Representing chemical formulas as a single number

[scratch123]

This idea was motivated by the idea of representing all 5 senses as numbers. It is already well known that the senses of sight and sound can be represented as waves and these waves can represented as numbers. That leaves smell, touch, and taste which are all related to chemicals. In order to represent chemicals as numbers I came up with the following method. Take all of the numbers that appear in the formula and all of the atomic numbers of these atoms and multiply them together. For example say you want to represent serotonin (C10H12N2O) as a single number. First you would take carbon (atomic number 6) and multiply it by the first number in the chemical formula (10) to get 60. Now do the same thing for hydrogen (12 * 1), nitrogen (2 * 7), and oxygen (1 * 8 ). When you multiply all these numbers together you get 80640. Shouldn't there be some use to doing this? For example you could take 2 chemical formulas that have the same number but different formulas and see if they have similar chemical properties. For example H2O and O2 both are equal to 16.

[idobox]

What you're doing is count the number of protons in a molecule, not a very interresting figure, since it doesn't give any of the properties, and it's ambiguous.
If you reaaaaally want to "numberize" molecules, you could make an array, something like [2,0,0,0,0,0,0,1] for H2O, or use the molecular weight.

But a more important question is: why do you want to do that? concentration of chemicals vs time look like a pretty numerical thing to me already.

[gmalivuk]

What you're doing is count the number of protons in a molecule, not a very interresting figure, since it doesn't give any of the properties, and it's ambiguous.

It's worse, actually, because scratch123 wants to multiply the numbers together, rather than add them. At least counting the number of protons would give you a physically meaningful result, namely the number of protons.

[Tass]

This idea was motivated by the idea of representing all 5 senses as numbers. It is already well known that the senses of sight and sound can be represented as waves and these waves can represented as numbers. That leaves smell, touch, and taste which are all related to chemicals. In order to represent chemicals as numbers I came up with the following method. Take all of the numbers that appear in the formula and all of the atomic numbers of these atoms and multiply them together. For example say you want to represent serotonin (C10H12N2O) as a single number. First you would take carbon (atomic number 6) and multiply it by the first number in the chemical formula (10) to get 60. Now do the same thing for hydrogen (12 * 1), nitrogen (2 * 7), and oxygen (1 * 8 ). When you multiply all these numbers together you get 80640. Shouldn't there be some use to doing this? For example you could take 2 chemical formulas that have the same number but different formulas and see if they have similar chemical properties. For example H2O and O2 both are equal to 16.

A simple though not optimally compressed method of representing every compound as a unique number: Write down the IUPAC name of the compound, convert it to binary using ascii code, read the binary code as a number.

The method you gave is, as you said, not unique; and there is no reason to assume that identical numbers would carry any significance.

[scratch123]

What you're doing is count the number of protons in a molecule, not a very interresting figure, since it doesn't give any of the properties, and it's ambiguous.
If you reaaaaally want to "numberize" molecules, you could make an array, something like [2,0,0,0,0,0,0,1] for H2O, or use the molecular weight.

But a more important question is: why do you want to do that? concentration of chemicals vs time look like a pretty numerical thing to me already.

The whole reason the periodic table is based on the number of protons is because they are an important quantity that determines many chemical properties. Also the reason I am not including addition in this formula is because it would lead to many molecules being given the same number.

[legend]

I don't see where this is going. Your notation isn't unique at all. E.g. H2=2=He or CH4=24=O3 and I don't really see what those molecules do have in common.

[gmalivuk]

The whole reason the periodic table is based on the number of protons is because they are an important quantity that determines many chemical properties.

Yes, but there's no reason to assume that twice as many of an atom with half the protons would result in a molecule at all similar to what you started with.

Also the reason I am not including addition in this formula is because it would lead to many molecules being given the same number.

You still have that problem, though, only without the (admittedly small) benefit of being able to at the very least say *something* about the compound in question, like how many protons it has.

[Sizik]

I don't see where this is going. Your notation isn't unique at all. E.g. H2=2=He or CH4=24=O3 and I don't really see what those molecules do have in common.

And even if the notation was unique, you'd still run into the problem of different molecules with the same molecular formula (i.e. Cotinine and 4-Methylaminorex, which share the same formula (C₁₀H₁₂N₂O)as serotonin).

