mental entities), or non-ambiguous measurements, and more importantly, the process of generating, manipulating, and understanding said relationships.
I agree wholeheartedly that our current encoding/names/expressions/forms/system of categorizing such things is completely human and largely incidental, but you could probably grab any decent mathematician and put her in an environment with completely different conventions without her having much trouble.
That's why you have a multiplier based on the number of total infractions of any and all companies that are subsidiaries of the same companies, have had the same companies as subsidiaries,or share majority shareholders/board members. It could go something like this: 1e6*2^n dollars where n is the number of infractions.
- it is a fact. The government is spending more money than any company, the government has more employees than any company, the government has more contractors than any company, the government is entangled in more businesses than any company.
Assuming they are true, none of these things rebut gp's statement.
Humans are good at doing these things called generalising and abstraction.
We can abstract away from receiving buttsecks to 'things that bring pleasure to the individual' or even more abstract concepts like 'maximising my utility function'. It gets fuzzy and difficult when trying to compare dissimilar utility functions, but that's why we have all these laws and public forums for debate and such like.
Another approach would be to augment this with a bottom up approach (for those words they can't quite get, or if all the languages die). It's fairly easy to get anough mathematics accross to communicate a simple audio and/or video codec (anyone competent enough to build microscopes and semiconductors is going to get the basic logical operations and from there some kind of assembly isn't hard).
Then include a bunch of sesame street and other stuff aimed at kids. Suppliment it with picture dictionaries along with our current understanding of linguistics and how it applies to the languages we know.
Explaining mathematics accessably is hard (much harder than merely providing a correct formal description), takes a long time, and is often only possible with a test audience. If you're willing to spend the time to add such explanations to wiki you're quite welcome.
Until then I'm going to be grateful for the already large amount of time and effort put in to providing what is already there.
I had a prof who used one of these as part of a package deal type thing they got along with some (arguably very good) other resources. When people from the class told him about the issues involved (buying used books, strange deadlines, OS/screen size/browser requirements etc) he removed it at the first opportunity (sadly not during that course, as once something is set in the paperwork as part of the course assessment it cannot be changed here).
Sometimes treating your prof as a human being works, try it some time.
Posting to call myself out somewhat as noone else seems to have.
I did a bit of reading on taxonomy, and there are good reasons for the modern versions of morphology based taxonomies. Lateral gene transfer, difficulty of placing things in the correct clades due to lack of information, altogether missing sections of the fossil record and so on.
Having things like (or rather continuing to teach first) reptiles (include all these things but exclude these two groups because we think they're cuddly) as a group still seem a little bizarre and anthropocentric, but this doesn't mean the correct answer is to go to the other extreme.
You are all arguing because traditional taxonomy is intensely stupid.
There is a reasonably hard point at which we can define the distinction between two creatures: the last common ancestor.
Yes it only works in hindsight.
Yes it is still a bit fuzzy (many populations cross breed slightly whilst diverging).
But it's a hell of a lot better than this stupidity.
You just draw monophyletic boundaries, rather than 'I'm including this, but not that because I think it looks funny'. Subsets of subsets and suddenly the problem goes away.
Renaming each group would help with the confusion, but personally I'm happy calling birds dinosaurs and calling both birds and humans bony fish. Draw the distinctions at what is fundamental (genes) rather than whatever some long dead biologist who didn't understand as much as we do thought.
The phrase (as it referred to stuff outside of physics) originally was used (reasonably accurately) for discrete rather than continuous (or imperceptably small) changes. I believe it entered the common lexicon from popularizations of the quantum model of bound electrons. This spread to anything about getting from state A to state B without spending much/any time in between.
I agree with the sentiment that it's a bit odd, thinking about it form a physical point of view it seems that it should refer to a single change to a single gene in a single generation.
Yes, but many of them are the worst of both worlds. Speculative and unproven whilst being presented as dogmatic fact. This increases the public perception that science is both certain/absolute and changes its mind frequently/frivolously, and makes it even harder to explain how it really works.
Slashdot Mirror
By ruined day I was more talking about spurious signals in your electronics (leading to unpredictable behavior) and ionization of your chemical explosive detonators (both of which may lead to premature detonation). I don't know if these issues have been solved and I can't cite a source other than that I've overheard several other physics types disucussing it and that it fits reasonably well with what I know (although checking the decay products/energies, it's not as bad as I recalled...maybe the issue had to do with protactinium and thorium impurities?).
The result was that it was not something you'd want to make a bomb you would keep out of.
If, on the other hand, there were some person/group with the technical ability to build said bomb and the ability to steal the uranium who wanted to detonate it immediately, then I would think there would be plenty of other things to worry about (such as said person sabotaging one of the archaic positive feedback reactors still in service).