[oxoiron]

The whole reason the periodic table is based on the number of protons is because they are an important quantity that determines many chemical properties.

The periods and groups in the table have more to do with electron energy levels and configurations than anything else. These electronic characteristics have much more influence on chemical properties than the number of protons does.

[ahammel]

If you wanted a unique notation, you could assign every element a prime number and multiply all the atoms in the compound together to get a unique composite. Eg:

H₂O = 2*2*19 = 76
CO₂ = 13*19*19 = 4693

But why?

[Ulc]

If you wanted a unique notation, you could assign every element a prime number and multiply all the atoms in the compound together to get a unique composite. Eg:

H₂O = 2*2*19 = 76
CO₂ = 13*19*19 = 4693

But why?

Which would still be unable to distinguish between a large number of compounds that have the same atoms, but different arrangement. And even though there is a reason behind the way the periodic table is arranged, it really doesn't tell all that much about a molecule what atoms are in it, arrangement is at least as important.

[ahammel]

Which would still be unable to distinguish between a large number of compounds that have the same atoms, but different arrangement.

Yes, but molecular formulae don't do that either. I was under the impression that that's what we're trying to replace.

[mfb]

If you just want some possibility to get a number: Find a way to determine the three-dimensional position of every atom in your molecule, averaging over fluctuations, temperature effects and so on.
This is even better than just using the connections, as molecules with the same structure of connections can fold in a different way (and can make you ill).
Take the barycenter of the molecule as origin of a coordinate system, align the axes with the principal axes of inertia (largest as x, smallest as z), find some way to handle ambiguous cases. Sort the atoms by their coordinates (does not matter how), store everything in a long number (atomnumber1 xposition1 yposition1 zposition1 atomnumber2 xposition2 yposition2 zposition2 ...) with arbitrary precision (maybe 1/100nm).
Done.

I am quite sure that you don't need a real algorithm for your theoretical work.

[Sagekilla]

What if you represented each element by an N x N matrix (N = number of elements) and you defined
multiplication to be the operation performed when two elements bond with each other.

That may have some interesting properties.

[Dopefish]

Take the barycenter of the molecule as origin of a coordinate system, align the axes with the principal axes of inertia (largest as x, smallest as z), find some way to handle ambiguous cases. Sort the atoms by their coordinates (does not matter how), store everything in a long number (atomnumber1 xposition1 yposition1 zposition1 atomnumber2 xposition2 yposition2 zposition2 ...) with arbitrary precision (maybe 1/100nm).
Done.

That's beginning to sounds like molecular specification in Gaussian.


Theres a lot of useful numbers you can calculate for a given molecule, but I don't think any are going to be found by just taking essentially random configurations of numbers showing up in the chemical formula and hoping for the best.

I think if I were to try and compress a molecule down to a single number, I'd opt for the ground state energy (to some precision) for the molecule (in the gas phase rather then in any solvent, in the absence of any external fields, or similar trickery). I suspect that'd be unique, and even has the bonus of differing for different molecules of the same formula. Of course, getting the energy is tricky, and going backwards would be nearly impossible, but that's a minor detail.

[Jplus]

All those ideas for enumerating chemical compounds are interesting, but I think they don't help to achieve scratch123's actual goal, i.e. to find an aromatic equivalent to spectral analysis as it is used in visual and auditory perception research (read the OP again to see what I mean). In auditory percetion, we translate a function from time to intensity into a function from spectral components to intensity. In visual perception, we translate a function from two-dimensional space to intensity into a function from two-dimensional spectral components to intensity (if we ignore color for the moment).

If we were to do something like that with olfactory perception, I think we would take a function from chemical compounds to intensity as the input and get a function from olfactory aspects to intensity as the output. That would be really hard because, IIRC, a human nose distinguishes a very high number of olfactory aspects and we don't really understand very well how all of that works. We would have to know about each chemical compound which olfactory sensors are triggered by it, and how much.

[Copper Bezel]

Yeah. Sight and sound can be represented, very roughly, as amplitude and frequency because they evolved to, very roughly, measure those characteristics. Taste and smell are chemistry, not physics. They rely on a series of chemical tests for specific (and, to a chemist at least, arbitrary) reactive characteristics that can't be plotted on a continuum.

[mfb]

Assuming a reasonable number of different sensor types for smelling, you could measure the time-dependent response of each sensor type. This is equivalent to the time-dependent and two-dimensional measurements of the eyes, just without an intuitive way to order the different sensor types.

[scratch123]

I don't see where this is going. Your notation isn't unique at all. E.g. H2=2=He or CH4=24=O3 and I don't really see what those molecules do have in common.

Both methane (ch4) and ozone (o3 ) are both found in the atmosphere so maybe that means something. I will see what else I can find.

[gmalivuk]

Both methane (ch4) and ozone (o3 ) are both found in the atmosphere so maybe that means something.

I guarantee you it doesn't. Chromium is 24 as well, and has nothing in particular in common with methane or ozone.

[Carlington]

Both methane (ch4) and ozone (o3 ) are both found in the atmosphere so maybe that means something.

I guarantee you it doesn't. Chromium is 24 as well, and has nothing in particular in common with methane or ozone.

Gaseous hexavalent chromium, ozone and methane and all lethal to humans if inhaled. Obviously, the numbers are useful for telling us which gases are unsuited to replacing O2 for humans.

[gmalivuk]

But then all gases other than oxygen would count, and yet they have quite different numbers.

[Minerva]

I think what you're talking about here sounds more and more like numerological nonsense.

[scratch123]

Since I know a lot of people who smoke (even though I hate it) I decided to investigate the numerical properties of nicotine to see what I could find. The chemical formula for nicotine is C10H14N2 which can be reduced to the sets (10, 6), (14, 1), (2, 7). These sets can be further reduced by taking the product of the numbers in each set which forms the set (60, 14, 14). My theory attempts to explain the presence of all of these numbers. The set (6, 10, 14) represents the first 3 semiprime numbers that can be written using 2 distinct numbers. For example 9 doesn't count because it uses the same number (3 *3) twice. The numbers 1 and 2 are explained by the fact that these are the only 2 numbers that are factors of 6, 10, and 14. The number 7 is a little tricky to explain but this is what I came up with. It is half of 14, the 4th prime number, and 4th odd number. Now the only number left is 60. The number 60 has 10 factors (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) which further references the 10 carbon atoms in nicotine.

[Carlington]

But then all gases other than oxygen would count, and yet they have quite different numbers.

The point - it was this.

Since I know a lot of people who smoke (even though I hate it) I decided to investigate the numerical properties of nicotine to see what I could find. The chemical formula for nicotine is C10H14N2 which can be reduced to the sets (10, 6), (14, 1), (2, 7). These sets can be further reduced by taking the product of the numbers in each set which forms the set (60, 14, 14). My theory attempts to explain the presence of all of these numbers. The set (6, 10, 14) represents the first 3 semiprime numbers that can be written using 2 distinct numbers. For example 9 doesn't count because it uses the same number (3 *3) twice. The numbers 1 and 2 are explained by the fact that these are the only 2 numbers that are factors of 6, 10, and 14. The number 7 is a little tricky to explain but this is what I came up with. It is half of 14, the 4th prime number, and 4th odd number. Now the only number left is 60. The number 60 has 10 factors (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) which further references the 10 carbon atoms in nicotine.

What...just what? I don't actually understand what you're trying to do here. Excellent. You found some semiprimes. But...what? If anyone can shed any light on what is going on in scratch123's mind, please let me know. Because to be honest, I didn't know it was even possible to be this wrong.