I'd classify myself as much a science nerd as computer nerd (if not more). And I know plenty of physicists who you could at a stretch call nuclear (mostly more along the lines of quantum) who read it frequently.
Also I was under the impression getting 233 from a thorium reactor was rather old news, and the gamma emissions would ruin your day if you actually tried to build a bomb with it.
No man, Java is the new COBOL, there's gunna be people maintaining and expanding on all the enterprisey java stuff for centuries.
I suppose my post was somewhat poorly worded.
.
To expand/try again somewhat, uhm
First a few things that aren't maths, or that maths is not.
For one, it does not generate entirely new axioms/rules. The results often seem novel, but they are directly implied by the axioms -- a small set of things simply taken to be obvious New mathematics comes from greater insight into previous assumptions, elimination of redundant assumptions, or examination of assumptions that noone previously bothered with taking as true/false
Another thing that maths isn't when done correctly is ambiguous. It should mean only one thing to anyone with the correct context. Two sufficiently capable mathematicians given equivalent axioms should come up with equivalent answers given the same question.
There is mathematics for dealing with vagueness and uncertainty; do not confuse this with ambiguity. Errors due to approximations can be quantified, and all sets of lower/upper bounds on answers should overlap even if different people are making different approximations. Some equations also cannot be solved (or approximated with known error) given our current knowledge.
There is also the whole field of applied mathematics (scientists, most statisticians, mathematicians who actually interact with real data etc do this) ambiguity is sometimes/often found here for various reasons (practicality, ambiguity of knowledge of what is being modelled etc) -- like anything dealing with the real world.
In short, properties of something that's maths:
The important/defining properties aren't altered by representation. Ie. it could be expressed in C++, Finnish, traditional Mathematics notation, some beads on a string, by sufficiently well defined interpretive dance, specially shaped toy blocks, or in a brain and still serve the same function.
It is not inductive (scientific/philosophical definition of inductive, not mathematical) in nature.
It is unambiguous, or is the direct application of something unambiguous.
I agree with your comment; although I don't see how what you said is relevant to what I said. GP was claiming that Maths was a product of logic (product of a way of reasoning), in response I claimed that logic was a subset of maths (ie. maths is a way of reasoning, one that encompasses the way of reasoing GP claimed maths was a product of).
Continuing with your line of discussion. There is some discussion of alternate logic in quantum physics. Usually largely in the realm of science philosophy/interpretation, but the notion of 'the particle is here (or the cat is alive if you prefer)' can be thought of as neither completely true nor completely false in some interpretations -- ie. that the superposition represents neither your confidence in your measure or reality, nor the probable end result of some unknown event(s), but that the truth of the particle being at point a is at 2/3 of the way from false to true, and the truth of the particle being at point b is 1/3 of the way from being false to true.
There are other non-traditional logics (a simple one is a three valued true, false, unknown) which see application as well as less used (in science/engineering at least) paraconsistent logics which are often studied in philosophy.
If the injectors can handle both oil and water, and you have a pressure release valve in your hot oil reservoir, I see no reason why partial mixing would be a problem. You would get a build up of grease and such, but engines do that anyway.
Recognising, identifying and using patterns is mathematics. By collecting things which demonstrate the fibbonaci sequence together your Kenyan kid is doing mathematics even if he is not very good at formally structuring his thoughts using the conventions form academia.
Ambiguous communication (ie. communcation can mean more than one of the available things that aren't degenerate in the current circumstances) is merely bad communication.
Approximations, qualitative analysis and context dependant communication (one of the reasons you can't input into a CAS using traditional notation or just using the same LaTeX as you would for presentation) are common in mathematics. If you don't believe me, go study chaos for a few years. There are plenty of other examples (such as statistics given in the rather hard to follow anon post above).
You don't often see the exact words you mentioned, or communication that depends that heavily on intuition and state of the recipient because it is (usually) too ambiguous to be useful.
Again, if you ask anyone that practices the art, they will be more inclined to say that mathematics is the process of organising, identifying, structuring etc. patterns than the current set of conventions and results we have. Communicating a precise thought unambiguously is important for this; this is why we use the languages/notations/etc that we do.
Then what do you refer to the study of, and manipulation of logical systems including non-tradition (ie. meta-consistent logic). It is sometimes done by those who identify as philosophers, but I think you'll find that the majority of such work is done by people who identify as mathematicians and call it mathematics.
Math (according to anyone I know who has studied it deeply at least) is the thought process. The models and tools which are then applied to the real world are more often referred to as results
To my mind this belies a misunderstanding of what mathematics is.