[aaaaay]

If you want a number to distinguish molecular formulas how about simply using the accurate mass? I mean, that's different enough to distinguish say, heptane and cyclohexanol, but has the advantage of being already established and corresponding to experiment (high resolution mass spec). In terms of actual 'codes' for different chemicals including those of the same empirical formula, the best we have I guess are CAS numbers http://en.wikipedia.org/wiki/Cas_number

[gmalivuk]

Since I know a lot of people who smoke (even though I hate it) I decided to investigate the numerical properties of nicotine to see what I could find. The chemical formula for nicotine is C10H14N2 which can be reduced to the sets (10, 6), (14, 1), (2, 7). These sets can be further reduced by taking the product of the numbers in each set which forms the set (60, 14, 14). My theory attempts to explain the presence of all of these numbers. The set (6, 10, 14) represents the first 3 semiprime numbers that can be written using 2 distinct numbers. For example 9 doesn't count because it uses the same number (3 *3) twice. The numbers 1 and 2 are explained by the fact that these are the only 2 numbers that are factors of 6, 10, and 14. The number 7 is a little tricky to explain but this is what I came up with. It is half of 14, the 4th prime number, and 4th odd number. Now the only number left is 60. The number 60 has 10 factors (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) which further references the 10 carbon atoms in nicotine.

Yep, numerological nonsense, for sure.

[ahammel]

If you want a number to distinguish molecular formulas how about simply using the accurate mass? I mean, that's different enough to distinguish say, heptane and cyclohexanol, but has the advantage of being already established and corresponding to experiment (high resolution mass spec).

Going from a mass to a formula seems a bit inconvenient. And by "inconvenient", I mean "probably NP-complete". Of course my prime-numbering scheme has the same problem.

I think it's time we consider that chemists already know what they're talking about.

[scratch123]

Since I know a lot of people who smoke (even though I hate it) I decided to investigate the numerical properties of nicotine to see what I could find. The chemical formula for nicotine is C10H14N2 which can be reduced to the sets (10, 6), (14, 1), (2, 7). These sets can be further reduced by taking the product of the numbers in each set which forms the set (60, 14, 14). My theory attempts to explain the presence of all of these numbers. The set (6, 10, 14) represents the first 3 semiprime numbers that can be written using 2 distinct numbers. For example 9 doesn't count because it uses the same number (3 *3) twice. The numbers 1 and 2 are explained by the fact that these are the only 2 numbers that are factors of 6, 10, and 14. The number 7 is a little tricky to explain but this is what I came up with. It is half of 14, the 4th prime number, and 4th odd number. Now the only number left is 60. The number 60 has 10 factors (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) which further references the 10 carbon atoms in nicotine.

Yep, numerological nonsense, for sure.

Just because you don't understand it don't call it numerological nonsense. All the numerology I have seen is a lot more arbitrary than this. It usually has to do with assigning numbers to letters without much justification. If you want to call this numerology you might as well call designing a compression algorithm numerology as well. What I have basically done is created a group (by assigning numbers to things that chemistry assigns them) with multiplication as the group operation and explained how all the numbers are related through it (primes are related to multiplication). I hope you are at least familiar with group theory. You could also try looking up these numbers on wikipedia.

"What...just what? I don't actually understand what you're trying to do here. Excellent. You found some semiprimes. But...what? If anyone can shed any light on what is going on in scratch123's mind, please let me know. Because to be honest, I didn't know it was even possible to be this wrong."

They are not just semiprimes but semiprimes that have distinct factors (6, 10, 14) = (2 * 3, 5 * 10, 7 * 2). Of all of the numbers in the set of semiprimes with distinct factors these are the first 3. This shows that these 3 numbers are related without introducing any other numbers or introducing addition into the group. I could just say 6 + 4 = 10 + 4 = 14 but that would be too arbitrary since I would have no justification for introducing addition or 4 into the group.

[eSOANEM]

Since I know a lot of people who smoke (even though I hate it) I decided to investigate the numerical properties of nicotine to see what I could find. The chemical formula for nicotine is C10H14N2 which can be reduced to the sets (10, 6), (14, 1), (2, 7). These sets can be further reduced by taking the product of the numbers in each set which forms the set (60, 14, 14). My theory attempts to explain the presence of all of these numbers. The set (6, 10, 14) represents the first 3 semiprime numbers that can be written using 2 distinct numbers. For example 9 doesn't count because it uses the same number (3 *3) twice. The numbers 1 and 2 are explained by the fact that these are the only 2 numbers that are factors of 6, 10, and 14. The number 7 is a little tricky to explain but this is what I came up with. It is half of 14, the 4th prime number, and 4th odd number. Now the only number left is 60. The number 60 has 10 factors (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) which further references the 10 carbon atoms in nicotine.

Yep, numerological nonsense, for sure.

Just because you don't understand it don't call it numerological nonsense. All the numerology I have seen is a lot more arbitrary than this. It usually has to do with assigning numbers to letters without much justification. If you want to call this numerology you might as well call designing a compression algorithm numerology as well. What I have basically done is created a group (by assigning numbers to things that chemistry assigns them) with multiplication as the group operation and explained how all the numbers are related through it (primes are related to multiplication). I hope you are at least familiar with group theory. You could also try looking up these numbers on wikipedia.

This has nothing to do with group theory, for one thing your set isn't even closed under multiplication let alone invertable.

It does have to do with you taking some numbers, doing things to them and spotting patterns. The brain is very good at spotting patterns in random samples too small to draw meaningful conclusions from.

This is certainly what has happened here. The fact that you have to add odd exceptions (such as why 9 doesn't count, that 7 has no inherent explanation, and that all the numbers you end up with link to the structure of nicotine in different and arbitrary ways, I'm sure there are lots of other ways in which they can be made to relate).

As it is, unless you have some justification as to why these processes should give meaningful answers (e.g. applying the exact same process to other chemicals and getting equivalent correct conclusions), what you have is numerological nonsense and trying to claim otherwise without justification simply reveals a rather unscientifically unskeptical mind.

[gmalivuk]

I hope you are at least familiar with group theory.

I am, but you clearly aren't. For instance, "group under multiplication" doesn't just mean "some numbers I got from multiplying things together".

[The Geoff]

You can already convert atoms, molecules and chemical compounds into a series of numbers, do sums with them, and make predictions about their behaviour - it's called quantum mechanics. One of the first big triumphs of quantum theory was explaining most of chemistry (in theory at least), so if your proposed system works you'll probably end up deriving quantum mechanics from the experimental results of chemistry, rather than mathematical theory.

[scratch123]

Since I know a lot of people who smoke (even though I hate it) I decided to investigate the numerical properties of nicotine to see what I could find. The chemical formula for nicotine is C10H14N2 which can be reduced to the sets (10, 6), (14, 1), (2, 7). These sets can be further reduced by taking the product of the numbers in each set which forms the set (60, 14, 14). My theory attempts to explain the presence of all of these numbers. The set (6, 10, 14) represents the first 3 semiprime numbers that can be written using 2 distinct numbers. For example 9 doesn't count because it uses the same number (3 *3) twice. The numbers 1 and 2 are explained by the fact that these are the only 2 numbers that are factors of 6, 10, and 14. The number 7 is a little tricky to explain but this is what I came up with. It is half of 14, the 4th prime number, and 4th odd number. Now the only number left is 60. The number 60 has 10 factors (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) which further references the 10 carbon atoms in nicotine.

Yep, numerological nonsense, for sure.

Just because you don't understand it don't call it numerological nonsense. All the numerology I have seen is a lot more arbitrary than this. It usually has to do with assigning numbers to letters without much justification. If you want to call this numerology you might as well call designing a compression algorithm numerology as well. What I have basically done is created a group (by assigning numbers to things that chemistry assigns them) with multiplication as the group operation and explained how all the numbers are related through it (primes are related to multiplication). I hope you are at least familiar with group theory. You could also try looking up these numbers on wikipedia.

This has nothing to do with group theory, for one thing your set isn't even closed under multiplication let alone invertable.

It does have to do with you taking some numbers, doing things to them and spotting patterns. The brain is very good at spotting patterns in random samples too small to draw meaningful conclusions from.

This is certainly what has happened here. The fact that you have to add odd exceptions (such as why 9 doesn't count, that 7 has no inherent explanation, and that all the numbers you end up with link to the structure of nicotine in different and arbitrary ways, I'm sure there are lots of other ways in which they can be made to relate).

As it is, unless you have some justification as to why these processes should give meaningful answers (e.g. applying the exact same process to other chemicals and getting equivalent correct conclusions), what you have is numerological nonsense and trying to claim otherwise without justification simply reveals a rather unscientifically unskeptical mind.