It does not depend on any one representation, or encoding. It encompasses any (non-ambiguous) expression of rules and relationships between things (be they real, ideals based on reality, or entirely fictional mental entities), or non-ambiguous measurements, and more importantly, the process of generating, manipulating, and understanding said relationships.
I agree wholeheartedly that our current encoding/names/expressions/forms/system of categorizing such things is completely human and largely incidental, but you could probably grab any decent mathematician and put her in an environment with completely different conventions without her having much trouble.
Hi rikxik,
How do I do that? I'm not sure.
PS. Still coming to the orgy on friday?
Aliens use cheap noname chinese laptops?
That's why you have a multiplier based on the number of total infractions of any and all companies that are subsidiaries of the same companies, have had the same companies as subsidiaries,or share majority shareholders/board members. It could go something like this: 1e6*2^n dollars where n is the number of infractions.
By putting it into landfill you are still transferring ownership.
- it is a fact. The government is spending more money than any company, the government has more employees than any company, the government has more contractors than any company, the government is entangled in more businesses than any company.
Assuming they are true, none of these things rebut gp's statement.
Humans are good at doing these things called generalising and abstraction.
We can abstract away from receiving buttsecks to 'things that bring pleasure to the individual' or even more abstract concepts like 'maximising my utility function'. It gets fuzzy and difficult when trying to compare dissimilar utility functions, but that's why we have all these laws and public forums for debate and such like.
Another approach would be to augment this with a bottom up approach (for those words they can't quite get, or if all the languages die). It's fairly easy to get anough mathematics accross to communicate a simple audio and/or video codec (anyone competent enough to build microscopes and semiconductors is going to get the basic logical operations and from there some kind of assembly isn't hard).
Then include a bunch of sesame street and other stuff aimed at kids. Suppliment it with picture dictionaries along with our current understanding of linguistics and how it applies to the languages we know.
So you're saying we should bring the fast food home and use it to destroy all the kids favourite toys then send them to their room with no dinner?
YES, BECAUSE ACTUAL CRIMINALS ARE MORE MORAL THAN THE REPUBLICAN PARTY! LOL! IT'S A JOKE!!!
I realise this, but what was the joke? Isn't humour usually based on some misrepresentation or exaggeration?
Explaining mathematics accessably is hard (much harder than merely providing a correct formal description), takes a long time, and is often only possible with a test audience. If you're willing to spend the time to add such explanations to wiki you're quite welcome.
Until then I'm going to be grateful for the already large amount of time and effort put in to providing what is already there.
Well I had him again the next semester and helped tutor both courses later. He had fixed it.
I had a prof who used one of these as part of a package deal type thing they got along with some (arguably very good) other resources. When people from the class told him about the issues involved (buying used books, strange deadlines, OS/screen size/browser requirements etc) he removed it at the first opportunity (sadly not during that course, as once something is set in the paperwork as part of the course assessment it cannot be changed here).
Sometimes treating your prof as a human being works, try it some time.
Posting to call myself out somewhat as noone else seems to have.
I did a bit of reading on taxonomy, and there are good reasons for the modern versions of morphology based taxonomies. Lateral gene transfer, difficulty of placing things in the correct clades due to lack of information, altogether missing sections of the fossil record and so on.
Having things like (or rather continuing to teach first) reptiles (include all these things but exclude these two groups because we think they're cuddly) as a group still seem a little bizarre and anthropocentric, but this doesn't mean the correct answer is to go to the other extreme.
You are all arguing because traditional taxonomy is intensely stupid.
There is a reasonably hard point at which we can define the distinction between two creatures: the last common ancestor.
Yes it only works in hindsight.
Yes it is still a bit fuzzy (many populations cross breed slightly whilst diverging).
But it's a hell of a lot better than this stupidity.
You just draw monophyletic boundaries, rather than 'I'm including this, but not that because I think it looks funny'. Subsets of subsets and suddenly the problem goes away.
Renaming each group would help with the confusion, but personally I'm happy calling birds dinosaurs and calling both birds and humans bony fish. Draw the distinctions at what is fundamental (genes) rather than whatever some long dead biologist who didn't understand as much as we do thought.
The phrase (as it referred to stuff outside of physics) originally was used (reasonably accurately) for discrete rather than continuous (or imperceptably small) changes. I believe it entered the common lexicon from popularizations of the quantum model of bound electrons. This spread to anything about getting from state A to state B without spending much/any time in between.
I agree with the sentiment that it's a bit odd, thinking about it form a physical point of view it seems that it should refer to a single change to a single gene in a single generation.
Yes, but many of them are the worst of both worlds. Speculative and unproven whilst being presented as dogmatic fact. This increases the public perception that science is both certain/absolute and changes its mind frequently/frivolously, and makes it even harder to explain how it really works.