Ok how about thinking about this in terms of it being a compression algorithm. You have the set (6, 10, 14) and you are compressing it to (semiprimes with 2 distinct factors). The reason the second set is smaller than the first under my method of encoding is because it uses no numbers except for 2 (the number 2 isn't that arbitrary because it appears so often in math and even has the alternating group related to it). I could see this being stored in a computer program as only a few bits. Also the reason I am against using addition is because multiplication (which is related to combination) describes chemical bonds better.

[eSOANEM]

Ok how about thinking about this in terms of it being a compression algorithm. You have the set (6, 10, 14) and you are compressing it to (semiprimes with 2 distinct factors). The reason the second set is smaller than the first under my method of encoding is because it uses no numbers except for 2 (the number 2 isn't that arbitrary because it appears so often in math and even has the alternating group related to it). I could see this being stored in a computer program as only a few bits. Also the reason I am against using addition is because multiplication (which is related to combination) describes chemical bonds better.

If it's a compression algorithm, it's a pretty poor one given how lossy it is.

Anyway, you missed my main point which was that, if this method is useful and not numerological nonsense, the exact same method should produce equivalent correct results for any other chemical. If you can demonstrate that this holds for even a handful of other chemicals then I will concede that it might have some truth in it. Until then, it looks like a load of rules chosen to create a pattern you've spotted where none exists.

[Soralin]

Yeah, if you want a really simple, although not very efficient algorithm, you could just do something like 1000¹ * (number of H atoms) + 1000² * (number of He atoms) + 1000³ * (number of Li atoms) + ... + 1000ⁿ * (number of element n atoms). You would have a number that uniquely represented the number and types of atoms in a molecule (wouldn't distinguish between two different molecules with the same atoms of course), that could be read off by a human relatively easy.

Of course, having that all in a single number, rather than say as elements in an array, or written down in separate columns, or in separate boxes, etc. makes no difference at all. And doing it this way over using primes just makes it easier to see the pattern, and to show that doing random math to an arbitrary pattern is rather pointless and isn't going to get you anything more than what you started with, at best.

[scratch123]

Ok how about thinking about this in terms of it being a compression algorithm. You have the set (6, 10, 14) and you are compressing it to (semiprimes with 2 distinct factors). The reason the second set is smaller than the first under my method of encoding is because it uses no numbers except for 2 (the number 2 isn't that arbitrary because it appears so often in math and even has the alternating group related to it). I could see this being stored in a computer program as only a few bits. Also the reason I am against using addition is because multiplication (which is related to combination) describes chemical bonds better.

If it's a compression algorithm, it's a pretty poor one given how lossy it is.

Anyway, you missed my main point which was that, if this method is useful and not numerological nonsense, the exact same method should produce equivalent correct results for any other chemical. If you can demonstrate that this holds for even a handful of other chemicals then I will concede that it might have some truth in it. Until then, it looks like a load of rules chosen to create a pattern you've spotted where none exists.

OK I will see if I can apply this to any other chemicals. Maybe some other addictive drugs.

[gmalivuk]

If it's useful, it also has to be applicable to things besides addictive drugs. So why don't you check some inert or otherwise biologically unimportant compounds?

[eSOANEM]

If it's useful, it also has to be applicable to things besides addictive drugs. So why don't you check some inert or otherwise biologically unimportant compounds?

This is a good point.

I will settle for the same method producing equivalent results for other addictive drugs but I would be even more impressed if its application were to be shown to be broader by testing other compounds as gmalivuk suggests or maybe even some inorganic compounds/complexes.

[gmalivuk]

But what quality is scratch attributing to the numbers from addictive substances? That they will have some semiprimes in them? In other words, what precisely would it mean to produce "equivalent" results for other addictive compounds?

I suspect that, in order to determine that rigorously, we'd need some way to distinguish between addictive and nonaddictive compounds. If you check the number for every drug and find some quality they share, but haven't bothered checking whether this quality is also shared by other substances, you haven't really done anything useful or interesting yet.

[eSOANEM]

But what quality is scratch attributing to the numbers from addictive substances? That they will have some semiprimes in them? In other words, what precisely would it mean to produce "equivalent" results for other addictive compounds?

I was thinking more in terms of the same relation existing between the final numbers scratch ends up with and the structure of the compound they put in.